HP 10bII+ Financial Calculator User’s Guide HP Part Number: NW239-90001 Edition 1, May 2010 i Legal Notice This manual and any examples contained herein are provided “as is” and are subject to change without notice. Hewlett-Packard Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability, non-infringement and fitness for a particular purpose. In this regard, HP shall not be liable for technical or editorial errors or omissions contained in the manual. Hewlett-Packard Company shall not be liable for any errors or for incidental or consequential damages in connection with the furnishing, performance, or use of this manual or the examples contained herein. Copyright © 2010 Hewlett-Packard Development Company, L.P. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws. Hewlett-Packard Company Palo Alto, CA 94304 USA ii HP 10bII+ Financial Calculator iii Keyboard Map Legend iv \ SHIFT Down (orange functions on key bevel) ] Number (row of keys) Primary Functions (white) 1 12 character, sevensegment screen display 2 Time Value of Money (TVM) 3 Input key, markup, cost, Date and change of price and margin days, IRR per year, NPV, beginning/end of payment period Calendar and coupon payment schedules, settlement and maturity dates (bonds) 4 K memory register, Swap, percent change, percent, cash flow cash flow count, delete amount, statistics entry, statistics, round backspace Break-even calculation 5 Change sign, recall and memory 6 Shift (blue, up) Shift (orange, down) 7 Numbered keys: 1, and Statistics, weighted 4-9 mean and estimation Statistical functions and regression modes 8 Clearing functions Clearing functions Clearing functions 9 On Off Operating modes 10 Numbered keys: 0 and Common mathematical Probability functions 2-3, decimal functions 11 Mathematical functions Common mathematical Trigonometric functions functions, parentheses 12 Annunciators Payments per year, interest conversion, amortization, SHIFT Up (blue functions above keys) Bond calculations Scientific notation, store, Depreciation, clear statistics, hyperbolic and parentheses trigonometric functions Table of Contents Legal Notice............................................................................................................... ii HP 10bII+ Financial Calculator.................................................................................... iii Keyboard Map Legend ............................................................................................... iv 1 At a Glance........................................................................................................................ 1 Basics of Key Functions................................................................................................1 Shift Keys...................................................................................................................2 Boxed Key Functions ...................................................................................................2 Percentages ...............................................................................................................3 Memory Keys .............................................................................................................4 Time Value of Money (TVM) .........................................................................................6 TVM What if... ...........................................................................................................7 Amortization ..............................................................................................................8 Depreciation ..............................................................................................................9 Interest Rate Conversion.............................................................................................10 Cash Flows, IRR/YR, NPV, and NFV ...........................................................................11 Date and Calendar ...................................................................................................13 Bonds......................................................................................................................14 Break-even ...............................................................................................................16 Statistical Calculations ...............................................................................................17 Probability ...............................................................................................................19 Trigonometric Functions .............................................................................................20 2 Getting Started................................................................................................................. 23 Power On and Off ....................................................................................................23 Manual Conventions and Examples.............................................................................23 Basics of Key Functions..............................................................................................24 Shift Keys.................................................................................................................25 Boxed Key Functions .................................................................................................25 Simple Arithmetic Calculations....................................................................................26 Understanding the Display and Keyboard ....................................................................29 Cursor .....................................................................................................................29 Clearing the Calculator..............................................................................................29 Annunciators ............................................................................................................30 Input Key .................................................................................................................32 Swap Key ................................................................................................................32 Statistics Keys ...........................................................................................................32 Time Value of Money (TVM), Cash Flows, Bond, and Break-even Keys ............................33 Math Functions .........................................................................................................33 Trigonometric and Hyperbolic Functions and Modes .....................................................35 Pi ............................................................................................................................36 Hyperbolic Functions .................................................................................................36 Two-Number Functions ..............................................................................................37 In-line Functions ........................................................................................................37 1 Arithmetic with One-and Two-number Functions............................................................ 39 Last Answer ............................................................................................................. 41 Display Format of Numbers ....................................................................................... 41 Scientific Notation .................................................................................................... 43 Interchanging the Period and Comma ......................................................................... 43 Rounding Numbers................................................................................................... 43 Messages ................................................................................................................ 44 3 Business Percentages.........................................................................................................45 The Business Percentage Keys .................................................................................... 45 Percent key .............................................................................................................. 45 Margin and Markup Calculations ............................................................................... 47 4 Number Storage and Storage Register Arithmetic ...............................................................49 Using Stored Numbers in Calculations ........................................................................ 49 5 Picturing Financial Problems ..............................................................................................55 How to approach a Financial Problem ........................................................................ 55 Signs of Cash Flows ................................................................................................. 56 Periods and Cash Flows ............................................................................................ 56 Simple and Compound Interest................................................................................... 56 Interest Rates............................................................................................................ 57 Two Types of Financial Problems ................................................................................ 58 Recognizing a Cash Flow Problem ............................................................................. 59 6 Time Value of Money Calculations .....................................................................................61 Using the TVM Application ........................................................................................ 61 The TVM Keys .......................................................................................................... 61 Begin and End Modes............................................................................................... 62 Loan Calculations ..................................................................................................... 62 Savings Calculations................................................................................................. 67 Lease Calculations .................................................................................................... 71 Amortization ............................................................................................................ 74 Interest Rate Conversions ........................................................................................... 79 Resetting the TVM Keys ............................................................................................. 82 7 Depreciation .....................................................................................................................83 The Depreciation Keys .............................................................................................. 83 Resetting the TVM Keys ............................................................................................. 86 2 8 Cash Flow Calculations ..................................................................................................... 87 How to Use the Cash Flow Application........................................................................87 Clearing the Cash Flow Memory.................................................................................88 Calculating Internal Rate of Return...............................................................................90 NPV and IRR/YR: Discounting Cash Flows ...................................................................91 Organizing Cash Flows .............................................................................................91 Viewing and Editing Cash Flows.................................................................................93 Calculating Net Present Value and Net Future Value .....................................................95 Automatic Storage of IRR/YR and NPV ........................................................................98 9 Calendar Formats and Date Calculations ........................................................................... 99 Calendar Format.......................................................................................................99 Date Format .............................................................................................................99 Date Calculations and Number of Days .....................................................................101 Number of Days .....................................................................................................102 10 Bonds .......................................................................................................................... 105 The Bond Keys........................................................................................................105 Resetting the bond keys ...........................................................................................108 11 Break-even .................................................................................................................. 109 The Break-even Keys................................................................................................109 Resetting the Break-even keys ...................................................................................112 12 Statistical Calculations .................................................................................................. 113 Clearing Statistical Data ..........................................................................................114 Entering Statistical Data ...........................................................................................114 Viewing and Editing Statistical Data ..........................................................................116 Summary of Statistical Calculations ...........................................................................119 Mean, Standard Deviations, and Summation Statistics .................................................120 Linear Regression, Estimation, and Regression Modes..................................................121 Weighted Mean .....................................................................................................124 Regression Models and Variables .............................................................................125 Probability Calculations ...........................................................................................126 Factorial ................................................................................................................126 Permutations...........................................................................................................126 Combinations .........................................................................................................127 Random Number and Seed......................................................................................127 Advanced Probability Distributions ............................................................................128 Normal Lower Tail Probability ..................................................................................129 Inverse of Normal Lower Tail Probability ....................................................................130 Student's T Probability Lower Tail ..............................................................................131 3 Inverse of Student’s t Probability Lower Tail................................................................ 132 Conversions from Lower Tail .................................................................................... 133 13 Additional Examples .....................................................................................................137 Business Applications.............................................................................................. 137 Loans and Mortgages ............................................................................................. 139 Savings ................................................................................................................. 148 Cash Flow Examples............................................................................................... 152 14 Appendix A: Batteries and Answers to Common Questions ..................................................I Power and Batteries ..................................................................................................... I Low Power Annunciator................................................................................................ I Installing Batteries........................................................................................................ I Determining if the Calculator Requires Service ................................................................II Answers to Common Questions ....................................................................................III Environmental Limits................................................................................................... IV 15 Appendix B: More About Calculations .................................................................................I IRR/YR Calculations..................................................................................................... I Equations ................................................................................................................... I 16 Appendix C: Messages .......................................................................................................I 17 Warranty, Regulatory, and Contact Information .................................................................1 Replacing the Batteries ................................................................................................ 1 HP Limited Hardware Warranty and Customer Care....................................................... 1 Limited Hardware Warranty Period .............................................................................. 1 General Terms ........................................................................................................... 2 Exclusions.................................................................................................................. 2 Regulatory Information ................................................................................................ 3 Federal Communications Commission Notice................................................................. 3 Modifications............................................................................................................. 3 Declaration of Conformity for Products Marked with FCC Logo, United States Only ............ 4 Canadian Notice ....................................................................................................... 4 Avis Canadien ........................................................................................................... 4 European Union Regulatory Notice............................................................................... 4 Japanese Notice ........................................................................................................ 5 Disposal of Waste Equipment by Users in Private Household in the European Union ........... 5 Perchlorate Material - special handling may apply.......................................................... 6 Customer Care........................................................................................................... 6 Contact Information .................................................................................................... 6 4 1 At a Glance... This section is designed for you if you’re already familiar with calculator operation or financial concepts. You can use it for quick reference. The rest of the manual is filled with explanations and examples of the concepts presented in this section. Basics of Key Functions Table 1-1 Basics of key functions Keys Display = 0.00 0.00 Description Turns calculator on. Displays shift annunciator ] . [blue] 0.00 Displays shift annunciator \ [orange] JGD| M \t \N ]Oj ]OY ]OJ ]O: \> . 12_ Erases last character. 0.00 Clears display. 0.00 Clears statistics memory. 12 P_Yr (message flashes, then Clears all memory. disappears) BOND CLR (message flashes, Clears bond memory. then disappears) BR EV CLR (message flashes, then disappears) Clears break-even memory. TVM CLR (message flashes, then Clears tvm registers. disappears) CFLO CLR (message flashes, then Clears cash flow disappears) memory. Turns calculator off. At a Glance... 1 Shift Keys Most keys on the HP 10bII+ have three functions: • a primary function printed in white on the key. • a secondary function printed in orange on the bevel of the key. • a tertiary function printed in blue above the key on the keyboard (see Figure 1). Figure 1 As an example, the functions associated with the equals key, 4, are illustrated in the text as follows: • • • 4 secondary function (display): \5 tertiary function (random): ]6 primary function (equals): Boxed Key Functions These special functions require subsequent key presses to operate. For example, the functions associated with the clear key, M, include: Table 1-2 Clearing functions 2 At a Glance... Keys Associated Function M \N ]Oj Clear display. Clear all memory. Clears bond memory. Table 1-2 Clearing functions Keys Associated Function ]OY ]OJ ]O: \t Clears break-even memory. Clears TVM memory. Clears cash flow memory. Clears statistics memory. For more information on the calculator’s keys and basic functions, refer to chapter 2, Getting Started. Percentages Table 1-3 Keys for percentage calculations Keys Description § \¨ À ¼ ® Ã Percent Percent change Cost Price Margin Markup Add 15% to 17.50. Table 1-4 Calculating the price Keys Jj7V:1 JV§4 Display Description 17.50 Enters number. 20.13 Adds 15%. Find the margin if the cost is 15.00 and selling price is 22.00. At a Glance... 3 Table 1-5 Finding the margin Keys JVÀ GG¼ ® Display Description 15.00 Enters cost. 22.00 Enters price. 31.82 Calculates margin. If the cost is 20.00 and the markup is 33%, what is the selling price? Table 1-6 Calculating the price Keys Display Description G:À DDÃ ¼ 20.00 Enters cost. 33.00 Enters markup. 26.60 Calculates price. For more information on percentages, refer to chapter 3, Business Percentages. Memory Keys Table 1-7 Memory keys Keys Description ª s p m \w Stores a constant operation. Stores a value in the M register (memory location). Recalls a value from the M register. Adds a value to the number stored in the M register. When followed by a number key, : to d, or 7 and : to d, stores a number in the display into a numbered data storage register. There are 20 storage registers, designated 019. Press v 4 At a Glance... \w7 followed by : through d to access registers 10-19. : to d, or 7 and : to d, recalls a number from a storage register. Pressv7 followed by : through d to access registers 10-19. When followed by a number key, Multiply 17, 22, and 25 by 7, storing ‘× 7’ as a constant operation. Table 1-8 Storing ‘x 7’ as a constant Keys JjPjª 4 GG4 GV4 Display 7.00 Description Stores ‘× 7’ as a constant operation. 119.00 Multiplies 17 × 7. 154.00 Multiplies 22 × 7. 175.00 Multiplies 25 × 7. Keys Display Description VJd\wG M vG 519.00 Stores 519 in register 2. Store 519 in register 2, then recall it. Table 1-9 Storing and recalling 0.00 519.00 Clears display. Recalls register 2. Store 1.25 into register 15, then add 3, and store the result in register 15. Table 1-10 Storage register arithmetic Keys Display J7GV \w7V 1.25 D\w17V 3.00 Description Inputs 1.25 into the display. Stores 1.25 in register 15. Adds 3 to 1.25 in register 15 stores the result in register 15. M v7V 0.00 Clears the display. 4.25 Recalls register 15. For more information on number storage and storage register arithmetic, refer to chapter 4, Number Storage and Storage Register Arithmetic. At a Glance... 5 Time Value of Money (TVM) Enter any four of the five values and solve for the fifth. A negative sign in the display represents money paid out, and money received is positive. Table 1-11 Keys for TVM calculations Keys Description ]OJ Ù \Ú Ò Ï Ì É \¯ \Í Clears TVM memory and the current P_YR is displayed. Number of payments. Multiplies a value by the number of payments per year and stores as N. Interest per year. Present value. Payment. Future value. Begin or End mode. Number of payments per year mode. If you borrow 14,000 (PV) for 360 months (N) at 10% interest (I/YR), what is the monthly repayment? Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 1-12 Calculating the monthly payment Keys ]OJ JG\Í DS:Ù J:Ò JY:::Ï 6 At a Glance... Display Description TVM CLR (message flashes, then Clears TVM memory and disappears) 12.00 360.00 10.00 14,000.00 displays the current P_YR. Sets payments per year. Enters number of payments. Enters interest per year. Enters present value. Table 1-12 Calculating the monthly payment Keys :É Ì Display 0.00 -122.86 Description Enters future value. Calculates payment if paid at end of period. TVM What if... It is not necessary to reenter TVM values for each example. Using the values you just entered, how much can you borrow if you want a payment of 100.00? Table 1-13 Calculating a new payment Keys Display Description J::yÌ -100.00 Enters new payment amount. (Money paid out is negative). Ï 11,395.08 Calculates amount you can borrow. ...how much can you borrow at a 9.5% interest rate? Table 1-14 Calculating a new interest rate Keys d7VÒ Ï Display Description 9.50 Enters new interest rate. 11,892.67 Calculates new present value for 100.00 payment and 9.5% interest. J:Ò JY:::Ï Ì 10.00 Reenters original interest rate. 14,000.00 Reenters original present value. -122.86 Calculates original payment. For more information on TVM concepts and problems, refer to chapter 5, Picturing Financial Problems, and chapter 6, Time Value of Money Calculations. At a Glance... 7 Amortization After calculating a payment using Time Value of Money (TVM), input the periods to amortize \Ê. Press \Ê once for periods 1-12, and once again for payments 1324. Press 4 to continually cycle through the principal, interest, and balance values (indicated and press by the PRIN, INT, and BAL annunciators respectively). Using the previous TVM example, amortize a single payment and then a range of payments. Amortize the 20th payment of the loan. Table 1-15 Amortizing the 20th payment of the loan Keys Display Description G:Æ \Ê 4 4 4 20.00 Enters period to amortize. 20 – 20 -7.25 -115.61 Displays period to amortize. Displays principal. Displays interest. (Money paid out is negative). 13,865.83 Displays the balance amount. Amortize the 1st through 24th loan payments. Table 1-16 Amortization example Keys JÆJG \Ê 4 4 4 \Ê 4 8 At a Glance... Display 12_ Description Enters range of periods to amortize. 1 – 12 Displays range of periods (payments). -77.82 -1,396.50 Displays principal. Displays interest. (Money paid out is negative). 13,922.18 Displays the balance amount. 13 – 24 Displays range of periods. -85.96 Displays principal. Table 1-16 Amortization example Keys Display Description 4 4 -1,388.36 Displays interest. 13,836.22 Displays the balance amount. For more information on amortization, refer to the section titled, Amortization in chapter 6, Time Value of Money Calculations. Depreciation Table 1-17 Depreciation keys Keys Description Ù Ò Ï É ]{ ]x ]u Expected useful life of the asset. Declining balance factor entered as a percentage. Depreciable cost of the asset at acquisition. Salvage value of the asset. Straight-line depreciation. Sum-of-the-years’-digits depreciation. Declining Balance depreciation. A metalworking machine, purchased for 10,000.00, is to be depreciated over five years. Its salvage value is estimated at 500.00. Using the straight-line method, find the depreciation and remaining depreciable value for each of the first two years of the machine's life. Table 1-18 Calculating the depreciation Keys J::::Ï V::É VÙ J]{ Display 10,000.00 500.00 Description Inputs cost of the item. Inputs the salvage value of the item. 5.00 Inputs the useful life of the asset. 1,900.00 Depreciation of the asset in year one. At a Glance... 9 Table 1-18 Calculating the depreciation Keys Display \« G]{ \« Description 7,600.00 Remaining depreciable value after year one. 1,900.00 Depreciation of the asset in year two. 5,700.00 Remaining depreciable value after year two. For more information on depreciation, refer to chapter 7, Depreciation. Interest Rate Conversion To convert between nominal and effective interest rates, enter the known rate and the number of periods per year, then solve for the unknown rate. Table 1-19 Keys for interest rate conversion Keys Description \Ó \Ð \Í Nominal interest percent. Effective interest percent. Periods per year. Find the annual effective interest rate of 10% nominal interest compounded monthly. Table 1-20 Calculating the interest rate Keys Display Description J:\Ó JG\Í \Ð 10.00 Enters nominal rate. 12.00 Enters payments per year. 10.47 Calculates annual effective interest. For more information on interest rate conversions, refer to the section titled, Interest Rate Conversions in chapter 6, Time Value of Money Calculations. 10 At a Glance... Cash Flows, IRR/YR, NPV, and NFV Table 1-21 Cash flows, IRR, NPV, and NFV keys Keys Description ]O: \Í Clears cash flow memory. Number of periods per year (default is 12). For annual cash flows, P/YR should be set to 1; for monthly cash flows, use the default setting, 12. ¤ Cash flows, up to 45. “J” identifies the cash flow number. When preceded by a number, pressing ¤ enters a cash flow amount. number1 Æ number 2 ¤ Enter a cash flow amount, followed by Æ. Enter a number for the cash flow count followed by ¤ to enter cash flow amount and count simultaneously. v¤ Opens editor for reviewing/editing entered cash flows. Press 1 or A to scroll through the cash flows. \¥ \Á \½ \½\« Number of consecutive times cash flow “J” occurs. Internal rate of return per year. Net present value. Net future value. At a Glance... 11 If you have an initial cash outflow of 40,000, followed by monthly cash inflows of 4,700, 7,000, 7,000, and 23,000, what is the IRR/YR? What is the IRR per month? Table 1-22 Calculating the IRR/YR and IRR per month Keys Display ]O: CFLO CLR Description Clears cash flow memory. (message flashes, then disappears) JG\Í Y::::y¤ Yj::¤ j:::ÆG¤ 12.00 -40,000.00 Sets payments per year. Enters initial outflow. (CF 0 flashes, then disappears) 4,700.00 Enters first cash flow. (CF 1 flashes, then disappears) 2.00 Enters both the cash flow (CFn 2 flashes, then disappears) amount (7000.00) and count (2.00) simultaneously for second cash flow. GD:::¤ v¤ 23,000.00 Enters third cash flow. (CF 3 flashes, then disappears) 0 -40,000.00 Reviews entered cash flows starting with the initial cash flow. Press 1 to scroll through the cash flow list to verify the cash flow number, the amounts, and count for each entry. Press to exit. \Á aJG4 15.96 Calculates IRR/YR. 1.33 Calculates IRR per month. What is the NPV and NFV if the discount rate is 10%? Table 1-23 Calculating NPV and NFV Keys Display Description J:Ò \½ 10.00 Enters I/YR. 622.85 Calculates NPV. 12 At a Glance... M Table 1-23 Calculating NPV and NFV Keys Display Description \½\« 643.88 Calculates NFV. For more information on cash flows, refer to chapter 8, Cash Flow Calculations in the HP 10bII+ Financial Calculator User’s Guide. Date and Calendar Table 1-24 Keys used for dates and calendar functions Keys Description ]È Enters dates in DD.MMYYYY or MM.DDYYYY formats. D.MY is the default. Numbers at the far right of a calculated date indicate days of the week. 1 is for Monday; 7 is for Sunday. ]Å \Ç Toggles between 360-and 365-day (Actual) calendars. Calculates the date and day, past or future, that is a given number of days from a given date. Based on your current setting, returned result is calculated using either 360-day or 365-day (Actual). \Ä Calculates the number of days between two dates. Returned result is always calculated based on the 365-day calendar (Actual). If the current date is February 28 2010, what is the date 52 days from now? Calculate the date using the 365-day calendar (actual) and the M.DY settings. If 360 is displayed, press ]Å. If D.MY is displayed, press ]È. Table 1-25 Calculating the date Keys G7GgG:J: \Ç VG4 Display 2.28 Description Inputs the date in the selected format. 4-21-2010 3 Inputs the number of days and calculates the date along with the day of the week. For more information on date and calendar functions, refer to chapter 9, Calendar Formats and Date Calculations. At a Glance... 13 Bonds Bond calculations, primarily calculating bond price and yield, are performed by two keys, ]Ñ and ]Ô. These keys permit you to input data or return results. Pressing ]Û only calculates a result. The other keys used in bond calculations only permit you to input the data required for the calculations. Table 1-26 Bond calculation keys Keys Description ]Oj ]Û ]Ô ]Ñ ]Î ]Ë Clears bond memory. Calculates accrued interest only. Yield% to maturity or yield% to call date for given price. Price per 100.00 face value for a given yield. Coupon rate stored as an annual %. Call value. Default is set for a call price per 100.00 face value. A bond at maturity has a call value of 100% of its face value. ]È ]Å Date format. Toggle between day-month-year (dd.mmyyyy) or month-day-year (mm.ddyyyy). Day count calendar. Toggle between Actual (365-day calendar) or 360 (30-day month/ 360-day year calendar). ]Â ]¾ ]° Bond coupon (payment). Toggle between semiannual and annual payment schedules. Settlement date. Displays the current settlement date. Maturity date or call date. The call date must coincide with a coupon date. Displays the current maturity. What price should you pay on April 28, 2010 for a 6.75% U.S. Treasury bond maturing on June 4, 2020, if you want a yield of 4.75%? Assume the bond is calculated on a semiannual coupon payment on an actual/actual basis. ]Â to select the semiannual coupon payment. If D.MY is displayed, press ]È to select M.DY format. If SEMI is not displayed, press 14 At a Glance... Table 1-27 Bond calculation Keys ]Oj Y7GgG:J: ]¾ S7:YG:G: ]° S7jV]Î J::]Ë Y7jV]Ô ]Ñ 1]Û 4 Display BOND CLR (message Description Clears bond memory. flashes, then disappears) 4-28-2010 3 Inputs the settlement date (mm.ddyyyy format). 6-4-2020 4 6.75 100.00 Inputs the maturity date. Inputs CPN%. Inputs call value. Optional, as default is 100. 4.75 115.89 2.69 Inputs Yield%. Calculates the price. Displays the current value for accrued interest. 118.59 Returns the result for total price (value of price + value of accrued interest). The net price you should pay for the bond is 118.59. For more information on bond calculations, refer to chapter 10, Bonds. At a Glance... 15 Break-even Table 1-28 Break-even keys Keys Description ]OY ]¬ ]© ]¦ ]£ ]~ Clears break-even memory. Stores the quantity of units required for a given profit or calculates it. Stores the sales price per unit or calculates it. Stores variable cost per unit for manufacturing or calculates it. Stores the fixed cost to develop and market or calculates it. Stores the expected profit or calculates it. The sale price of an item is 300.00, the cost 250.00, and fixed cost 150,000.00. For a profit of 10,000.00, how many units would have to be sold? Table 1-29 Calculating break-even Keys ]OY JV::::] £ GV:]¦ D::]© J::::]~ ]¬ Display Description BR EV CLR (message flashes, Clears break-even memory. then disappears) 150,000.00 Inputs fixed cost. 250.00 Inputs variable cost per unit. 300.00 Inputs price. 10,000.00 Inputs profit. 3,200.00 Calculates the current value for the unknown item, UNITS. For more information on break-even calculations, refer to chapter 11, Break-even. 16 At a Glance... Statistical Calculations Table 1-30 Statistics keys Keys Description \t Clear statistical registers. Enter one-variable statistical x-data ¡ data. Delete one-variable statistical x-data \¢ data. Enter two-variable statistical x-data Æ y-data ¡ data. Delete two-variable statistical Æ y-data \¢ v¡ \k \« \T \« \h \« \e \« data. x-data Opens editor for reviewing/ editing entered statistical data. Means of x and y. Mean of x weighted by y. Also calculates b, intercept. Sample standard deviations of x and y. Population standard deviations of x and y. Estimate of x and correlation y-data \Z \« coefficient. Estimate of y and slope. \W \« ]L x-data Permits selection of six regression models; linear is default. At a Glance... 17 Using the following data, find the means of x and y, the sample standard deviations of x and y, and the y-intercept and the slope of the linear regression forecast line. Then, use summation statistics to find Σ xy. x-data 2 4 6 y-data 50 90 160 Table 1-31 Statistics example Keys \t GÆV:¡ YÆd:¡ SÆJS:¡ v¡ Display Description 0.00 Clears statistics registers. 1.00 Enters first x,y pair. 2.00 Enters second x,y pair. 3.00 Enters third x,y pair. 1 2.00 Reviews entered statistical data, starting with the initial x-value. Press 1 to scroll through and verify the entered statistical data. Press \k \« \h \« \T\« \W\« ]f M to exit. 4.00 Displays mean of x. 100.00 Displays mean of y. 2.00 Displays sample standard deviation of x. 55.68 Displays sample standard deviation of y. -10.00 Displays y-intercept of regression line. 27.50 Displays slope of regression line. 1,420.00 Displays Σ xy, sum of the products of x- and y-values. For more information on statistical calculations, refer to chapter 12, Statistical Calculations. 18 At a Glance... Probability Table 1-32 Probability keys Keys Description ]F ]o F ]I Calculates a cumulative normal probability given a Z-value. Calculates a Z-value given a cumulative normal probability. Calculates the cumulative Student’s T probability given degrees of freedom and a T-value. ]o I ]< ]9 ]E Calculates a T-value given degrees of freedom and the cumulative Student’s T probability. Calculates number of permutations of n items taken r at a time. Calculates number of combinations of n taken r at a time. Calculates factorial of n (where -253 < n < 253). Enter .5 as a Z-value and calculate the cumulative probability of the Z-value and the Z-value from a given cumulative probability. Table 1-33 Calculating the probability Keys \5V Display 0.00000 Description Sets number display to five digits to the right of the decimal. 7V]F 17GV4 ]oF .69146 Calculates the cumulative probability of the Z-value. .94146 Adds .25. 1.56717 Calculates the Z-value from the cumulative probability. For more information on probability, refer to the section titled, Probability in chapter 12, Statistical Calculations. At a Glance... 19 Trigonometric Functions Table 1-34 Trigonometry keys Keys Description Calculates sine, cosine, and tangent. ] c, R, or C Calculates inverse sine, inverse cosine, ]o and inverse tangent. c, R, or C Calculates hyperbolic sine, cosine and ]r tangent. c, R, or C ]ro Calculates inverse hyperbolic sine, cosine, and tangent. c, R, or C ]3 Toggles between radians and degrees modes. Degrees is the default setting. Find Sin θ =.62 in degrees. If RAD is displayed, press ]3. Table 1-35 Trigonometry example Keys 7SG ]oc 20 At a Glance... Display .62 38.32 Description Enters value of sine for θ . Calculates θ . Convert the results to radians using Pi. Table 1-36 Converting to radians Keys P\;aJg :4 Display .67 Description Converts degrees to radians. For more information on trigonometric functions, refer to chapter 2, Getting Started. At a Glance... 21 22 At a Glance... 2 Getting Started Power On and Off =. To turn the calculator off, press the orange shift key, \, then >. To change the brightness of the display, hold down = and then simultaneously press 1 or A. To turn on your HP 10bII+, press Since the calculator has continuous memory, turning it off does not affect the information you have stored. To conserve energy, the calculator turns itself off after five minutes of inactivity. The calculator uses two CR2032 coin batteries. If you see the low-battery symbol ( ) in the display, replace the batteries. For more information, refer to the section titled, Installing Batteries in Appendix A. Manual Conventions and Examples In this manual, key symbols are used to indicate the key presses used in the example problems. These symbols vary in appearance according to whether they indicate the primary, secondary, or tertiary functions required for the problem. For example, the functions associ- 4, are illustrated in the text as follows: primary function (equals): 4 secondary function (display): \5 tertiary function (random): ]6 ated with the equals key, • • • Note the symbol for the primary function of the key, in this case, =, appears on each of the key symbols depicted above. This repetition is intended to serve as a visual aid. By looking for the symbol of the primary function on the key, you can quickly locate the keys used for the secondary and tertiary functions on the calculator. Displayed text Text that appears in the display screen of the calculator is presented in BOLD CAPITAL letters throughout the manual. Examples Example problems appear throughout the manual to help illustrate concepts and demonstrate how applications work. Unless otherwise noted, these examples are calculated with CHAIN set as the active operating mode. To view the current mode, press v]?. The current mode, CHAIN or ALGEBRAIC, will flash, then disappear. To change the mode, press ] followed by ?. Getting Started 23 Basics of Key Functions Table 2-1 Basics of key functions Keys = ][blue] \[orange] JGD| ]3 M \t \N ]Oj ]OY ]OJ ]O: \> 24 Getting Started Display 0.00 Description Turns calculator on. 0.00 Displays shift annunciator . Displays shift annunciator . 0.00 12_ Erases last character. RAD Toggles between radians and degrees. The item before the / is the alternate; the item after the / is the default setting. Except for the operating mode, annunciators in the display indicate alternate settings are active. (at the bottom of the display) 0.00 Clears display. 0.00 Clears statistics memory. 12 P_Yr (message flashes, then Clears all memory. disappears) BOND CLR (message flashes, then disappears) Clears bond memory. BR EV CLR (message flashes, then disappears) Clears break-even memory. TVM CLR (message flashes, then Clears tvm memory. disappears) CFLO CLR (message flashes, then Clears cash flow memory. disappears) Turns calculator off. Shift Keys Most keys on the HP 10bII+ have three functions: • a primary function printed in white on the key. • a secondary function printed in orange on the bevel of the key. • a tertiary function printed in blue above the key on the keyboard (see Figure 1). Figure 1 \ or ], a shift annunciator or is displayed to indicate that the shifted functions are active. For example, press \ followed by 2 to multiply a number in the display by itself. To turn the shift annunciators off, press \ or ] again. When you press Boxed Key Functions There are three shifted key functions on the calculator that are used to change the operation of another key's function. These three tertiary functions, ]O, ]o and ]r, are bound by blue boxes to show that they operate differently. These special functions require subsequent key presses to operate. For example, the functions associated with the clear key, M, include: Table 2-2 Clearing functions Keys Associated Function M \N \t ]Oj Clear display. Clear all memory. Clear statistics memory. Clears bond memory. Getting Started 25 Table 2-2 Clearing functions Keys Associated Function ]OY ]OJ ]O: Clears break-even memory. Clears TVM memory. Clears cash flow memory. Simple Arithmetic Calculations Operating Modes To change the operating mode, press the blue shift key, ] followed by ? to toggle between Algebraic and Chain modes. A brief message is displayed indicating the selected operating mode. To view the current mode, press v]?. The current mode will flash, then disappear. Arithmetic Operators The following examples demonstrate using the arithmetic operators 1, A, P, and a. If you press more than one operator consecutively, for example 1, A, 1, P 1, all are ignored except the last one. If you make a typing mistake while entering a number, press | to erase the incorrect digits. Table 2-3 Example displaying calculations using arithmetic operators Keys Display GY7jJ1SG7Yj4 When a calculation has been completed (by pressing 87.18 Description Adds 24.71 and 62.47. 4), pressing a number key starts a new calculation. Table 2-4 Completing a calculation Keys Display Description JdPJG7Sg4 240.92 Calculates 19 × 12.68. 26 Getting Started If you press an operator key after completing a calculation, the calculation is continued. Table 2-5 Continuing a calculation Keys Display Description 1JJV7V4 356.42 Completes calculation of 240.92 + 115.5. Calculations in Chain Mode Calculations in Chain mode are interpreted in the order in which they are entered. For example, entering the following numbers and operations as written from left to right, J1GPD4, returns 9. If you press an operator key, 1,A,P, or a, after 4, the calculation is continued using the currently displayed value. You can do chain calculations without using 4 after each step. Table 2-6 Chain calculations Keys Display S7dPV7DVa 36.92 Description Pressing a displays intermediate result (6.9 × 5.35). 7dJ4 40.57 Completes calculation. Without clearing, now calculate 4 + 9 × 3. Table 2-7 Chain calculations Keys Display Y1dP D4 13.00 Adds 4 and 9. 39.00 Completes calculation. In Chain mode, if you wish to override the left to right order of entry, use parentheses \q and \n to prioritize operations. Getting Started 27 For example, to calculate 1 + (2 x 3), you may enter the problem as written from left to right, with parentheses to prioritize the multiplication operation. When entered with parentheses, this expression returns a result of 7. Calculations in Algebraic Mode In Algebraic mode, multiplication and division have a higher priority than addition and subtraction. For example, in Algebraic mode, pressing J1GPD4 returns a result of 7.00. In Chain mode, the same key presses return a result of 9.00. In Algebraic mode, operations between two numbers have the following priority: • Highest priority: combinations and permutations, T probability calculations, % change, and date calculations x • Second priority: the power function ( • Third priority: multiplication and division • Forth priority: addition and subtraction. y ) The calculator is limited to 12 pending operations. An operation is pending when it is waiting for the input of a number or the result of an operation of higher priority. Using Parentheses in Calculations Use parentheses to postpone calculating an intermediate result until you’ve entered more numbers. You can enter up to four open parentheses in each calculation. For example, suppose you want to calculate: 30 ---------------------- × 9 ( 85 – 12 ) If you enter D:agVA, the calculator displays the intermediate result, 0.35. This is because calculations without parentheses are performed from left to right as you enter them. To delay the division until you’ve subtracted 12 from 85, use parentheses. Closing parentheses at the end of the expression can be omitted. For example, entering 25 ÷ (3 × (9 + 12 = is equivalent to 25 ÷ (3 × (9 + 12)) =. If you type in a number, for example, 53, followed by the parenthesis symbol, the calculator considers this implicit multiplication. Example Table 2-8 Using parentheses in calculations Keys Display Description D:a\qgVA JG\n 85.00 No calculation yet. 73.00 Calculates 85 - 12. 28 Getting Started Table 2-8 Using parentheses in calculations Keys Display P d4 Description 0.41 Calculates 30 ÷ 73. 3.70 Multiplies the result by 9. Negative Numbers Enter the number and press y to change the sign. Calculate -75 ÷ 3. Table 2-9 Changing the sign of numbers Keys Display Description jVy aD4 -75_ Changes the sign of 75. –25.00 Calculates result. Understanding the Display and Keyboard Cursor The blinking cursor ( _ ) is visible when you are entering a number. Clearing the Calculator Backspace When the cursor is on, | erases the last digit you entered. Otherwise, | clears the display and cancels the calculation. Clear M clears the current item on the display and replaces it with 0. If entry is in progress, pressing M clears the current entry and replaces it with 0, but the current calculation continues. Otherwise, M clears the display of its current contents and cancels the current calculation. Clear Memory ]O followed by j,Y,J,: clears a selected memory type (register). Other memory is left intact. Getting Started 29 Table 2-10 Clear memory keys Keys Description ]Oj ]OY ]OJ ]O: \t Clears bond memory. Clears break-even memory. Clears TVM memory. Clears cash flow memory. Clears statistics memory. Clear All \N all clears all memory in the calculator, with the exception of the payments per year (P/Yr) setting. To clear all memory and reset calculator modes, press and hold down =, then press and hold down both Ù and Ï. When you release all three, all memory is cleared. The All Clear message is displayed. Clearing Messages When the HP 10bII+ is displaying an error message, |or M clears the message and restores the original contents of the display. Annunciators Annunciators are symbols in the display that indicate the status of the calculator. For functions that toggle between settings, annunciators indicate alternate settings are active. For the defaults, no annunciators appear in the display. For example, when selecting a date format, the default setting is month-day-year (M.DY). When day-month-year (D.MY) is active, the D.MY in the display indicates it is the active setting. Table 2-11 lists all the annunciators that appear in the display screen. 30 Getting Started Table 2-11 Annunciators and status Annunciator Status , A shift key has been pressed. When another key is pressed, the functions labeled in orange or blue are executed. INV Inverse mode is active for trigonometric or probability functions. RAD Radians mode is active. BEG Begin mode is active; payments are at the beginning of a period. D.MY Day-month-year date format (DD.MMYYYY) is active. 360 360-day calendar is active. SEMI Semi-annual coupon payment schedule (bonds) is active. PEND An operation is waiting for another operand. INPUT The Æ key has been pressed and a number stored. Battery power is low. AMORT The amortization annunciator is lit, together with one of the following four annunciators: PER The range of periods for an amortization is displayed. PRIN The principal of an amortization is displayed. INT The interest of an amortization is displayed. BAL The balance of an amortization is displayed. CFLO The cash flow annunciator is lit, together with one of the following two annunciators: CF The cash flow number appears briefly, then the cash flow is shown. N The cash flow number appears briefly, then the number of times the cash flow is repeated is shown. STAT The statistics annunciator is lit, together with one of the following two annunciators: X The number of the data point, n, followed by an x-value is shown, or, if STAT is not lit, indicates that the first of two results is displayed. Y The number of the data point, n, followed by a y-value is shown, or, if STAT is not lit, indicates that the second of two results is displayed. ERROR The error annunciator is lit, together with one of the following four annunciators: TVM There is a TVM error (such as an invalid P/Yr), or, when ERROR is not lit, a TVM calculation returned a second result. FULL Available memory for cash flows or statistics is full, or the pending operator memory is full. STAT Incorrect data used in a statistics calculation or, when ERROR is not lit, a statistical calculation has been performed. Getting Started 31 Table 2-11 Annunciators and status Annunciator Status FUNC A math error has occurred (for example, division by zero). Input Key Æ key is used to separate two numbers when using two-number functions or twovariable statistics. The Æ key can also be used to enter cash flows and cash flow counts, The ordered pairs, and evaluate any pending arithmetic operations, in which case the result is the same as pressing 4. Swap Key Pressing The \« exchanges the following: • The last two numbers that you entered; for instance, to change the order of division or subtraction. • The results of functions that return two values. « key toggles the item in the Æ register, or swaps the top two items in the mathematical stack. This function is used to retrieve a secondary value returned during a calculation, as well as to swap two items during a calculation. Statistics Keys The statistics keys are used to access summary statistics from the statistics memory registers. When you press ] followed by a statistics key, you can recall one of six summary statistics with the next keystroke. For example, press ] followed by the X key to recall the sum of the x-values entered. Table 2-12 Statistics keys 32 Getting Started Keys Description ]l ]i ]f ][ Sum of the squares of the xvalues. Sum of the squares of the yvalues. Sum of the products of the x- and y-values. Number of data points entered. Table 2-12 Statistics keys Keys Description ]U ]X Sum of the y-values. Sum of the x-values. Time Value of Money (TVM), Cash Flows, Bond, and Break-even Keys When entering data for TVM, cash flows, bond, depreciation and break-even calculations, results are calculated based on data entered into specific memory registers. When pressed, the keys used for these operations: • • store data. enter data for a variable that is used during calculations (input only). • calculate unknown variables based on stored data. For more information on how these keys function, refer to the specific chapters which cover TVM problems, cash flows, and bond and break-even calculations. Math Functions One-Number Functions Math functions involving one number use the number in the display. To execute one-number functions, with a number displayed, press the key or key combination corresponding to the operation you wish to execute. The result is displayed. See Table 2-14 for a list of one-number functions. Before doing any trigonometric calculations, check whether the angle mode is set for degrees or radians (Rad). Degrees is the default setting. The RAD annunciator in the display indicates radians is active. Press ]3 to toggle between the settings. You will need to change the setting if the active mode is not what your problem requires. Table 2-13 Example displaying one number functions Keys gd7GV\B D7Vj1G7DS\b 4 Display Description 9.45 Calculates square root. 0.42 1/2.36 is calculated first. 3.99 Adds 3.57 and 1/2.36. Table 2-14 lists the one-number functions of the calculator. Getting Started 33 Table 2-14 One-number functions Keys Description § \} \b \B \2 \K \H \E ] Divide a number by 100. Rounds x to the number specified by the display format. Calculates 1/x. Calculates the square root of x. Calculates the square of x. Calculates natural exponent to the power of x. Calculates natural log. Calculates factorial of n (where -253 < n < 253). The Gamma function is used to calculate n! for non-integers or negative numbers. Calculates sine, cosine, or tangent. c, R, or C ]o c, R, or C ]r c, R, or C ]ro c, R, or C ]F ]oF Calculates inverse sine, cosine, or tangent. Calculates hyperbolic sine, cosine, or tangent. Calculates inverse hyperbolic sine, cosine, or tangent. Calculates a cumulative normal probability given a Z-value. Calculates a Z-value given a cumulative normal probability. ]6, and Pi \; are special operators. They insert values The random function for Pi, or a random number in the range 0 < x <1, into calculations. 34 Getting Started Trigonometric and Hyperbolic Functions and Modes Selecting Angle Format The trigonometric angle format determines how numbers are interpreted when using trigonometry functions. The default format for angles on the 10bII+ is degrees. To change to radians mode, press ]3. When radians mode is active, the RAD annunciator is displayed. Trigonometric Functions Table 2-15 Trigonometric functions Keys Description ]c ]R ]C ]oc ]oR ]oC Calculates sine, written as sin. Calculates cosine, written as cos. Calculates tangent, written as tan. Calculates inverse sine, also written, arcsin, asin, or sin-1. Calculates inverse cosine, also written, arccos, acos, or cos-1. Calculates inverse tangent, also written, arctan, atan, or tan-1. Example Perform the following trigonometric calculations. If RAD is lit in the display, press ]3. Table 2-16 Example using various trigonometric calculations Keys Display Description \5Y JV]c J1S:]C 4 7DV]oR 0.0000 Set display to four decimal places. 0.2588 Displays sine of 15o. 1.7321 Displays tangent of 60o. 2.7321 Calculates 1 + tangent of 60o. 69.5127 Displays inverse cosine of 0.35. Getting Started 35 Table 2-16 Example using various trigonometric calculations Keys Display Description A7SG]oR 4 \5G 51.6839 Displays inverse cosine of 0.62. 17.8288 Calculates arccos 0.35 - arccos 0.62. 17.83 Return display to default format. Pi Pressing \; displays the value of π . Although the displayed value is appears in the current display format, the 12 digit value is actually used for calculations. π is often used during calculations in radians mode, as there are 2 π radians in a circle. Example Find the surface area of a sphere with a radius of 4.5 centimeters. Use the formula: 2 A = 4πr Table 2-17 Example using Pi Keys Display YP\; PY7V\2 4 3.14 Description Displays π. 20.25 Displays 4.52. 254.47 Calculates sphere surface area in square centimeters. Hyperbolic Functions Table 2-18 Hyperbolic and inverse hyperbolic functions 36 Getting Started Keys Description ]rc ]rR ]rC ]roc ]roR ]roC Calculates hyperbolic sine, written as, sinh. Calculates hyperbolic cosine, written as, cosh. Calculates hyperbolic tangent, written as, tanh. Calculates inverse hyperbolic sine, written as, arcsinh, asinh, or, sinh-1. Calculates inverse hyperbolic sine, also written, arccosh, acosh, or cosh-1. Calculates inverse hyperbolic tangent, also written, arctanh, atanh, or tanh-1. Example Perform the following hyperbolic calculations. Table 2-19 Example performing various hyperbolic calculations Keys Display Description \5Y J7GV]rc 17Vd]rC 4 ]roR \5G 0.0000 Sets display to four decimal places. 1.6019 Display sinh 1.25. 0.5299 Displays tanh 0.59. 2.1318 Calculates sinh 1.25 + tanh 0.59. 1.3899 Calculates acosh 2.1318. 1.39 Returns display to default format. Two-Number Functions When a function requires two numbers, other than for addition, subtraction, multiplication, x division, and the power function, ( y ), you may key in the numbers as follows: number1 number 2 followed by the operation. Pressing Æ Æ evaluates the current expression and displays the INPUT annunciator. In-line Functions \¨, \Ä, \Ç, ]9, ]<,]I, and ]oI, which require two numbers, you may also For calculations involving key in the first number followed by the function keys, and then key in the second number 4 to return results. Throughout the manual, when examples are entered in this manner without using Æ, they are referred to as in-line functions. For example, the following keystrokes calculate the percent change between 17 and 29 using the \¨ followed by keys as an in-line function: Getting Started 37 Table 2-20 Example calculating percent change as an in-line function Keys Jj\¨ Gd 4 Press Display 17.00 29_ 70.59 Description Enters number1, displays the PEND annunciator indicating the calculator is awaiting instructions. Enters number 2. Calculates the percent change. M, and now calculate the same example using the Æ key to store the first number, then key in the second number and perform the operation. Table 2-21 Example calculating percent change using ‘INPUT’ Keys Display Description JjÆ 17.00 Enters number1, and displays the INPUT annunciator indicating the number has been stored. Gd\¨ 70.59 Enters number 2 and calculates the percent change. Although the in-line function has fewer key strokes, performing this example using the key permits you to store a value and then perform other calculations following Æ Æwithout using parentheses. Table 2-22 Example displaying two-number functions with chain calculation Keys JjÆ Gd1DD Display 17.00 38 Getting Started Enters number1, and displays the INPUT annunciator. 87_ Enters and performs the chain calculation. Results are stored and used in the next operation. The PEND annunciator and the blinking cursor indicate an operation is pending as the calculator awaits instructions. 70.59 Calculates the percent change between 17 and the result of the chain operation (29). 1VYAgj \¨ Description The Table 2-23 below lists the two-number functions of the calculator. Table 2-23 Two-number functions Keys Description 1APa \Q \¨ ]9 ]< \Ç Addition, subtraction, multiplication, division. The power function. % Change. Combinations. Permutations. The date and day, past or future, that is a given number of days from a given date. \Ä ]I The number of days between two dates. ]oI Calculates a t-value given degrees of freedom and the cumulative Student’s t probability. Calculates the cumulative Student’s t probability given degrees of freedom and a tvalue. Two-number functions may be performed in either CHAIN or ALGEBRAIC mode. Arithmetic with One-and Two-number Functions Math functions operate on the number in the display. Example 1 Calculate 1/4 , then calculate 20 + 47.2 + 1.12. Table 2-24 Calculating the expression Keys Y\b G:\B Display Description 0.25 Calculates the reciprocal of 4. 4.47 Calculates 20 . Getting Started 39 Table 2-24 Calculating the expression Keys 1Yj7G1 J7J\2 4 Display Description 51.67 Calculates 1.21 Calculates 1.12. 52.88 20 + 47.20. Completes the calculation. Example 2 Calculate natural logarithm (e2.5). Then calculate 790 + 4! Table 2-25 Calculating the logarithm value Keys Display G7V\K \H jd:1Y\E 4 Description 12.18 Calculates e2.5. 2.50 Calculates natural logarithm of the result. 24.00 Calculates 4 factorial. 814.00 Completes calculation. Example 3 x The power operator, y , raises the preceding number (y-value) to the power of the following number (x-value). Calculate 1253, then find the cube root of 125. Table 2-26 Calculating the cube root Keys JGV\QD4 JGV\QD\b4 40 Getting Started Display 1,953,125.00 5.00 Description Calculates 1253. Calculates the cube root of 125, or 1251/3. Last Answer When a calculation is completed by pressing 4, or a calculation is completed during another operation, the result is stored in a memory location that contains the last calculated result. This enables the last result of a calculation to be used during the next calculation. To access the last calculated answer, press v4. Unlike the other stored memory registers however, this register is automatically updated when you complete a calculation. Example 1 Table 2-27 Using last answer Keys VAJ7GV4 D\Qv4 4 Display Description 3.75 Calculate 5-1.25 3.75 Recall last answer. 61.55 Calculate 33.75. Example 2 Table 2-28 Using last answer with ‘INPUT’ Keys Display Description V:Æ GG1JY\¨ S:Æ v4 \¨ 50.00 Store 50 in the INPUT register. -28.00 Calculate percent change. 60.00 Store 60 in the INPUT register. 36.00 Recalls last calculation, 22+14. -40.00 Calculate percent change. Display Format of Numbers When you turn on the HP 10bII+ for the first time, numbers are displayed with two decimal places and a period as the decimal point. The display format controls how many digits appear in the display. If the result of a calculation is a number containing more significant digits than can be displayed in the current display format, the number is rounded to fit the current display setting. Getting Started 41 Regardless of the current display format, each number is stored internally as a signed, 12-digit number with a signed, three-digit exponent. Specifying Displayed Decimal Places To specify the number of displayed decimal places: 1. 2. \5 followed by :–d for the desired decimal setting. \5 followed by 7, v, or s changes the display mode. Pressing \7 provides the best estimate and displays as many digits as required. v is the value for 10, and s for 11. Press Table 2-29 Example displaying the number of decimal places Keys \M \5D YV7SP 7JGVS4 \5d \5G Display 0.00 Description Clears display. 0.000 Displays three decimal places. 5.727 5.727360000 Displays nine decimal places. 5.73 Restores two decimal places. When a number is too large or too small to be displayed in DISP format, it automatically displays in scientific notation. Displaying the Full Precision of Numbers To set your calculator to display numbers as precisely as possible, press \57 (trailing zeros are not displayed.) To temporarily view all 12 digits of the number in the display (regardless of the current display format setting), press \5 and hold 4. The number 4. The decimal point is not shown. Start with two decimal places \5G. is displayed as long as you continue holding 42 Getting Started Table 2-30 Example displaying all digits Keys Display Jaj4 \54 1.43 142857142857 Description Divides. Displays all 12 digits. Scientific Notation Scientific notation is used to represent numbers that are too large or too small to fit in the display. For example, if you enter the number 10,000,000 x 10,000,000 =, the result is 1.00E14, which means one times ten to the fourteenth power, or 1.00 with the decimal point moved fourteen places to the right. You can enter this number by pressing J\ zJY. The E stands for exponent of ten. Exponents can also be negative for very small numbers. The number 0.000000000004 is displayed as 4.00E–12, which means four times ten to the negative twelfth power, or 4.0 with the decimal point moved 12 places to the left. You can enter this number by pressing Y\zyJG. Interchanging the Period and Comma To switch between the period and comma (United States and International display) used as the decimal point and digit separator, press \8. For example, one million can be displayed as 1,000,000.00 or 1.000.000,00. Pressing \8, toggles between these options. Rounding Numbers The calculator stores and calculates using 12-digit numbers. When 12 digit accuracy is not desirable, use \} to round the number to the displayed format before using it in a calculation. Rounding numbers is useful when you want the actual (dollars and cents) monthly payment. Getting Started 43 Table 2-31 Example displaying rounding off numbers Keys d7gjSVYD GJ \5G \54 (while you press 4). \} Display 9.87654321_ Description Enters a number with more than two nonzero decimal places. 9.88 Displays two decimal places. 987654321000 Displays all digits without the decimal. 9.88 Rounds to two decimal places (specified by pressing \5G). \54 988000000000 Shows rounded, stored number. Messages The HP 10bII+ displays messages about the status of the calculator or informs you that you have attempted an incorrect operation. To clear a message from the display, press |. For a complete list of error messages, refer to Appendix C. 44 Getting Started M or 3 Business Percentages The Business Percentage Keys When entering data for business percentage calculations, results are calculated based on data entered into specific memory registers. When pressed, the keys used for these operations: • • • store data. enter known data for variables used during calculations. calculate unknown variables based on stored data. You can use the 10bII+ to calculate simple percent, percent change, cost, price, margin, and markup. Percent key The § key has two functions: • Finding a percent • Adding or subtracting a percent Finding a Percent § key divides a number by 100 unless it is preceded by an addition or subtraction The sign. Example Find 25% of 200. Table 3-1 Finding a percent Keys Display Description G::P GV§ 4 200.00 Enters 200. 0.25 50.00 Converts 25% to a decimal. Multiplies 200 by 25%. Adding or Subtracting a Percent You can add or subtract a percent in one calculation. Example 1 Decrease 200 by 25%. Business Percentages 45 Table 3-2 Subtracting a percent in a calculation Keys Display Description G::A GV§ 4 200.00 Enters 200. 50.00 Multiplies 200 by 0.25 and subtracts 50 from 200. 150.00 Completes the calculation. Example 2 You borrow 1,250 from a relative, and you agree to repay the loan in a year with 7% simple interest. How much money will you owe? Table 3-3 Adding a percent in a calculation Keys JGV:1j§ 4 Display 1,337.50 Description Calculates loan interest, 87.50 and adds 87.50 and 1250.00 to show the repayment amount. Percent Change Calculate the percent change between two numbers. Example 1 Calculate the percent change between 291.7 and 316.8 using the in-line feature. Table 3-4 Calculating the percent change Keys Display Description GdJ7j\¨ DJS7g4 291.70 Enters number1. 8.60 Calculates percent change. Example 2 Calculate the percent change between (12 × 5) and (65 + 18) using Æ. Table 3-5 Calculating the percent change between two numbers Keys Display Description JGPVÆ SV1Jg\¨ 60.00 Calculates and enters number1. Note the INPUT annunciator. 38.33 Calculates percent change. For more information on in-line features, refer to chapter 2, Getting Started. 46 Business Percentages Margin and Markup Calculations The 10bII+ can calculate cost, selling price, margin, or markup. Table 3-6 Keys for margin and markup Application Margin Markup Keys Description À, ¼, ® À, ¼, Ã Margin is markup expressed as a percent of price. Markup calculations are expressed as a percent of cost. v and then the key you wish to see. For example, to see the value stored as À, press vÀ. To see any value used by the margin and markup application, press Margin Calculations Example Kilowatt Electronics purchases televisions for 255. The televisions are sold for 300. What is the margin? Table 3-7 Calculating the margin Keys Display Description GVVÀ D::¼ ® 255.00 Stores cost in CST. 300.00 Stores selling price in PRC. 15.00 Calculates margin. Markup on Cost Calculations Example The standard markup on costume jewelry at Kleiner’s Kosmetique is 60%. They just received a shipment of chokers costing 19.00 each. What is the retail price per choker? Table 3-8 Calculating the retail price Keys JdÀ S:Ã Display Description 19.00 Stores cost. 60.00 Stores markup. Business Percentages 47 Table 3-8 Calculating the retail price Keys Display Description ¼ 30.40 Calculates retail price. Using Margin and Markup Together Example A food cooperative buys cases of canned soup with an invoice cost of 9.60 per case. If the co-op routinely uses a 15% markup, for what price should it sell a case of soup? What is the margin? Table 3-9 Calculating the margin Keys d7SÀ JVÃ ¼ ® 48 Business Percentages Display Description 9.60 Stores invoice cost. 15.00 Stores markup. 11.04 Calculates the price on a case of soup. 13.04 Calculates margin. 4 Number Storage and Storage Register Arithmetic Using Stored Numbers in Calculations You can store numbers for reuse in several different ways: • • ª (Constant) to store a number and its operator for repetitive operations. Use 3 Key Memory (s, p, and m) to store, recall, and sum numbers with a single Use keystroke. • Use \w and v to store to, and recall from, the 20 numbered registers. Using Constants ª to store a number and arithmetic operator for repetitive calculations. Once the constant operation is stored, enter a number and press 4. The stored operation is Use performed on the number in the display. Example 1 Calculate 5 + 2, 6 + 2, and 7 + 2. Table 4-1 Storing ‘+2’ as constant Keys V1Gª 4 S4 j4 Display Description 2.00 Stores + 2 as constant. 7.00 Adds 5 + 2. 8.00 Adds 6 + 2. 9.00 Adds 7 + 2. Number Storage and Storage Register Arithmetic 49 Example 2 Calculate 10 + 10%, 11 + 10%, and 25 + 10%. Table 4-2 Storing ‘+ 10%’ as a constant Keys J:1J:§ª 4 4 GV4 Display Description 1.00 Stores + 10% as a constant. 11.00 Adds 10% to 10. 12.10 Adds 10% to 11. 27.50 Adds 10% to 25. Example 3 Calculate 23 and 43. Table 4-3 Storing ‘y3’ as a constant Keys G\QDª 4 Y4 50 Number Storage and Storage Register Arithmetic Display Description 3.00 Stores y3 as constant. 8.00 Calculates 23. 64.00 Calculates 43. Example 4 Calculate the percent change between 55 and 32 and store it as a constant. Then calculate the percent change between 50 and 32, and 45 and 32. Table 4-4 Calculating percent change Keys Display Description VV\¨DGª 4 V:4 YV4 32.00 Stores % change 32 as constant. -41.82 Calculates the % change between 55 and 32. -36.00 Calculates the % change between 50 and 32. -28.89 Calculates the % change between 45 and 32. All of the other two-number functions on the calculator may be used with ª in the same manner as shown in example 4. For a complete list of two-number functions, refer to the section titled, Two-Number Functions in chapter 2. Using the M Register s, p, and m keys perform memory operations on a single storage register, called the M register. In most cases, it is unnecessary to clear the M register, since s replaces the previous contents. However, you can clear the M register by pressing :s. To add a series of numbers to the M register, use s to store the first number and m to The add subsequent numbers. To subtract the displayed number from the number in the M register, press y followed by m. Table 4-5 Keys for performing memory operations Keys Description s p m Stores displayed number in the M register. Recalls number from the M register. Adds displayed number to the M register. Number Storage and Storage Register Arithmetic 51 Example Use the M register to add 17, 14.25, and 16.95. Then subtract 4.65 and recall the result. Table 4-6 Calculating basic arithmetic operations using M register Keys Display Jjs JY7GVm JS7dVm Y7SVym p Description 17.00 Stores 17 in M register. 14.25 Adds 14.25 to M register. 16.95 Adds 16.95 to M register. -4.65 Adds -4.65 to M register. 43.55 Recalls contents of the M register. Using Numbered Registers \w and v keys access the 20 user registers, designated 0-19. The \w key is used to copy the displayed number to a designated register. The v key The is used to copy a number from a register to the display. To store or recall a number in two steps: • • • \w or v. To cancel this step, press | or M. Press \w followed by a number key, : to d, or 7 and : to d, to store a number in the display into a numbered data storage register. Press \w7 followed by : through d to access registers 10-19. Press v followed by a number key, : to d, or 7 and : to d, to recall a number from a storage register. Press v7 followed by : through d to access registers Press 10-19. Example In the following example, two storage registers are used. Set the calculator for CHAIN mode ]?) and calculate the following: ( 475.6 + 475.6---------------- and 560.1 -------------------------------------39.15 39.15 52 Number Storage and Storage Register Arithmetic Table 4-7 Calculating the expression using two storage registers Keys Display Description YjV7S \w7Y aDd7JV \wG 4 VS:7J1 v7Y 475.60 Stores 475.60 (displayed number) in R14. 39.15 Stores 39.15 in R2. 12.15 Completes first calculation. 1,035.70 Recalls R14. NOTE: If the calculator is set for Algebraic mode, press 4 at the end of this step. avG 4 39.15 Recalls R2. 26.45 Completes second calculation. With the exception of the statistics registers, you can also use \w and v for \wÒ stores the number from the display in the Ò register. vÒ copies the contents from Ò to the display. application registers. For example, In most cases, it is unnecessary to clear a storage register since storing a number replaces the previous contents. However, you can clear a single register by storing 0 in it. To clear all the registers at once, press \N. Doing Arithmetic Inside Registers You can do arithmetic inside storage registers R0 through R19. The result is stored in the register. Table 4-8 Keys for performing arithmetic inside registers Keys New Number in Register \w1 register number \wA register number \wP register number Old contents + displayed number. Old contents - displayed number. Old contents × displayed number. Number Storage and Storage Register Arithmetic 53 Table 4-8 Keys for performing arithmetic inside registers Keys New Number in Register \wa register number Old contents ÷ displayed number. Example 1 Store 45.7 in R3, multiply by 2.5, and store the result in R3. Table 4-9 Calculating and storing the result in the storage register Keys Display Description YV7j \wD G7V \wPD vD 45.70 Stores 45.7 in R3. 2.50 Multiplies 45.7 in R3 by 2.5 and stores result (114.25) in R3. 114.25 Displays R3. Example 2 Store 1.25 into register 15, then add 3, and store the result in register 15. Table 4-10 Storage register arithmetic Keys J7GV \w7V D\w17V M v7V 54 Number Storage and Storage Register Arithmetic Display Description 1.25 Inputs 1.25 into the display. 1.25 Stores 1.25 in R15. 3.00 Adds 3 to 1.25 in R15 and stores the result R15. 0.00 Clears the display. 4.25 Recalls R15. 5 Picturing Financial Problems How to approach a Financial Problem The financial vocabulary of the HP 10bII+ is simplified to apply to all financial fields. For example, your profession may use the term balance, balloon payment, residual, maturity value, or remaining amount to designate a value that the HP 10bII+ knows as É (future value). The simplified terminology of the HP 10bII+ is based on cash flow diagrams. Cash flow diagrams are pictures of financial problems that show cash flows over time. Drawing a cash flow diagram is the first step to solving a financial problem. The following cash flow diagram represents investments in a mutual fund. The original investment was 7,000.00, followed by investments of 5,000.00 and 6,000.00 at the end of the third and sixth months. At the end of the 11th month, 5,000.00 was withdrawn. At the end of the 16th month, 16,567.20 was withdrawn. Figure 2 Cash flow diagram Any cash flow example can be represented by a cash flow diagram. As you draw a cash flow diagram, identify what is known and unknown about the transaction. Time is represented by a horizontal line divided into regular time periods. Cash flows are placed on the horizontal line when they occur. Where no arrows are drawn, no cash flows occur. Picturing Financial Problems 55 Signs of Cash Flows In cash flow diagrams, money invested is shown as negative and money withdrawn is shown as positive. Cash flowing out is negative, cash flowing in is positive. For example, from the lender’s perspective, cash flows to customers for loans are represented as negative. Likewise, when a lender receives money from customers, cash flows are represented as positive. In contrast, from the borrower’s perspective, cash borrowed is positive while cash paid back is negative. Periods and Cash Flows In addition to the sign convention (cash flowing out is negative, cash flowing in is positive) on cash flow diagrams, there are several more considerations: • The time line is divided into equal time intervals. The most common period is a month, but days, quarters, and annual periods are also common. The period is normally defined in a contract and must be known before you can begin calculating. • To solve a financial problem with the HP 10bII+, all cash flows must occur at either the beginning or end of a period. • If more than one cash flow occurs at the same place on the cash flow diagram, they are added together or netted. For example, a negative cash flow of -250.00 and a positive cash flow of 750.00 occurring at the same time on the cash flow diagram are entered as a 500.00 cash flow (750 - 250 = 500). • A valid financial transaction must have at least one positive and one negative cash flow. Simple and Compound Interest Financial calculations are based on the fact that money earns interest over time. There are two types of interest: • Simple interest • Compound interest The basis for Time Value of Money and cash flow calculations is compound interest. Simple Interest In simple-interest contracts, interest is a percent of the original principal. The interest and principal are due at the end of the contract. For example, say you loan 500 to a friend for a year, and you want to be repaid with 10% simple interest. At the end of the year, your friend owes you 550.00 (50 is 10% of 500). Simple interest calculations are done using the § key on your HP 10bII+. An example of a simple interest calculation can be found in chapter 6 under the section titled, Interest Rate Conversions. 56 Picturing Financial Problems Compound Interest A compound-interest contract is like a series of simple-interest contracts that are connected. The length of each simple-interest contract is equal to one compounding period. At the end of each period the interest earned on each simple-interest contract is added to the principal. For example, if you deposit 1,000.00 in a savings account that pays 6% annual interest, compounded monthly, your earnings for the first month look like a simple-interest contract written for 1 month at 1/2 % (6% ÷ 12). At the end of the first month the balance of the account is 1,005.00 (5 is 1/2 % of 1,000). The second month, the same process takes place on the new balance of 1,005.00. The amount of interest paid at the end of the second month is 1/2 % of 1,005.00, or 5.03. The compounding process continues for the third, fourth, and fifth months. The intermediate results in this illustration are rounded to dollars and cents. Figure 3 Annual interest compounded monthly The word compound in compound interest comes from the idea that interest previously earned or owed is added to the principal. Thus, it can earn more interest. The financial calculation capabilities of the HP 10bII+ are based on compound interest. Interest Rates When you approach a financial problem, it is important to recognize that the interest rate or rate of return can be described in at least three different ways: Picturing Financial Problems 57 • As a periodic rate. This is the rate that is applied to your money from period to period. • As an annual nominal rate. This is the periodic rate multiplied by the number of periods in a year. • As an annual effective rate. This is an annual rate that considers compounding. In the previous example of a 1,000.00 savings account, the periodic rate is 1/2 % (per month), quoted as an annual nominal rate of 6% ( 1/2 × 12). This same periodic rate could be quoted as an annual effective rate, which considers compounding. The balance after 12 months of compounding is 1,061.68, which means the annual effective interest rate is 6.168%. Examples of converting between nominal and annual effective rates can be found in the section titled, Interest Rate Conversions in the next chapter. Two Types of Financial Problems The financial problems in this manual use compound interest unless specifically stated as simple interest calculations. Financial problems are divided into two groups: • TVM problems • Cash flow problems Recognizing a TVM Problem If uniform cash flows occur between the first and last periods on the cash flow diagram, the financial problem is a TVM (time value of money) problem. There are five main keys used to solve a TVM problem. Table 5-1 Keys for solving a TVM problem Keys Description Ù Ò Ï Ì É Number of periods or payments Annual percentage interest rate (usually the annual nominal rate) Present value (the cash flow at the beginning of the time line) Periodic payment Future value (the cash flow at the end of the cash flow diagram, in addition to any regular periodic payment). You can calculate any value after entering the other four values. Cash flow diagrams for loans, mortgages, leases, savings accounts, or any contract with regular cash flows of the same amount are normally treated as TVM problems. For example, following is a cash flow diagram, from the borrower’s perspective, for a 30-year, 150,000.00 mortgage, with a payment of 1,041.40, at 7.5% annual interest, with a 10,000 balloon payment. 58 Picturing Financial Problems Figure 4 Cash flow diagram (Borrower’s perspective) One of the values for PV, PMT, FV can be zero. For example, following is a cash flow diagram (from the saver’s perspective) for a savings account with a single deposit and a single withdrawal five years later. Interest compounds monthly. In this example, PMT is zero. Figure 5 Cash flow diagram (Saving perspective) Time value of money calculations are described in the next chapter titled, Time Value of Money Calculations. Recognizing a Cash Flow Problem A financial problem that does not have regular, uniform payments (sometimes called uneven cash flows) is a cash flow problem rather than a TVM problem. Picturing Financial Problems 59 The following is a cash flow diagram for an investment in a mutual fund. This is an example of a problem that is solved using either \½ (Net Present Value) or \Á (Internal Rate of Return per Year). Figure 6 Cash flow diagram (Investment in a mutual fund) Cash flow problems are described in chapter 8 titled, Cash Flow Calculations. 60 Picturing Financial Problems 6 Time Value of Money Calculations Using the TVM Application The time value of money (TVM) application is used for compound interest calculations that involve regular, uniform cash flows – called payments. Once the values are entered you can vary one value at a time, without entering all the values again. To use TVM, several prerequisites must be met: • The amount of each payment must be the same. If the payment amounts vary, use the procedures described in chapter 8 titled, Cash Flow Calculations. • Payments must occur at regular intervals. • The payment period must coincide with the interest compounding period. If it does not, convert the interest rate using the \Ó, \Ð, and \Í keys described below in the section titled, Interest Rate Conversions. • There must be at least one positive and one negative cash flow. The TVM Keys When entering data for TVM calculations, results are calculated based on data entered into specific memory registers. When pressed, the keys used for these operations: • • • store data. enter known data for variables used during calculations. calculate unknown variables based on stored data. Table 6-1 Keys for performing TVM calculations Keys Stores or Calculates Ù Ò Ï Ì É \Í \Ú Number of payments or compounding periods. Annual nominal interest rate. Present value of future cash flows. PV is usually an initial investment or loan amount and always occurs at the beginning of the first period. Amount of periodic payments. All payments are equal, and none are skipped; payments can occur at the beginning or end of each period. Future value. FV is either a final cash flow or compounded value of a series of previous cash flows. FV occurs at the end of the last period. Stores the number of periods per year. The default is 12. Reset only when you wish to change it. Optional shortcut for storing N: number in display is multiplied by the value in P/YR and the result is stored in N. Time Value of Money Calculations 61 Table 6-1 Keys for performing TVM calculations Keys Stores or Calculates \¯ \Ê Switches between Begin and End mode. In Begin mode, the BEGIN annunciator is displayed. Calculates an amortization table. vÙ, vÒ, vÏ, vÌ, and vÉ. Pressing v\Ú recalls the total number of payments in years and v\Í To verify values, press shows you the number of payments per year. Recalling these numbers does not change the content of the registers. Begin and End Modes Before you start a TVM calculation, identify whether the first periodic payment occurs at the beginning or end of the first period. If the first payment occurs at the end of the first period, set your HP 10bII+ to End mode; if it occurs at the beginning of the first period, set your calculator to Begin mode. To switch between modes, press \¯. The BEGIN annunciator is displayed when your calculator is in Begin mode. No annunciator is displayed when you are in End mode. Mortgages and loans typically use End mode. Leases and savings plans typically use Begin mode. Loan Calculations Example: A Car Loan You are financing a new car with a three year loan at 10.5% annual nominal interest, compounded monthly. The price of the car is 14,500. Your down payment is 1,500. Part 1 What are your monthly payments at 10.5% interest? (Assume your payments start one month after the purchase or at the end of the first period.) 62 Time Value of Money Calculations Figure 7 Cash flow diagram (Calculate PMT) Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 6-2 Calculating the monthly payment Keys JG\Í DPJGÙ J:7VÒ JYV::A JV::Ï :É Ì Display Description 12.00 Sets periods per year (optional, as 12 is the default). 36.00 Stores number of periods in loan. 10.50 Stores annual nominal interest rate. 13,000.00 Stores amount borrowed. 0.00 Stores the amount left to pay after 3 years. -422.53 Calculates the monthly payment. The negative sign indicates money paid out. Part 2 At a price of 14,500, what interest rate is necessary to lower your payment by 50.00, to 372.53? Time Value of Money Calculations 63 Table 6-3 Calculating the interest rate Keys Display Description 1V:Ì Ò -372.53 Decreases payment from 422.53. 2.03 Calculates annual interest rate for the reduced payment. Part 3 If interest is 10.5%, what is the maximum you can spend on the car to lower your car payment to 375.00? Table 6-4 Calculating the amount Keys Display Description J:7VÒ DjVyÌ Ï 1JV::4 10.50 Stores original interest rate. -375.00 Stores desired payment. 11,537.59 Calculates amount of money to finance. 13,037.59 Adds the down payment to the amount financed for total price of the car. Example: A Home Mortgage You decide that the maximum monthly mortgage payment you can afford is 930.00. You can make a 12,000 down payment, and annual interest rates are currently 7.5%. If you obtain a 30 year mortgage, what is the maximum purchase price you can afford? Figure 8 Cash flow diagram (Calculate PV) 64 Time Value of Money Calculations Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 6-5 Calculating the maximum purchase price Keys JG\Í D:\Ú :É j7VÒ dD:yÌ Ï 1JG:::4 Display Description 12.00 Sets periods per year. 360.00 Stores the length of the mortgage (30 × 12). 0.00 Pays mortgage off in 30 years. 7.50 Stores interest rate. -930.00 Stores desired payment (money paid out is negative). 133,006.39 Calculates the loan you can afford with a 930 payment. 145,006.39 Adds 12,000 down payment for the total purchase price. Example: A Mortgage With a Balloon Payment You’ve obtained a 25 year, 172,500 mortgage at 8.8% annual interest. You anticipate that you will own the house for four years and then sell it, repaying the loan with a balloon payment. What will your balloon payment be? Solve this problem using two steps: 1. Calculate the loan payment using a 25 year term. 2. Calculate the remaining balance after 4 years. Step 1 First calculate the loan payment using a 25 year term. Time Value of Money Calculations 65 Figure 9 Cash flow diagram (Calculate PMT) Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 6-6 Calculating the monthly payment Keys JG\Í GV\Ú :É JjGV::Ï g7gÒ Ì Display 12.00 300.00 Description Sets periods per year. Stores length of mortgage (25 × 12 = 300 months). 0.00 Stores loan balance after 25 years. 172,500.00 Stores original loan balance. 8.80 -1,424.06 Stores annual interest rate. Calculates the monthly payment. Step 2 Since the payment is at the end of the month, the past payment and the balloon payment occur at the same time. The final payment is the sum of PMT and FV. 66 Time Value of Money Calculations Figure 10 Cash flow diagram (Calculate FV) The value in PMT should always be rounded to two decimal places when calculating FV or PV to avoid small, accumulative discrepancies between non-rounded numbers and actual (dollars and cents) payments. If the display is not set to two decimal places, press \5G. Table 6-7 Calculating the final amount Keys \}Ì YgÙ É 1vÌ4 Display -1,424.06 Description Rounds payment to two decimal places, then stores. 48.00 Stores four year term (12 × 4) that you expect to own house. -163,388.39 Calculates loan balance after four years. -164,812.45 Calculates the total 48th payment (PMT and FV) to pay off the loan (money paid out is negative). Savings Calculations Example: A Savings Account If you deposit 2,000 in a savings account that pays 7.2% annual interest compounded annually, and make no other deposits to the account, how long will it take for the account to grow to 3,000? Time Value of Money Calculations 67 Figure 11 Cash flow diagram (Calculate the number of years) Since this account has no regular payments (PMT = 0), the payment mode (End or Begin) is irrelevant. Table 6-8 Calculating the number of years Keys ]OJ J\Í G:::yÏ D:::É j7GÒ Ù Display Description 0.00 Clears TVM memory. 1.00 Sets P/YR to 1 since interest is compounded annually. -2,000.00 Stores amount paid out for the first deposit. 3,000.00 Stores the amount you wish to accumulate. 7.20 Stores annual interest rate. 5.83 Calculates the number of years it takes to reach 3,000. Since the calculated value of N is between 5 and 6, it will take six years of annual compounding to achieve a balance of at least 3,000. Calculate the actual balance at the end of six years. 68 Time Value of Money Calculations Table 6-9 Calculating the balance after six years Keys Display SÙ É 6.00 3,035.28 Description Sets n to 6 years. Calculates the amount you can withdraw after six years. Example: An Individual Retirement Account You opened an individual retirement account on April 14, 1995, with a deposit of 2,000. 80.00 is deducted from your paycheck and you are paid twice a month. The account pays 6.3% annual interest compounded semimonthly. How much will be in the account on April 14, 2010? Figure 12 Cash flow diagram (Calculate FV) Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 6-10 Calculating the balance amount Keys Display Description GY\Í G:::yÏ g:yÌ 24.00 Sets number of periods per year. -2,000.00 -80.00 Stores initial deposit. Stores regular semimonthly deposits. Time Value of Money Calculations 69 Table 6-10 Calculating the balance amount Keys Display S7DÒ JV\Ú É 6.30 360.00 52,975.60 Description Stores interest rate. Stores the number of deposits. Calculates the balance amount. Example: An Annuity Account You opt for an early retirement after a successful business career. You have accumulated a savings of 400,000 that earns an average of 7% annual interest, compounded monthly. What annuity (repetitive, uniform, withdrawal of funds) will you receive at the beginning of each month if you wish that savings account to support you for the next 50 years? Figure 13 Cash flow diagram (Calculate the amount) Set to Begin mode. Press \¯ if BEGIN annunciator is not displayed. Table 6-11 Calculating the amount at the beginning of each month Keys JG\Í Y:::::yÏ jÒ V:\Ú :É Ì 70 Time Value of Money Calculations Display 12.00 -400,000.00 Description Sets payments per year. Stores your nest egg as an outgoing deposit. 7.00 Stores annual interest rate you expect to earn. 600.00 Stores number of withdrawals. 0.00 Stores balance of account after 50 years. 2,392.80 Calculates the amount that you can withdraw at the beginning of each month. Lease Calculations A lease is a loan of valuable property (like real estate, automobiles, or equipment) for a specific amount of time, in exchange for regular payments. Some leases are written as purchase agreements, with an option to buy at the end of the lease (sometimes for as little as 1.00). The defined future value (FV) of the property at the end of a lease is sometimes called the residual value or buy out value. All five TVM application keys can be used in lease calculations. There are two common lease calculations. • Finding the lease payment necessary to achieve a specified yield. • Finding the present value (capitalized value) of a lease. The first payment on a lease usually occurs at the beginning of the first period. Thus, most lease calculations use Begin mode. Example: Calculating a Lease Payment A customer wishes to lease a 13,500 car for three years. The lease includes an option to buy the car for 7,500 at the end of the lease. The first monthly payment is due the day the customer drives the car off the lot. If you want to yield 10% annually, compounded monthly, what will the payments be? Calculate the payments from your (the dealer’s) point of view. Figure 14 Cash flow diagram (Calculate the monthly lease payment) Set to Begin mode. Press \¯ if BEGIN annunciator is not displayed. Time Value of Money Calculations 71 Table 6-12 Calculating the monthly lease payment Keys Display JG\Í J:Ò JDV::yÏ jV::É DSÙ Ì Description 12.00 Sets payments per year. 10.00 Stores desired annual yield. -13,500.00 7,500.00 Stores lease price. Stores residual (buy out value). 36.00 Stores length of lease, in months. 253.99 Calculates the monthly lease payment. Notice that even if the customer chooses not to buy the car, the lessor still includes a cash flow coming in at the end of the lease equal to the residual value of the car. Whether the customer buys the car or it is sold on the open market, the lessor expects to recover 7,500. Example: Lease With Advance Payments Your company, Quick-Kit Pole Barns, plans to lease a forklift for the warehouse. The lease is written for a term of four years with monthly payments of 2,400. Payments are due at the beginning of the month with the first and last payments due at the onset of the lease. You have an option to buy the forklift for 15,000 at the end of the leasing period. If the annual interest rate is 9%, what is the capitalized value of the lease? Figure 15 Cash flow diagram (Calculate PV of the lease) 72 Time Value of Money Calculations This solution requires four steps: 1. Calculate the present value of the 47 monthly payments: (4 × 12) - 1 = 47. 2. Add the value of the additional advance payment. 3. Find the present value of the buy option. 4. Sum the values calculated in steps 2 and 3. Step 1 Find the present value of the monthly payments. Set to Begin mode. Press \¯ if BEGIN annunciator is not displayed. Table 6-13 Calculating the present value Keys JG\Í YjÙ GY::yÌ :É dÒ Ï Display Description 12.00 Sets payments per year. 47.00 Stores number of payments. -2,400.00 Stores monthly payment. 0.00 Stores FV for Step 1. 9.00 Stores interest rate. 95,477.55 Calculates the present value of 47 monthly payments. Step 2 Add the additional advance payment to PV. Store the answer. Table 6-14 Adding the advance payment Keys 1vÌy4 s Display Description 97,877.55 Adds additional advance. payment 97,877.55 Stores result in M register. Step 3 Find the present value of the buy option. Table 6-15 Calculating the present value of the last cash flow Keys Display Description YgÙ 48.00 Stores month when buy option occurs. Time Value of Money Calculations 73 Table 6-15 Calculating the present value of the last cash flow Keys Display :Ì JV:::yÉ Ï 0.00 Description Stores zero payment for this step of solution. -15,000.00 Stores value to discount. 10,479.21 Calculates the present value of last cash flow. Step 4 Add the results of ’Step 2’ and ’Step 3’. Table 6-16 Calculating the present value of lease Keys 1p4 Display 108,356.77 Description Calculates the present (capitalized) value of lease. (Rounding discrepancies are explained on page 67.) Amortization Amortization is the process of dividing a payment into the amount that applies to interest and the amount that applies to principal. Payments near the beginning of a loan contribute more interest, and less principal, than payments near the end of a loan. Figure 16 Graph 74 Time Value of Money Calculations The AMORT key on the HP 10bII+ allows you to calculate. The • The amount applied to interest in a range of payments. • The amount applied to principal in a range of payments. • The loan balance after a specified number of payments are made. \Ê function assumes you have just calculated a payment or you have stored the appropriate amortization values in I/YR, PV, FV, PMT, and P/YR. Table 6-17 Keys for storing the amortization values Keys Description Ò Ï É Ì \Í Annual nominal interest rate. Starting balance. Ending balance. Payment amount (rounded to the display format). Number of payments per year. The numbers displayed for interest, principal, and balance are rounded to the current display setting. To Amortize To amortize a single payment, enter the period number and press \Ê . The HP 10bII+ displays the annunciator PER followed by the starting and ending payments that will be amortized. 4 to see interest (INT). Press 4 again to see the principal (PRIN) and again to see the balance (BAL). Continue pressing 4 to cycle through the same values again. To amortize a range of payments, enter starting period number Æ ending period number, then press \Ê. The HP 10bII+ displays the annunciator PER followed by the starting and ending payments that will be amortized. Then press 4 repeatedly to cycle through Press interest, principal, and balance. Press \Ê again to move to the next set of periods. This auto-increment feature saves you the keystrokes of entering the new starting and ending periods. Time Value of Money Calculations 75 If you store, recall, or perform any other calculations during amortization, pressing 4 will no longer cycle through interest, principal, and balance. To resume amortization with the same set of periods, press v\Ê. Example: Amortizing a Range of Payments Calculate the first two years of the annual amortization schedule for a 30 year, 180,000 mortgage, at 7.75% annual interest with monthly payments. Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 6-18 Calculating the monthly payment Keys JG\Í D:\Ú j7jVÒ Jg::::Ï :É Ì Display 12.00 360.00 7.75 180,000.00 0.00 -1,289.54 Description Sets payments per year. Stores total number of payments. Stores interest per year. Stores present value. Stores future value. Calculates the monthly payment. If you already know the mortgage payment, you can enter and store it just like you store the other four values. Next, amortize the first year. Table 6-19 Calculating the loan balance after a year Keys JÆJG \Ê 4 Display 12_ 1– 12 Description Enters starting and ending periods. Displays the PER and AMORT annunciators and range. -1,579.84 Displays the PRIN annunciator and the principal paid in the first year. 4 -13,894.67 Displays the INT annunciator and the interest paid in the first year. 4 178,420.16 Displays the BAL annunciator and the loan balance after one year. 76 Time Value of Money Calculations The amount paid toward interest and principal (13,894.67 + 1,579.84 = 15,474.51) equals the total of 12 monthly payments (12 × 1,289.54 = 15,474.51). The remaining balance equals the initial mortgage, less the amount applied toward principal (180,000 - 1,579.84 = 178,420.16). Amortize the second year: Table 6-20 Calculating the remaining balance Keys Display Description JDÆGY \Ê 4 4 4 13 – 24 Displays PER and the next range of periods. -1,706.69 Displays PRIN and the principal paid in the second year. -13,767.79 Displays INT and the interest paid in the second year. 176,713.49 Displays BAL and the loan balance after 24 payments. The amount paid toward interest and principal (13,767.79 + 1,706.69 = 15,474.51) equals the total of 12 monthly payments (12 × 1,289.54 = 15,474.51). The remaining balance equals the initial mortgage less the amount applied toward principal (180,000 - 1,579.84 - 1,706.69 = 176,713.49). More money is applied to principal during the second year rather than the first year. The succeeding years continue in the same fashion. Example: Amortizing a Single Payment Amortize the 1st, 25th, and 54th payments of a five year car lease. The lease amount is 14,250 and the interest rate is 11.5%. Payments are monthly and begin immediately. Set to Begin mode. Press \¯ if BEGIN annunciator is not displayed. Table 6-21 Calculating the monthly payment Keys JG\Í V\Ú JJ7VÒ JYGV:Ï :É Display Description 12.00 Sets payments per year. 60.00 Stores number of payments. 11.50 Stores interest per year. 14,250.00 0.00 Stores present value. Stores future value. Time Value of Money Calculations 77 Table 6-21 Calculating the monthly payment Keys Display Description Ì -310.42 Calculates the monthly payment. Amortize the 1st, 25th, and 54th payments Table 6-22 Calculating the amount Keys JÆ \Ê 4 4 4 GVÆ \Ê 4 4 4 VYÆ \Ê 4 4 4 78 Time Value of Money Calculations Display Description 1.00 Enters first payment. 1–1 Displays PER and the amortized payment period. -310.42 0.00 13,939.58 25.00 Displays PRIN and the first principal payment. Displays INT and the interest. Displays BAL and the loan balance after one payment. Enters payment to amortize. 25 – 25 Displays PER and the amortized payment period. -220.21 Displays PRIN and the principal paid on the 25th payment. -90.21 Displays INT and the interest paid on the 25th payment. 9,193.28 Displays BAL and the balance after the 25th payment. 54.00 Enters payment to amortize. 54 – 54 Displays PER and the amortized payment period. -290.37 Displays PRIN and the principal paid on the 54th payment. -20.05 Displays INT and the interest paid on the 54th payment. 1,801.57 Displays BAL and the balance after the 54th payment. Interest Rate Conversions The Interest Conversion application uses three keys: \Ó, \Ð, and \Í. They convert between nominal and annual effective interest rates. If you know an annual nominal interest rate and you wish to solve for the corresponding annual effective rate: 1. Enter the nominal rate and press \Ó. 2. Enter the number of compounding periods and press 3. Calculate the effective rate by pressing \Í. \Ð. To calculate a nominal rate from a known effective rate: 1. Enter the effective rate and press \Ð. 2. Enter the number of compounding periods and press \Í. \Ó. In the TVM application, \Ó and Ò share the same memory. 3. Calculate the nominal rate by pressing Interest conversions are used primarily for two types of problems: • Comparing investments with different compounding periods. • Solving TVM problems where the payment period and the interest period differ. Investments With Different Compounding Periods Example: Comparing Investments You are considering opening a savings account in one of three banks. Which bank has the most favorable interest rate? First Bank 6.70% annual interest, compounded quarterly Second Bank 6.65% annual interest, compounded monthly Third Bank 6.63% annual interest, compounded 360 times per year First Bank Table 6-23 Calculating the interest rate (First bank) Keys S7j\Ó Y\Í Display Description 6.70 Stores nominal rate. 4.00 Stores quarterly compounding periods. Time Value of Money Calculations 79 Table 6-23 Calculating the interest rate (First bank) Keys \Ð Display 6.87 Description Calculates the annual effective rate. Second Bank Table 6-24 Calculating the interest rate (Second bank) Keys Display S7SV\Ó JG\Í \Ð Description 6.65 Stores nominal rate. 12.00 Stores monthly compounding periods. 6.86 Calculates the annual effective rate. Third Bank Table 6-25 Calculating the interest rate (Third bank) Keys S7SD\Ó DS:\Í \Ð Display 6.63 360.00 6.85 Description Stores nominal rate. Stores compounding periods. Calculates the annual effective rate. First Bank offers a slightly better deal since 6.87 is greater than 6.86 and 6.85. Compounding and Payment Periods Differ The TVM application assumes that the compounding periods and the payment periods are the same. Some loan installments or savings deposits and withdrawals do not coincide with the bank’s compounding periods. If the payment period differs from the compounding period, adjust the interest rate to match the payment period before solving the problem. To adjust an interest rate when the compounding period differs from the payment period complete the following steps: 1. 2. \Ó. Enter the number of compounding periods in a year and press \Í. Solve for the effective rate by pressing \Ð. Enter the number of payment periods in a year and press \Í. Solve for the adjusted nominal rate by pressing \Ó. Enter the nominal rate and press 80 Time Value of Money Calculations Example: Monthly Payments, Daily Compounding Starting today, you make monthly deposits of 25 to an account paying 5% interest, compounded daily (using a 365 day year). What will the balance be in seven years? Step 1 Calculate the equivalent rate with monthly compounding. Table 6-26 Calculating the equivalent nominal percentage rate Keys Display V\Ó DSV\Í \Ð JG\Í \Ó 5.00 365.00 5.13 Description Stores nominal percentage rate. Stores bank’s compounding periods per year. Calculates annual effective rate. 12.00 Stores monthly periods. 5.01 Calculates the equivalent nominal percentage rate for monthly compounding. Since NOM% and I/YR share the same memory, this value is ready for use in the rest of the problem. Step 2 Calculate the future value. Set to Begin mode. Press \¯ if BEGIN annunciator is not displayed. Table 6-27 Calculating the future value Keys :Ï GVyÌ j\Ú É Display 0.00 Description Stores present value -25.00 Stores payment 84.00 Stores total number of payments 2,519.61 Calculates the balance after 7 years. Time Value of Money Calculations 81 Resetting the TVM Keys Press ]OJ to clear the TVM registers. This sets N, I/YR, PV, PMT, and FV to zero and briefly displays TVM CLR, followed by the current value in P/Yr. 82 Time Value of Money Calculations 7 Depreciation On the 10bII+, depreciation calculations are performed using the functions printed in blue on the keyboard located under the blue bracket titled, DEPRECIATION. Depreciation calculations are based on data entered into the Time Value of Money (TVM) keys: Ï, É, Ò, and Ù. Table 7-1 Depreciation keys TVM Key Description ]OJ Ù Ï É ]{ Clear TVM memory. Since the TVM and depreciation applications share the same memory, clearing TVM resets depreciation also. ]x The expected useful life of the asset in years. The depreciable cost of the asset at acquisition. The salvage value of the asset at the end of its useful life. Straight line is a method of calculating depreciation presuming an asset loses a certain percentage of its value annually at an amount evenly distributed throughout its useful life. Sum-of-the-years' digits is an accelerated depreciation method. In SOYD, the depreciation in year y is (Life-y +1)/SOY of the asset, where SOY is the sum-of-the-years for the asset, or, for an asset with a 5-year life, 5+4+3+2+1=15. ]u Declining balance is an accelerated depreciation method that presumes an asset will lose the majority of its value during the first few years of its useful life. Ò \« The declining balance factor as a percentage. This is used for declining balance method. With the calculated depreciation displayed, press \« to display the remaining depreciable value at the end of the given year. The Depreciation Keys When entering data for depreciation calculations, results are calculated based on data entered into specific memory registers. When pressed, the keys used for these operations: • • • store data. enter known data for variables used during calculations. calculate unknown variables based on stored data. Depreciation 83 To perform a depreciation calculation: 1. Enter the original cost of the asset, using Ï. 2. Enter the salvage value of the asset, using FV. If the salvage value is zero, press :É. 3. Enter the expected useful life of the asset (in years), followed by Ù. 4. If the declining-balance method is being used, enter the declining-balance factor (as a Ò percentage), followed by . For example, 1-1/4 times the straight-line rate — 125 percent declining-balance — would be entered as 125. 5. Key in the number of the year for which depreciation is to be calculated followed by the desired depreciation method: • • • ]{ for depreciation using the straight-line method. ]u for depreciation using the sum-of-the-years digits method. ]x for depreciation using the declining-balance method. ]{, ]u, and ]x each place the amount of depreciation in the display, and the TVM and X annunciators are displayed. Press \« to display the remaining depreciable value (the book value less the salvage value). After pressing \« to display the remaining depreciable value, note the X annunciator changes to Y. Example 1 A metalworking machine, purchased for 10,000.00, is to be depreciated over five years. Its salvage value is estimated at 500.00. Using the straight-line method, find the depreciation and remaining depreciable value for each of the first two years of the machine's life. See Table 7-2. Table 7-2 Depreciation example using SL Keys ]OJ J::::Ï V::É 84 Depreciation Display TVM CLR (message flashes then disappears) 10,000.00 500.00 Description Clears TVM registers. Enters 10,000.00 for the depreciable cost of the item in the selected format. Enters 500.00 for the salvage value of the item in the selected format. Table 7-2 Depreciation example using SL Keys Display VÙ J]{ Description 5.00 Inputs 5 for the expected useful life of the asset in the selected format. 1,900.00 Enters the year for which depreciation is to be calculated and calculates the depreciation of the asset in year one. TVM and X are displayed. \« 7,600.00 Displays remaining depreciable value after year one. X changes to Y in the display. G]{ 1,900.00 Enters the year for which depreciation is to be calculated and calculates the depreciation of the asset in year two. \« 5,700.00 Displays remaining depreciable value after year two. Example 2 A machine was purchased for 4,000 and is to be depreciated over four years with a 1,000 salvage value. Using the sum-of-the-year's digit method, what is the depreciation during the machine's first year and third years? What is the remaining depreciable value? Table 7-3 Depreciation example using SOYD Keys ]OJ Y:::Ï YÙ J:::É J]x D]x \« Display TVM CLR (message flashes then disappears) Description Clears TVM registers. 4,000.00 Enters the depreciable cost of the asset at acquisition. 4.00 Enters the expected useful life of the asset. 1,000.00 Enters the salvage value. 1,200.00 Calculates the depreciation for the first year. 600.00 Calculates the depreciation for the third year. 300.00 Displays the remaining depreciable value. Depreciation 85 Example 3 A machine was purchased for 5,000 and is to be depreciated over seven years with no salvage value. Using the double declining balance method, what is the depreciation for the first three years of the machine's life? What is the remaining depreciable value? Table 7-4 Depreciation example using Declining Balance Keys Display ]OJ V:::Ï jÙ G::Ò :É J]u G]u D]u \« TVM CLR (message flashes then disappears) Description Clears TVM registers. 5,000.00 Enters the depreciable cost of the asset at acquisition. 7.00 Enters the expected useful life of the asset. 200.00 0.00 Enters the double declining balance factor as a percentage. Enters the salvage value. 1,428.57 Calculates the depreciation for the first year. 1,020.41 Calculates the depreciation for the second year. 728.86 Calculates the depreciation for the third year. 1,822.16 Displays the remaining depreciable value. Resetting the TVM Keys To clear the TVM registers and reset the TVM and depreciation functions to their default values, press ]O, followed by J. The messages, TVM CLR and 12 P_yr appear briefly to indicate the TVM registers have been reset. 86 Depreciation 8 Cash Flow Calculations How to Use the Cash Flow Application The cash flow application is used to solve problems where cash flows occur over regular intervals. Problems with regular, equal, periodic cash flows are handled more easily using the TVM keys. To operate the cash flow system, cash flow amounts and repeat values are keyed in either individually or together. In the following chapter, the term repeat value is used to describe the number of times a cash flow occurs. Terms such as cash flow count, number of occurrences, or cash flow group are also used to describe the repeat value. If a new cash flow is entered, the calculator auto-increments the current cash flow count by 1. A value of 1 is automatically entered for a repeat value. To enter a repeat value for the current \¥. To enter the cash flow and a repeat value together, enter the cash flow value followed by Æ, then enter the repeat value followed by ¤. cash flow entry, enter a value using In general, use the following steps for cash flow calculations on the HP 10bII+: 1. Organize your cash flows on paper. A cash flow diagram is useful. 2. Clear the cash flow memory. 3. Enter the number of periods per year. 4. Enter the amount of the initial investment (CF0) using ¤ to enter the cash flow value. The CF0 value may have a repeated value. To enter the cash flow amount and repeat value simultaneously, enter a cash flow amount, followed by for the repeat value followed by Æ, then enter a number ¤. 5. Unless the cash flow and repeat value have already been entered as described in step 4 using Æ and ¤, as an alternative, enter the repeat value using \¥. 6. Repeat steps 4 and 5 for each cash flow and repeat value. 7. To calculate net present value and net future value, you must first enter a value for the annual interest rate and press 8. Ò; then press \½. With NPV calculated, press \«to display Net Future Value. To calculate IRR, press \Á. Cash Flow Calculations 87 Table 8-1 Cash Flow Keys Key Description ]O: \Í number1 ¤ Clears cash flow memory. Æ number 2 ¤ number1 \¥ v¤ number 2 Number of periods per year (default is 12). For annual cash flows, P/YR should be set to 1; for monthly cash flows, use the default setting, 12. Cash flows, up to 45. J identifies the cash flow number. When preceded by a ¤ enters a cash flow amount. Enter a cash flow amount, followed by Æ. Enter a number for the repeat value followed by ¤. This enters cash flow amount and repeat value number, pressing simultaneously. An alternative for entering repeat value for cash flow J . Opens editor for reviewing or editing entered cash flows. Press 1 or A to scroll through the cash flow data. Internal rate of return per year. \Á Net present value. \½ \½\« Net future value. With cash flow editor open, displays total of cash flows. ]X With cash flow editor open, displays total number of cash flows. ]U Clearing the Cash Flow Memory It is always a good idea to clear the cash flow memory before beginning. To clear cash flows, use ]O:. A brief message appears, CFLO CLR, to indicate the cash flow memory has been reset. On the 10bII+, there is always space reserved for up to 15 cash flows. In addition, up to 30 additional cash flows may be stored in memory shared with the statistics memory, as shown in Figure 1 below. 88 Cash Flow Calculations Figure 1 As illustrated in Figure 1, if no more than 15 data points are stored in the statistics memory, you may store up to 45 cash flows with the shared memory space. If more than 15 data points are stored in the statistics memory, the total memory available for storing cash flows is reduced. For example, in Figure 2, there are 25 data points stored, and the amount of available shared memory has therefore decreased by 10 slots. Figure 2 If data storage in the calculator memory resembles Figure 2, and you have a cash flow calculation requiring more than 35 data points, clearing unneeded statistical information will free up more space for information. When available memory is reached (see Figure 3), the FULL annunciator indicates there is not enough space to continue saving data. If you attempt to enter another cash flow at this point, the ERROR annunciator is displayed. In this case, no additional cash flow data can be entered until some data in the statistics memory is removed and the shared memory is once again available. Figure 3 Example 1: A Short Term Investment The following cash flow diagram represents an investment in stock over three months. Purchases were made at the beginning of each month, and the stock was sold at the end of the third month. Calculate the annual internal rate of return and the monthly rate of return. Cash Flow Calculations 89 Calculating Internal Rate of Return 1. 2. 3. ]O:, and store the desired number of periods per year in P/YR. Enter the cash flows using Æ and ¤. Press \Á. Press Figure 4 Cash flow diagram (Investments in stock) Table 8-2 Example 1: a short term investment Keys ]O: JG\Í V:::y¤ G:::y¤ 90 Cash Flow Calculations Display CFLO CLR Description Clears cash flow memory. (message flashes, then disappears) 12.00 -5,000.00 (CF 0 flashes, then disappears) -2,000.00 (CF 1 flashes, then disappears) Set payments per year. Enters initial cash flow. Note the CFLO and CF annunciators. Enters first cash flow. Note the CFLO and CF annunciators. Table 8-2 Example 1: a short term investment Keys Y:::y¤ JJjSV7Gd¤ \Á aJG Display -4,000.00 (CF 2 flashes, then disappears) 11,765.29 (CF 3 flashes, then disappears) 38.98 3.25 Description Enters second cash flow. Note the CFLO and CF annunciators. Enters third cash flow. Note the CFLO and CF annunciators. Calculates annual nominal yield. Monthly yield. NPV and IRR/YR: Discounting Cash Flows Chapter 5 titled, Picturing Financial Problems demonstrates the use of cash flow diagrams to clarify financial problems. This section describes discounted cash flows. The NPV, NFV and IRR/YR functions are frequently referred to as discounted cash flow functions. When a cash flow is discounted, you calculate its present value. When multiple cash flows are discounted, you calculate the present values and add them together. The net present value (NPV) function finds the present value of a series of cash flows. The annual nominal interest rate must be known to calculate NPV. The net future value (NFV) function finds the value of the cash flows at the time of the last cash flow, discounting the earlier cash flows by the value set for the annual nominal interest rate. The internal rate of return (IRR/YR) function calculates the annual nominal interest rate that is required to give a net present value of zero. The utility of these two financial tools becomes clear after working a few examples. The next two sections describe organizing and entering your cash flows. Examples of NPV, NFV, and IRR/YR calculations follow. Organizing Cash Flows The cash flow series is organized into an initial cash flow (CF0) and succeeding cash flow groups (up to 44 cash flows). CF0 occurs at the beginning of the first period. A cash flow group consists of a cash flow amount and the number of times it repeats. For example, in the following cash flow diagram, the initial cash flow is -11,000. The next group of cash flows consists of six flows of zero each, followed by a group of three 1,000 cash flows. The final group consists of one 10,000 cash flow. Cash Flow Calculations 91 Figure 5 Initial cash flow and cash flow groups Whenever you enter a series of cash flows, it is important to account for every period on the cash flow diagram, even periods with cash flows of zero. Example Enter the cash flows from the preceding diagram and calculate the IRR/YR. Assume there are 12 periods per year. Table 8-3 Example calculating IRR and effective interest rate Keys ]O: JG\Í JJ:::y¤ :¤ S\¥ 92 Cash Flow Calculations Display CFLO CLR Description Clears cash flow memory. (message flashes, then disappears) 12.00 -11,000.00 (CF 0 flashes, then disappears) 0.00 (CF 1 flashes, then disappears) 6.00 (CFn 1 flashes, then disappears) Set payments per year. Enters initial cash flow. Displays cash flow group number and amount. Note the CFLO and CF annunciators. Enters first cash flow group amount. Note the CF annunciator. Enters number of repetitions. Note the CFLO and N annunciators. Table 8-3 Example calculating IRR and effective interest rate Keys Display J:::¤ D\¥ J::::¤ 1,000.00 (CF 2 flashes, then disappears) 3.00 (CFn 2 flashes, then disappears) 10,000.00 (CF 3 flashes, then disappears) \Á 21.22 Description Enters second cash flow group amount. Note the CFLO and CF annunciators. Enters number of repetitions. Note the CFLO and N annunciators. Enters third cash flow. Note the CFLO and CF annunciators. Calculates the annual nominal yield. Viewing and Editing Cash Flows The cash flow editor application allows you to review entered data quickly to ensure accuracy. In addition, you may edit, add, or delete cash flow data as needed. 1. Press v¤ to open the editor. The current repeat value and the current cash flow value are displayed. The CFLO annunciator appears, and either CF or N identifies which value is being displayed. 2. Press 1 to move up through the current cash flow information. When you pass the maximum of the data, an empty cash flow pair is displayed before wrapping around to CF0, provided there is enough memory for another cash flow pair to be entered. 3. Press A to move down through the current cash flow information. At CF 0 the display wraps around to the maximum cash flow pair count. ¤ to return to CF . To jump to a specific cash flow, type the desired whole number of the desired cash flow item, J, and press ¤. 4. At any time with the editor open, press 0 The editor jumps to that position. If the number is higher than your maximum current cash flow item count, it will place you at the highest cash flow value. If an invalid entry is typed, such as a negative number or a non-whole number, the editor remains in its current location. a. To add a new cash flow with a value of 0 and a repeat value of 1 before the currently displayed item, press P. 5. To delete the current cash flow pair, press Cash Flow Calculations 93 6. To replace the currently displayed value, simply type a new number and press 7. Æ. Only valid entries are accepted. If you type an invalid entry, such as a value of 0 for the count, the ERROR annunciator appears and the value is rejected. To clear the current cash flow or repeat value without removing the entire pair, press |. If the cash flow amount is displayed, it will be set to a value of 0. If the cash flow repeat value is displayed, it will be set to a value of 1. 8. To view the current cash flow total, press cash flows, press 9. Press ]X. To view the current total number of ]U. M to exit. After completing the last example, open the cash flow list and modify the following cash flows with the data in the table below. Calculate the new IRR/YR. Table 8-4 Enter the new data Cash Flow Group New Cash Flow Amount New Cash Flow Count CF 0 -11,000.00 1 CF 1 0 3 CF 2 1,000.00 2 CF 3 7,500.00 2 CF 4 -1,200.00 2 Table 8-5 Editing cash flows Keys v¤ J¤1 DÆ 11GÆ D¤ 94 Cash Flow Calculations Display Description 0 -11,000.00 Open the cash flow list, starting with the initial cash flow CF0. 1 6.00 Jumps to the group, CF1, and the repeat value, 6.00. 1 3.00 Inputs new repeat value, 3.00, for CF1. 2 2.00 Displays cash flow repeat value and inputs new repeat value for CF2. 3 10,000.00 Displays the group, CF3, and the cash flow amount, 10,000.00. Table 8-5 Editing cash flows Keys Display Description jV::Æ1GÆ 3 2.00 Inputs new cash flow amount and repeat value. Displays the new repeat value, 2.00, for CF3. 1JG::yÆ1G Æ ]X M \Á Inputs new cash flow, CF4, 4 is displayed first, with and repeat value. no value followed by 4 -1,200, then 4 2.00 3,600.00 Displays total of the cash flows. 0.00 Exit the editor. 58.97 Calculate the new annual yield. Calculating Net Present Value and Net Future Value The net present value (NPV) function is used to discount all cash flows to the front of the time line using an annual nominal interest rate that you supply. To calculate NPV or NFV: 1. Press ]O: and store the desired number of periods per year in P/YR. 2. Enter the cash flow data. 3. Store the annual nominal interest rate in I/YR and press 4. If you have just calculated NPV, press \½. \« to calculate NFV. Example: A Discounted Contract, Uneven Cash flows You have an opportunity to purchase a contract with the following cash flows: Table 8-6 Example of a contract with uneven cash flows End of Month Amount 4 5,000.00 9 5,000.00 10 5,000.00 15 7,500.00 25 10,000.00 Cash Flow Calculations 95 How much should you pay for the contract if you wish to yield a yearly rate of 15% on your investment? Figure 6 Cash flow diagram (Calculate the amount) The following example uses the Æ and ¤ keys to enter the cash flow amount and repeat value simultaneously. When the cash flow count is 1 for a given cash flow amount, the cash flow amount may be entered simply by pressing the amount followed by ¤, as the default Æ key to enter the cash flow amount, you must then follow Æwith the repeat value followed by ¤, even if the repeat value is 1. This for the count is 1. However, when using the process is shown here to demonstrate this application and for consistency with entering the data for the example. Table 8-7 Entering uneven cash flows Keys ]O: JG\Í :ÆY¤ Display CFLO CLR Description Clear cash flow memory. (message flashes, then disappears) 12.00 Set payments per year. 4.00 Input initial cash flow of zero and (CFn 0 flashes, then the repeat value. disappears) V:::ÆJ¤ Input second cash flow amount and (CFn 1 flashes, then repeat value. Note the N annunciator. disappears) :ÆY¤ Input third cash flow amount and (CFn 2 flashes, then repeat value. disappears) V:::ÆG¤ 96 Cash Flow Calculations 1.00 4.00 2.00 Input fourth cash flow amount and (CFn 3 flashes, then repeat value. disappears) Keys :ÆY¤ jV::ÆJ¤ Display Description Input fifth cash flow amount and (CFn 4 flashes, then repeat value. disappears) 4.00 1.00 Input sixth cash flow amount and (CFn 5 flashes, then repeat value. disappears) :Æd¤ Input seventh cash flow amount and (CFn 6 flashes, then repeat value. disappears) J::::ÆJ¤ Input eighth cash flow amount and (CFn 7 flashes, then repeat value. disappears) 9.00 1.00 The cash flows that describe your prospective investment are now in the calculator. Press v¤. Press 1 or A to scroll through the list and verify the cash flows and the repeat value is entered correctly. Press M to exit. Now that you have entered the cash flows, store the interest rate and calculate the net present value and net future value. Table 8-8 Calculating NPV and NFV Keys JVÒ \½ \« Display 15.00 Description Store annual interest rate 27,199.92 Calculate net present value of stored cash flows. 37,105.94 Calculate NFV of stored cash flows. This result shows that if you want a yield of 15% per year, you should pay 27,199.92 for the contract. Notice that this amount is positive. The net present value is simply the summed (or netted) value of a series of cash flows when they are discounted to the front of the time line. Cash Flow Calculations 97 Figure 7 Cash flow diagram (Calculates NPV) Automatic Storage of IRR/YR and NPV When you calculate NPV, the result is stored in PV for your convenience. To recall that result, vÏ. If you haven’t changed the TVM values from the last example using NPV, when you press vÏ the result is 27,199.92. When you calculate IRR/YR, the result is stored in I/YR. Press vÒ to display the annualized yield. More examples of NPV, NFV press and IRR/YR calculations can be found in the chapter 13 titled, Additional Examples. 98 Cash Flow Calculations 9 Calendar Formats and Date Calculations Calendar Format The calendar options for bonds and date calculations are Actual (ACT) and 360. Press ]Å to toggle between these options. The default setting, Actual, is based on a 365day calendar. The alternate setting, 360, is based on a 360-day calendar. It is important to note date and bond calculations return different values for each of these settings, so verify the calendar mode is appropriate for your problem before you begin. Table 9-1 Date and Calendar Keys Keys Description ]È Enters dates in DD.MMYYYY or MM.DDYYYY formats. D.MY is the default. Numbers at the far right of a calculated date indicate days of the week. 1 is for Monday; 7 is for Sunday. ]Å \Ç Toggles between 360-and 365-day (Actual) calendars. Calculates the date and day, past or future, that is a given number of days from a given date. Note the returned result is always calculated on the 365-day calendar (Actual), regardless of the calendar setting. \Ä Calculates the number of days between two dates. Based on your current setting, returned result is calculated on either the 365-day (Actual) or the 360-day calendar. Date Format The valid range of dates for the calendar functions of the HP 10bII+ is October 15, 1582 through December 31, 9999. For the date, the number of days between two dates, and bond calculations, dates may be entered and displayed either in month-day-year (M.DY) or daymonth-year (D.MY) formats. In addition to a different display mode for the date and date calculations, these functions also return different values based on the 365-day (ACT) and 360day (360) calendars. Press ]È to toggle between the formats. The default setting is day-month-year (dd.mmyyyy). Press ]Å to toggle between the 360-and 365-day (actual) calendars. To specify the number of displayed decimal places: 1. Press \5. Calendar Formats and Date Calculations 99 : through d that you wish to appear after the decimal point. To view the entire date, press S. For more information on changing the number 2. Enter the number of digits display, refer to the section titled, Specifying Displayed Decimal Places in chapter 2. To key in a date in M.DY format: 1. Key in one or two digits for the month. 2. Press 7. 3. Key in two digits for the day. 4. Key in four digits for the year. \Ç or \Ä to display the date in the selected number 5. Press either display format. To key in a date in D.MY, press 1. ]È until the D.MY annunciator appears. Key in one or two digits for the day. 2. Press 7. 3. Key in two digits for the month. 4. Key in four digits for the year. \Ç or \Ä to display the date in the selected number 5. Press either display format. Using the INPUT key You can also enter dates for date calculations and the number of days using To enter a date in M.DY format using 1. Æ. Æ: Key in one or two digits for the month. 2. Press 7. 3. Key in two digits for the day. 4. Key in four digits for the year. 5. Press Æ. For more information about using the data and number of days functions as in-line functions, or with the Æ key, see the examples below and refer to the section titled, In-Line Functions in chapter 2. 100 Calendar Formats and Date Calculations Date Calculations and Number of Days To calculate the date and day, past or future, that is a given number of days from a given date as an in-line function: 1. Key in the given date and press \Ç. 2. Key in the number of days. 3. If the other date is in the past, press 4. Press y. 4 to display the date in the selected number display format. To calculate the date and day, past or future, that is a given number of days from a given date using 1. Æ: Key in the given date and press Æ. 2. Key in the number of days. 3. If the other date is in the past, press 4. Press y. \Ç to display the date in the selected number display format. Regardless of the setting for displayed places after the decimal point, or whether you use Æ or the in-line feature, the answer calculated by the \Ç function is displayed in a special format. The numbers of the month, day, and year (or day, month, and year) are separated by digit separators. The digit at the right of the displayed answer indicates the day of the week: 1 is for Monday; 7 is for Sunday. Date Calculation Example 1 What is the date 100 days after December 18, 2011? Press ]È if the D.MY annunciator is displayed. Calculate this example using the date feature as an in-line function and with the Æ key. Calendar Formats and Date Calculations 101 Table 9-2 Date calculation example as an in-line function Keys Display JG7JgG:JJ \ÇJ::4 To enter the data for this example using the Description 12.182011_ Keys in the date in MM.DDYYYY format. 3-27-2012 2 Calculates the date. Æ key: Table 9-3 Date calculation example using the ‘INPUT’ key Keys Display JG7JgG:JJ ÆJ::\Ç Description 12.182011_ Keys in the date in MM.DDYYYY format. 3-27-2012 2 Returns the same results using the Æ key. Number of Days \Ä function to calculate the number of days between two dates. Key in the earlier date and press \Ä. Key in the later date and press \Ä to calculate the number of days between the Use the 1. 2. two dates in actual days. Example 1 How many days remain in the 2010 fiscal year if today's date is June 4, 2010? Assume the fiscal year ends on October 31st, and you wish to calculate the actual number of days (Actual) using the D.MY format. Press ]Å if the 360 annunciator is displayed. Calculate the example as an in-line function. 102 Calendar Formats and Date Calculations Table 9-4 Calculating the actual number of days as an in-line function Keys Display Description ]È 0.00 Sets the desired date format. Note the D.MY annunciator. ]Å 0.00 Sets the desired calendar format, in this case, actual days (optional if the 360 annunciator is not displayed, as Actual is the default). \5S 0.000000 Sets the number of displayed decimal places so the entire date is displayed (optional). Y7:SG:J:\Ä DJ7J:G:J: 4 4.062010 Inputs the starting date in the selected format. 149.000000 Inputs the ending date in the selected format and calculates the number of actual days between the starting and ending dates. 149.00 Returns the number of displayed decimal places to the default (optional). \5G Example 2 How many days are there between October 17, 2012 and June 4, 2015? Use the M.DY setting and compute the number of days in Actual (Act) mode. Press ]Å if the 360 ]È if the D.MY annunciator is displayed. Calculate this example using the number of days feature as an in-line function and also with the Æ annunciator is displayed; press key. Table 9-5 Calculating the actual number of days as an in-line function Keys J:7JjG:JG \ÄS7:YG:JV4 Display 10.172012_ 960.00 Description Keys in the date in MM.DDYYYY format. Calculates the days between based on the 360-day calendar. Calendar Formats and Date Calculations 103 Using the Æ key: Table 9-6 Calculating the actual number of days using the ‘INPUT’ key Keys M J:7JjG:JGÆ S7:YG:JV\Ä 104 Calendar Formats and Date Calculations Display Description 0.00 Clear display. 10.17 Keys in the date in MM.DDYYYY format and displays digits in the selected display format (2). 960.00 Returns the same results. 10 Bonds The Bond Keys On the 10bII+, bond calculations are based on data or settings stored in the ten keys which make up the top two rows of the keyboard. The functions used in bond calculations are printed in blue above the keys on the keyboard. To access the bond functions, press ] followed by the desired function. See the table below for a description of the bond keys. Table 10-1 Bond keys Keys Description ]Oj ]Û ]Ô ]Ñ ]Î ]Ë ]È ]Å ]Â ]¾ ]° Clears bond memory. Calculates accrued interest only. Yield% to maturity or yield% to call date for given price. Price per 100.00 face value for a given yield. Coupon rate stored as an annual %. Call value. Default is set for a call price per 100.00 face value. A bond at maturity has a call value of 100% of its face value. Date format. Toggle between day-month-year (dd.mmyyyy) or month-day-year (mm.ddyyyy). Day count calendar. Toggle between Actual (365-day calendar) or 360 (30-day month/360-day year calendar). Bond coupon (payment). Toggle between semiannual and annual payment schedules. Settlement date. Displays the current settlement date. Maturity date or call date. The call date must coincide with a coupon date. Displays the current maturity. Bond calculations, primarily calculating bond price and yield, are performed by two keys, ]Ñ and ]Ô. Bonds 105 When entering data for bond calculations, results are calculated based on data entered into specific memory registers. When pressed, the keys used for these operations: • • • store data. enter data for variables used during calculations (input only). calculate unknown variables based on stored data. Most of the other keys used in bond calculations allow you to enter data for a variable, but you cannot solve for that variable. The exception is the ]Û key. This key permits you to return results for accumulated interest, but you cannot enter data into this key. Before you perform a bond calculation, be sure to verify the date format is set appropriately for your problem. The default setting is mm.ddyyyy, but it can be set for dd.mmyyyy. For more information about entering dates and date formats, see chapter 9, Calendar Formats and Date Calculations. The range of acceptable dates is October 15, 1582 to December 31, 9999. Verify that bond day counts (360/365) and annual or semiannual coupon payment schedules are appropriate for your problem prior to inputting your data. Example 1 What price should you pay on April 28, 2010 for a 6.75% U.S. Treasury bond maturing on June 4, 2020, if you want a yield of 4.75%? Assume the bond is calculated on a semiannual coupon payment on an actual/actual basis. If D.MY is displayed, press ]È before beginning. See Table . Table 10-2 Bond calculation example Keys ]Oj ]Â Y7GgG:J: ]¾ Display BOND CLR Description Clears bond memory. (message flashes, then disappears) 0.00 Selects semiannual coupon payment, as required by the example. Note the annunciator in the display. 4-28-2010 3 Inputs April 28, 2010 for the settlement date (mm.ddyyyy format). Note: the 3 in the far right of the display indicates the day of the week. This number indicates the day of the week corresponding to that date. Monday is 1, and Sunday is 7. April 4, 2010 is a Wednesday. 106 Bonds Table 10-2 Bond calculation example Keys S7:YG:G: ]° S7jV]Î J::]Ë Display 6-4-2020 4 6.75 100.00 Description Inputs June 4, 2020 for the maturity date. Inputs 6.75% for the value for CPN%. Inputs call value. Optional, as default is 100. Note: if Call requires another value, key in the number followed by ]Ë. Y7jV]Ô ]Ñ 1]Û 4 4.75 115.89 2.69 118.58 Inputs 4.75% for Yield%. Calculates the price. Displays the current value for accrued interest. Returns the result for total price (value of price + value of accrued interest). The net price you should pay for the bond is 118.58. Example 2 A bond has a call provision at 104 and a coupon rate of 5.5%. If the bond matures on October 15, 2020 and is presently selling at 101, what is the yield-to-call on April 15, 2012? Assume the bond is calculated on a semiannual coupon payment on an actual/actual basis. Table 10-3 Keys ]Oj V7V]Î J:Y]Ë J:J]Ñ Display BOND CLR Description Clears bond memory. (message flashes, then disappears) 5.50 Inputs coupon rate as an annual%. 104.00 Inputs call value. 101.00 Inputs price. Bonds 107 Table 10-3 Keys Display J:7JVG:G: ]° Y7JVG:JG ]¾ ]Ô 10-15-2020-4 4-15-2012-7 5.72 Description Inputs October 15, 2020 for the maturity date. Inputs April 15, 2012 for the settlement date. Calculates yield as a %. Continuing with the same bond problem, assume the bond will not be called. What is the expected yield to maturity? Table 10-4 Keys Display Description J::]Ë 100.00 Inputs new call value. Since the bond will not be called, the bond at maturity has a call value of 100% of its face value. ]Ô 5.35 Calculates new yield%. Resetting the bond keys To reset the Bond keys to their default values, press ]Oj. The message, BOND CLR flashes briefly on the screen to indicate the bond registers have been reset. To return to the default calculator screen, press 108 Bonds M. 11 Break-even The break-even function allows you to study problems involving a profit, when a quantity of items, with a cost to manufacture and a fixed price to develop and market, is sold at a given price. On the 10bII+, break-even calculations are performed using the functions printed in blue on the keyboard located under the blue bracket titled, BREAKEVEN. Break-even calculations are based on data entered into these keys, which are listed in the table below: Table 11-1 Break-even keys Key Description ]OY ]¬ ]© ]¦ ]£ ]~ Clears break-even memory. Stores the quantity of units required for a given profit or calculates it. Stores the sales price per unit or calculates it. Stores variable cost per unit for manufacturing or calculates it. Stores the fixed cost to develop and market or calculates it. Stores the expected profit or calculates it. The Break-even Keys When entering data for break-even calculations, results are calculated based on data entered into specific memory registers. When pressed, the keys used for these operations: • • • store data. enter known data for variables used during calculations. calculate unknown variables based on stored data. Break-even 109 Example 1 The sale price of an item is 300.00, the cost is 250.00, and the fixed cost is 150,000.00. How many units would have to be sold to make a profit of 10,000.00? Table 11-2 Break-even example Keys ]OY JV::::]£ GV:]¦ D::]© J::::]~ ]¬ 110 Break-even Display BK EV CLR Description Clears break-even memory. (message flashes, then disappears) 150,000.00 Inputs fixed cost. 250.00 Inputs variable cost per unit. 300.00 Inputs price. 10,000.00 Inputs profit. 3,200.00 Calculates the current value for the unknown item, UNITS. Example 2 What is the estimated maximum fixed cost you can afford to manufacture 10,000 water filters, if your desired selling price is 45.00? Assume the cost per unit is 23.00. Since you want to calculate the maximum fixed cost, your profit for the purpose of the example will be 0.00. Table 11-3 Calculating the projected maximum fixed cost Keys ]OY J::::]¬ YV]© GD]¦ :]~ ]£ Display BK EV CLR Description Clears break-even memory. (message flashes, then disappears) 10,000.00 Inputs the projected number of units. 45.00 Inputs the projected selling price. 23.00 Inputs the variable cost per unit. 0.00 Inputs the profit, in this case, 0. 220,000.00 Calculates the maximum projected fixed cost to develop and market the water filter. Break-even 111 Resetting the Break-even keys To reset the break-even keys to their default values, press ]OY. A brief message flashes on the screen to indicate the break-even registers have been reset. To return to the default calculator screen, press 112 Break-even M. 12 Statistical Calculations The 10bII+ allows you to enter data for one- and two-variable statistics easily. Once data is entered, you can use the statistical functions to calculate the following: • Mean and standard deviation • Regression statistics or a best fit • Estimation and forecasting • Weighted mean • Summation statistics: n, Σx, Σx2, Σ y, Σy2, and Σxy. Table 12-1 Statistics keys Keys Description \t x-value ¡ x-value \¢ x-valueÆ y-value ¡ x-value Æ y-value \¢ v¡ \k\« \T\« \h\« \e\« \Z\« \W\« ]L Clear statistics memory. Enter one-variable statistical data. Delete one-variable statistical data. Enter two-variable statistical data. Delete two-variable statistical data. Opens editor for reviewing or editing statistical data. Means of x and y. Mean of x weighted by y. Also calculates b coefficient. Sample standard deviations of x and y. Population standard deviations of x and y. Estimation of x. Also calculates r correlation coefficient. Estimation of y. Also calculates slope and m coefficient. Permits selection of six regression models or a best fit. Default is linear. Statistical Calculations 113 Clearing Statistical Data Clear the statistical data before entering new data. If you don't clear the statistical data, new information stored will be added to the current calculations. To clear all statistical data, press \t. The message STAT CLR flashes briefly and the display is cleared. The regression model is also reset to its default setting, LINEAR. Entering Statistical Data The 10bII+ uses a combination of list-based and register-based statistics when storing statistical data. List-based statistics store every value and permit you to review and edit entered data. Register-based statistics accumulate information, but you cannot easily edit or review this information. On the 10bII+, there is always space reserved for up to 15 data points. In addition, up to 30 additional data points may be stored in memory shared with the cash flow memory. See Figure 1. Figure 1 As illustrated in Figure 1, if no more than 15 cash flows are stored in the cash flow memory, you may store up to 45 data points for statistical usage. If more than 15 cash flows are stored in the cash flow memory, the total memory available for storing statistical data is reduced. For example, in Figure 2, there are 25 cash flows stored, and the amount of available shared memory has therefore decreased by 10 slots. Figure 2 If data storage in the calculator memory resembles Figure 2, and you have a statistical calculation requiring more than 35 data points, clearing unneeded cash flow information will free up more space for information. If there are more data points than available memory, the 10bII+ automatically switches to register-based statistics to allow continued work. When available memory is reached, the FULL annunciator indicates there is not enough space to continue saving data. See Figure 3. 114 Statistical Calculations Figure 3 When the calculator switches to register-based mode, some key points to consider: • You may enter an unlimited number of data points. • The statistics editor, accessed with • While use of • The only regression mode available is a linear regression. v¡, is not available. \¢ is allowed, viewing previously entered data is not possible. One-Variable Statistics To enter x-data for one-variable statistics complete the following steps: 1. Clear the statistical registers by pressing 2. Enter the first value and press accumulated. \t. ¡. The HP 10bII+ displays n, the number of items 3. Continue accumulating values by entering the numbers and pressing is increased with each entry. ¡. The n-value Two-Variable Statistics and Weighted Mean To enter x,y pairs of statistical data complete these steps: 1. Clear the statistical registers by pressing \t. Æ. The HP 10bII+ displays the x-value. Enter the corresponding y-value and press ¡. The HP 10bII+ displays n, the number 2. Enter the first x-value and press 3. of pairs of items accumulated. 4. Continue entering x,y pairs. The n-value is increased with each entry. To enter data for calculating the weighted mean, enter each data value as x, and its corresponding weight as y in the statistics memory. Press \T to calculate the weighted mean. Statistical Calculations 115 Viewing and Editing Statistical Data 1. v¡ Press to open the editor. The number of items accumulated, n, is displayed, along with the current x-or y-value. The STAT annunciator appears, and the X or Y identifies the displayed value. 1 2. Press to move up through the current statistical data. When you pass the maximum of the data, an empty statistical pair displays before wrapping back to x1, provided there is enough memory for more data. 3. Press A to move down through the current statistical data. At x , the display wraps 0 back to the maximum y-value. ¡ to return to x . To jump to a specific data pair, type the whole number which represents the pair’s n-value and press ¡. The 4. At any time with the editor open, press 1 editor will jump to that data pair, unless your entered number is higher than your maximum data pair, in which case it will jump to the highest x-value. If you type in an invalid number, such as a negative number, or a non-whole number, the editor remains in its current position. 5. To delete the currently displayed statistical data pair, press with the x- and y-values equal to zero, press a. To add a new pair P. 6. To replace the currently displayed value, simply type in the new number and press Æ. 7. To clear the currently displayed x-or y-value without removing the entire pair, press to set the value to 0. 8. Press | M to exit the editor. Example 1 A tropical beach resort has been having some very hot weather lately. A manager at the beach resort has noticed an increase in the number of cold drinks sold during hot days and wants to be able to predict how many employees are needed to sell drinks tomorrow. Each employee can sell 200 drinks a day at most. Table 12-2 Data 116 Statistical Calculations Past 3 Days Temperature (Celsius) Cold Drinks Sold 32 415 35 515 38 725 At what temperature would the manager predict to sell 800 drinks? How many employees will be needed for tomorrow's predicted temperature of 43oC? Table 12-3 Example entering statistical data, opening the editor, and predicting Keys \t DGÆYJV¡ DVÆVJV¡ DgÆjGV¡ v¡ 11111 M ]LY Display STAT CLR Description Clears the statistics memory. (message flashes briefly, then disappears) 1.00 Enters first ordered pair. 2.00 Enters the second ordered pair. 3.00 Enters the third ordered pair. 1 32.00 Open the editor. Displays X annunciator. 3 725.00 Scroll and verify the data points, starting with the x-value of the first pair. The y-value of the third pair is displayed. Exit the editor. 0.00 Set the regression model to power. 4–POWER flashes briefly after Y is pressed, then disappears. g::\Z \«\5d YD\W\5G aG::4 39.49 Predict the temperature. .988080878 Display the correlation coefficient. 1,053.49 Predict the number of drinks sold tomorrow. 5.27 Manager should have at least 6 employees at work tomorrow to cover the expected load. Continuing with this example, modify this data by adding more points: two additional days of sales and their corresponding temperatures. The first day’s temperature of 43oC resulted in the sale of 1,023 cold drinks. The next day’s temperature at 37oC resulted in the sale of 685 drinks. Statistical Calculations 117 Table 12-4 Adding more data Keys YDÆJ:GD¡ DjÆSgV¡ Display Description 4.00 Enters fourth ordered pair. 5.00 Enters fifth ordered pair. After modifying the data, predict the next day’s activity at a record 45oC. Table 12-5 A new prediction Keys YV\W ]L: YV\W 118 Statistical Calculations Display Description 1,204.67 Predicts the drinks sold at 45oC. But is this the best fit? 0.00 Sets regression mode to 0-BEST FIT. 1,128.12 All regressions are calculated and LINEAR is selected as being a better fit than POWER. The result, 1128, is well within the limit of six employees. Summary of Statistical Calculations The STAT annunciator indicates that a statistical calculation was performed. Some functions return two values. In this instance, the X annunciator is displayed along with STAT. Press \« to see the second value. In this case, the X annunciator changes to a Y, indicating the second value is being displayed. Table 12-6 Statistical calculations that return two values Keys Description \«Displays: \k \h Arithmetic mean (average) of the x-values. Mean (average) of the y-values if you entered y-data. Sample standard deviation of the x-values. Sample standard deviation of the yvalues if you entered y-data. \e NOTE: The sample standard deviation assumes that the data is a sampling of a larger, complete set of data. The population standard deviation assumes that the data constitutes the entire population. NOTE: The sample standard deviation assumes that the data is a sampling of a larger, complete set of data. The population standard deviation assumes that the data constitutes the entire population. Population standard deviation of the x-values. Population standard deviation of the y-values if you entered y-data. NOTE: The sample standard deviation NOTE: The sample standard assumes that the data is a sampling of a larger, complete set of data. The population deviation assumes that the data is a sampling of a larger, complete set of standard deviation assumes that the data data. The population standard constitutes the entire population. deviation assumes that the data constitutes the entire population. \Z Estimate of x for a given value of y. \W \T Estimate of y for a given value of x. Coefficient m of the current regression. Mean of the x-values weighted by the yvalues. Coefficient b of the current regression. y-value x-value Correlation coefficient. NOTE: The correlation coefficient is a number in the range -1 through +1 that measures how closely the data fits the calculated line. A value of +1 indicates a perfect positive correlation, and -1 indicates a perfect negative correlation. A value close to zero indicates the line is a poor fit. Statistical Calculations 119 Mean, Standard Deviations, and Summation Statistics You can calculate the mean ( x ), sample standard deviation (Sx), and population standard deviation ( σ x), and summation statistics, n, Σ x, and Σ x 2 of x-data. For x,y data, you can also calculate the mean, sample standard deviation, and population standard deviation of the ydata and the summation statistics Σ y, Σ y 2, and Σ xy. Example 2 A yacht captain wants to determine how long it takes to change a sail. She randomly chooses six members of her crew, observes them as they carry out the sail change, and records the numbers of minutes required: 4.5, 4, 2, 3.25, 3.5, 3.75. Calculate the mean and sample standard deviation of the times. Also, calculate the root mean square, using the formula, ∑ x2 ⁄ n . Table 12-7 Example calculating mean, standard deviation, and summation statistics Keys \t Y7V¡ Y¡ G¡ D7GV¡ D7V¡ D7jV¡ \k \h ]l a][ 4\B 120 Statistical Calculations Display STAT CLR Description Clears statistics memory. (message flashes briefly, then disappears) 1.00 Enters first time. 2.00 Enters second time. 3.00 Enters third time. 4.00 Enters fourth time. 5.00 Enters fifth time. 6.00 Enters sixth time 3.50 Calculates the mean. 0.85 Calculates the sample standard deviation. 77.13 Displays 6.00 Displays n. 3.59 Calculates the root mean square. Σx2 . The standard deviations calculated by \h and \h\« are the sample standard deviations. They assume that the data is a sampling of a larger, complete set of data. If the data constitutes the entire population, the true population standard deviations can be calculated by pressing \e and \e\«. Example 3 The coach has four new players on the team with heights of 193, 182, 177, and 185 centimeters and weights of 90, 81, 83, and 77 kilograms. Find the mean and population standard deviation of both their heights and weights, then sum the y-data. Table 12-8 Example 3 Keys \t JdDÆd:¡ JgGÆgJ¡ JjjÆgD¡ JgVÆjj¡ \k \« \e \« ]U Display STAT CLR Description Clears statistics memory. (message flashes briefly, then disappears) 1.00 Enters height and weight of player 1. 2.00 Enters height and weight of player 2. 3.00 Enters height and weight of player 3. 4.00 Enters height and weight of player 4. 184.25 Calculates mean of heights (x). 82.75 Displays mean of weights (y). 5.80 Calculates population standard deviation for heights (x). 4.71 Displays population standard deviation for weights (y). 331.00 Displays the total of the y -values. Linear Regression, Estimation, and Regression Modes Linear regression is a statistical method for estimation and forecasting. It is used to find a straight line that best fits a set of x,y data. There must be at least two different x,y pairs. The straight line provides a relationship between the x- and y-variables: y = mx + b, where m is the slope and b is the y-intercept. Statistical Calculations 121 Linear Regression. Calculate r (the correlation coefficient), m, b, and as follows: 1. Clear the statistical registers by pressing \t. Æ. The x-value is displayed. Enter the corresponding y-value and press ¡. The HP 10bII+ displays n, the number 2. Enter the first x-value and press 3. of pairs of items accumulated. 4. Continue entering x,y pairs. The n-value is increased with each entry. \Z\«. To display m, the slope, press \W\«. To display b (the y-intercept), press \T\«. 5. To display r, the correlation coefficient, press 6. 7. Linear Estimation. The straight line calculated by linear regression can be used to estimate a y-value for a given x-value, or vice versa: 1. Enter the x,y data. 2. Enter the known x-value or y-value. • • \Z. To estimate y for the given x, enter the x-value, then press \W. To estimate x for the given y, enter the y-value, then press Example: 4 Ali’s Azaleas advertises on a local radio station. For the past six weeks, the manager has kept records of the number of minutes of advertising that were purchased, and the sales for that week. Table 12-9 Recording the number of minutes of the advertisements and sales Week Minutes of Advertising (x-values) Sales (y-values) 1 2 1,400 2 1 920 3 3 1,100 4 5 2,265 5 5 2,890 6 4 2,200 What is the y-intercept, the slope, and the correlation coefficient? 122 Statistical Calculations Figure 4 Diagram on forecasting sales and minutes for advertising Table 12-10 Example for forecasting Keys \t GÆJY::¡ JÆdG:¡ DÆJJ::¡ VÆGGSV¡ VÆGgd:¡ YÆGG::¡ \T\« \W\« Display STAT CLR Description Clears statistics memory. (message flashes briefly, then disappears) 1.00 Enters minutes and sales for consecutive weeks. 2.00 3.00 4.00 5.00 6.00 376.25 Calculates y-intercept. 425.88 Displays slope. Statistical Calculations 123 Table 12-10 Example for forecasting Keys \Z\« Display 0.90 Description Calculates correlation coefficient. Estimate what the level of sales would be if the business purchased 7 or 8 minutes of advertising. Table 12-11 Estimating the level of sales Keys j\W g\W Display Description 3,357.38 Estimates sales if 7 minutes of advertising were purchased. 3,783.25 Estimates sales if 8 minutes were purchased. How many minutes of advertising should Ali’s buy to attain sales of 3,000? Table 12-12 Estimating the minutes of advertising for 3,000 sales Keys D:::\Z Display 6.16 Description Estimates minutes of advertising required for 3,000 in sales. Weighted Mean The following procedure calculates the weighted mean of data points x1, x2, …, xn occurring with weights y1, y2, …, yn. 1. 2. Æ and ¡ to enter x,y pairs. The y-values are the weights of the x-values. Press \T. Use Example 5 A survey of 266 one-bedroom rental apartments reveals that 54 of them rent for 500 per month, 32 for 505, 88 for 510, and 92 for 516. What is the average monthly rent? 124 Statistical Calculations Table 12-13 Calculating the average monthly rent Keys Display \t STAT CLR Description Clears statistics memory. (message flashes briefly, then disappears) V::ÆVY¡ V:VÆDG¡ VJ:Ægg¡ VJSÆdG¡ \T 1.00 Enters first rent and its weight. 2.00 Enters second rent and its weight. 3.00 Enters third rent and its weight. 4.00 Enters fourth rent and its weight. 509.44 Calculates the weighted mean. Regression Models and Variables The 10bII+ has six built-in regression models, as well as the ability to calculate which model best fits the current data. These six regression modes are listed in the table below. Table 12-14 Regression models Number and Mode Description 0-Best Fit Automatically selects fit 1-Linear m*x+b 2-Logarithm m*ln(x)+b 3-Exponential b*e(m*x) 4-Power b*xm 5-Exponent b*mx 6-Inverse m/x+b ]L to open the regression selection application. The initially displayed option is the current setting. Press 1 or A to scroll through the available regressions. With the desired model displayed, press Æ to select it. To exit without changing the current model, press M. As an alternative to scrolling, and if you know the number of the desired model, press ]L followed by the desired number of the fit option. Press Statistical Calculations 125 If BEST FIT is selected, the 10bII+ calculates the best fit when \Z, \W, or \T is pressed. When selected, BEST FIT flashes briefly, followed by the chosen fit. The selected regression will remain set until a new one is selected, or the statistics memory is cleared. When the statistics memory is cleared using \t, the current regression model is set back to LINEAR. Probability Calculations In many probability calculations, specific methods of counting possible outcomes are required as part of a process to determine the likelihood of certain results. The three main operations that allow this are: • ! • nPr factorial permutations • nCr combinations Factorial Factorial (!) is a mathematical operator that instructs you to multiply the current number by all previous whole numbers. Writing out so many numbers can be cumbersome, so mathematicians use ! to signify this process. For example: 5! is equivalent to 5 x 4 x 3 x 2 x 1 = 120. On the 10bII+, the input value n must be within -253 < n < 253. The gamma function is used to calculate n! for non-integer or negative values. Permutations The nPr function calculates the number of different arrangements, or permutations, of n items taken r at a time. No item can occur more than once in a set of r items, and different orders of the same r items are counted separately. This is calculated using the formula: n! PERMUTATIONS = ----------------( n – r )! 126 Statistical Calculations Example Using five books labeled A, B, C, D, and E, how many different ways can three books be placed on a shelf? Table 12-15 Example calculating permutations Keys Display Description V]<D4 or, using Æ: VÆD]< 60.00 Calculates permutations of n items taken r at a time. 60.00 Combinations The nCr function calculates the number of different sets, or combinations, of n items taken r at a time. No item can occur more than once in the set of r items, and different orders of the same r items are not counted separately. This is calculated using the formula: n! COMBINATIONS = --------------------( n – r )!r! Example Using five colored balls, how many different color combinations of three colors can be chosen? Table 12-16 Example calculating combinations Keys Display Description V]9D4 or, using Æ: VÆD]9 10.00 Calculates combinations of n items taken r at a time. 10.00 . Random Number and Seed The 10bII+ includes a random number generator function that generates a pseudo-random number in the range 0 < x < 1. To store a seed value, type a positive number and press \w]6. Storing a value of 0 will select a random number and store it as the seed value. Statistical Calculations 127 Example Store a seed value of 42; set the number display to 9. Then generate three random numbers. Table 12-17 Example storing a seed value and generating random numbers Keys Display Description YG\w]6 \5d ]6 ]6 ]6 \5G 42.00 Stores 42 as the random number generator seed. 42.000000000 Set display precision. .199873749 Generate first random number. .863046890 Generate second random number. .504024868 Generate third random number. .50 Reset display to default setting. Advanced Probability Distributions The 10bII+ allows easy calculation of the Z and Student's T probability distribution values. In addition, it allows inverse calculations of both functions. The values are calculated using the lower tail probability. This lower tail probability corresponds to the area under the curve to the left of the input. If you need a value other than a lower tail, such as a two-sided value, please see the conversion instructions at the end of this chapter. Table 12-18 Advanced probability keys Keys Description ]F ]oF ]I Calculates a cumulative normal probability given a Z-value. Calculates a Z-value given a cumulative normal probability. Calculates the cumulative Student’s T probability given degrees of freedom and a T-value. ]oI Calculates a T-value given degrees of freedom and the cumulative Student’s T probability. These distribution functions replace the statistical tables found in the back of textbooks. Unlike the textbook, the calculator can calculate any value, not just a limited selection found in the table. 128 Statistical Calculations Normal Lower Tail Probability To calculate the area under the curve to the left of z (the lower tail probability), enter the zvalue and press ]F . This function calculates the probability that a standard normal random variable, Z, is less than z. Figure 5 Example The variable Z is a standard normal random variable. What is the probability that Z is less than -1.7.? Table 12-19 Probability example Keys Display \5S J7jy]F Figure 6 Description .000000 Set display precision. .044565 Calculate the probability. Figure 7 Statistical Calculations 129 Inverse of Normal Lower Tail Probability Figure 8 What is the z-value corresponding to a lower tail cumulative probability of .025? Table 12-20 Example calculating z-value (lower tail) Keys Display 7:GV]oF Figure 9 130 Statistical Calculations -1.959964 Description Calculate the corresponding zvalue. Figure 10 Student's T Probability Lower Tail Figure 11 To calculate the area under the Student's T Distribution curve, first enter the degrees of freedom, followed by the t-value. It is a two-number function, so it may be entered as either an in-line function, or by using Æ. Example: What is the lower tail probability associated with a Student’s T distribution with 8 degrees of freedom (df1) with a t-value of -1.86? Table 12-21 Example of Student’s t (lower tail) Keys Display g]IJ7gSy4 or, using Æ: gÆJ7gSy]I Figure 12 .0499653 Description Calculates the lower tail probability. Returns the same results. Figure 13 Statistical Calculations 131 Inverse of Student’s t Probability Lower Tail If you know the lower tail probability, P, and you want to calculate t, enter the degrees of freedom (df1), followed by Æ, then P. Press ]oIto calculate t. Figure 14 Example A hypothesis test requires a critical t-value from the Student’s T distribution with 26 degrees of freedom. Find the t-value for a lower tail probability of .05. Table 12-22 Example calculating the t-value (lower tail) Keys Display GS]oI7:V4 -1.705618 Description Enter degrees of freedom and the probability, and calculates the lower tail t- value. Æ: GSÆ7:V]oI or, using Figure 15 132 Statistical Calculations Returns the same results. Figure 16 Conversions from Lower Tail The distribution functions on the 10bII+ return values for the lower tail cumulative probability. The lower tail probability corresponds to the area under the curve to the left of the given value. Sometimes you will want to work with areas other than the lower tail. It is easy to convert from lower tail to another area as long as you keep in mind that the total area under the curve is equal to 1, and the Normal and the Student’s T distributions are symmetrical. In other words, the portion of the curve to the left of zero is a mirror image of the portion of the curve to the right of zero. Example 1 The random variable Z is a standard normal random variable. What is the probability that z is greater than -1.7? Figure 17 The probability that z is greater than -1.7 is the area of the curve to the right of -1.7. You can calculate the area to the left of -1.7 and subtract it from 1 (total area of the curve). Table 12-23 Example converting from lower tail Keys Display Description J7jy]F .044565 Calculate the lower tail area. Since the area is -1.7, change the sign. y1J4 .955435 Subtracts the lower tail from 1. Statistical Calculations 133 Example 2 The variable Z is a standard normal random variable. What is the probability that z is greater than 1.2 or less than -1.2? Figure 18 The desired area is to the right of 1.2 and to the left of -1.2. Since normal distributions are symmetrical, and the areas are the same, you can calculate the lower tail area and simply multiply by 2. Table 12-24 Example converting from lower tail Keys Display Description J7Gy]F PG4 .115070 Calculate the lower tail area and store the value. .230139 Calculates the result. 134 Statistical Calculations Example 3 The variable Z is a standard normal random variable. Find z so that the probability that Z is less than z and greater than -z is equal to 0.95. Figure 19 The given area is 0.95. The area not included is 1-0.95/2 = 0.025. Since the normal distribution is symmetrical, half of the desired area is in the lower tail, .05/2=.025. The desired area corresponds to a lower tail probability of .025. Table 12-25 Example converting from lower tail (the inner area) Keys 7:GV]oF Display -1.959964 Description Returns desired value of z. Statistical Calculations 135 136 Statistical Calculations 13 Additional Examples Business Applications Setting a Sales Price One method for setting the per unit sales price is to determine the cost of production per unit, and then multiply by the desired rate of return. For this method to be accurate, you must identify all costs associated with the product. The following equation calculates unit price based on total cost and rate of return: PRICE = TOTAL COST ÷ NUMBER OF UNITS × (1 + (%RTN ÷ 100)) Example To produce 2,000 units, your cost is 40,000. You want a 20% rate of return. What price should you charge per unit? Table 13-1 Calculating the price charged per unit Keys Y:::::a G:::P \qJ1\q G:aJ::4 Display Description 40,000.00 Enters cost. 20.00 Calculates unit cost. 24.00 Calculates the unit sales price. Forecasting Based on History One method of forecasting sales, manufacturing rates, or expenses is reviewing historical trends. Once you have historical data, the data are fit to a curve that has time on the x-axis and quantity on the y-axis. Example Given the following sales data, what are the sales estimates for years six and seven? Table 13-2 Sales data Year Sales 1 10,000 2 11,210 3 13,060 4 16,075 5 20,590 Additional Examples 137 Table 13-3 Calculating the sales estimates for years six and seven Keys Display \t JÆJ::::¡ GÆJJGJ:¡ DÆJD:S:¡ YÆJS:jV¡ VÆG:Vd:¡ S\W j\W Description 0.00 Clears statistics registers. 1.00 Enters first year and sales for that year. 2.00 Enters second year’s data. 3.00 Continues data entry. 4.00 5.00 22,000.50 Estimates sales for year six. 24,605.00 Estimates sales for year seven. Cost of Not Taking a Cash Discount A cash discount gives a buyer a reduction in price if the payment is made within a specified time period. For example, “2/10, NET/30” means that the buyer can deduct 2 percent if payment is made within 10 days. If payment is not made within 10 days, the full amount must be paid by the 30th day. You can use the equation shown below to calculate the cost of failing to take the cash discount. The cost is calculated as an annual interest rate charged for delaying payment. DISC% × 360 × 100 COST% = ------------------------------------------------------------------------------------------------------------------------------------------( ( 100 – DISC% ) × ( TOTAL DAYS – DISC DAYS ) ) DISC% is the discount percent if the payment is made early. TOTAL DAYS is the total number of days until the bill must be paid. DISC DAYS is the number of days for which the discount is available. Example You receive a bill with the credit terms 2/10, NET/30. What is the cost of not taking the cash discount? 138 Additional Examples Table 13-4 Calculating the cost without the cash discount Keys Display GPDS:PJ ::a \q\qJ: :AG\n P\qD:A J:4 72,000.00 Description Calculates numerator in equation. 98.00 Parentheses force order of calculation. 36.73 Calculates, as an annual percentage rate, cost of not taking discount. Loans and Mortgages Simple Annual Interest Example Your good friend needs a loan to start his latest enterprise and has asked you to lend him 450 for 60 days. You lend him the money at 10% simple annual interest, to be calculated on a 365-day basis. How much interest will he owe you in 60 days, and what is the total amount owed? This equation is used for calculating simple annual interest using a 365 day year: LOAN AMOUNT × INTEREST% × TERM OF LOAN ( IN DAYS )INTEREST = ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------365 Table 13-5 Calculating the total amount owed Keys Display YV:sPJ:§ PS:aDSV4 1p4 Description 0.10 Stores interest. 7.40 Calculates interest owed. 457.40 Calculates the total amount owed. Continuous Compounding The equation for calculating an effective rate for continuous compounding is: EFF% = ( e ( NOM% ÷ 100 ) – 1 ) × 100 Additional Examples 139 To solve a continuous compounding problem complete these steps: 1. Compute the annual effective rate using the above equation. 2. Either use this effective rate in your calculations with an annual period (P/YR = 1) or convert this rate so that it applies to your payment period. In the following example, P/YR = 12 so you have to calculate a new NOM% using the interest rate conversion application with P/YR equal to 12. Example You currently have 4,572.80 in an account at Dream World Investments that earns 18% annual interest compounded continuously. At the end of each month, you deposit 250.00 in the account. What will the balance be after 15 years? Table 13-6 Calculating the annual nominal rate Keys Display Jg§ \K AJPJ::4 \Ð JG\Í \Ó Set to End Mode. Press Description 0.18 Divides nominal rate by 100. 1.20 Raises e to 0.18 power. 19.72 Calculates annual effective rate. 19.72 Stores effective rate. 12.00 Sets payments per year. 18.14 Calculates the annual nominal rate for a monthly payment period. \¯ if BEGIN annunciator is displayed. Table 13-7 Calculating the balance amount after 15 years Keys Display Description JV\Ú GV:yÌ YVjG7gy Ï É 180.00 Stores number of months. -250.00 Stores regular payment. 140 Additional Examples -4,572.80 297,640.27 Stores current balance as a negative value (like an initial investment). Calculates the account balance after 15 years of payments with 18% interest compounded continuously. Yield of a Discounted (or Premium) Mortgage The annual yield of a mortgage bought at a discount or premium can be calculated given the original mortgage amount (PV), interest rate (I/YR), periodic payment (PMT), balloon payment amount (FV), and the price paid for the mortgage (new PV). Remember the cash flow sign convention: money paid out is negative; money received is positive. Example An investor wishes to purchase a 100,000 mortgage taken out at 9% for 20 years. Since the mortgage was issued, 42 monthly payments have been made. The loan is to be paid in full (a balloon payment) at the end of its fifth year. What is the yield to the purchaser if the price of the mortgage is 79,000? Step 1 Calculate PMT. Make sure FV = 0. Set to End Mode. Press \¯ if BEGIN annunciator is displayed. Table 13-8 Calculating the monthly payment Keys JG\Í dÒ G:\Ú J:::::y Ï :É Ì Display Description 12.00 Sets payments per year. 9.00 Stores interest rate. 240.00 Stores number of months. -100,000.00 Stores original amount of mortgage. 0.00 899.73 Enters amount left to pay after 20 years. Calculates the regular payment. Step 2 Enter the new value for N indicating when the balloon occurs, then find FV, the amount of the balloon. É Table 13-9 Calculating the balloon payment Keys Display Description \}Ì 899.73 Rounds payment to two decimal places for accuracy. Additional Examples 141 Table 13-9 Calculating the balloon payment Keys Display Description V\Ú É 60.00 Stores number of payments until balloon. 88,706.74 Calculates the balloon payment (add to final payment). Step 3 Enter actual, current values for N and PV; then find the new I/YR for the discounted mortgage with balloon. Table 13-10 Keys Display Description vÙAYGÙ jd:::yÏ Ò 18.00 Stores remaining number of payments. -79,000.00 20.72 Stores price of mortgage. Calculates the return on this discounted mortgage. Annual Percentage Rate for a Loan With Fees The Annual Percentage Rate, APR, incorporates fees usually charged when a mortgage is issued, which effectively raises the interest rate. The actual amount received by the borrower (the PV) is reduced, while the periodic payments remain the same. The APR can be calculated given the term of the mortgage (N periods), the annual interest rate (I/PR), the mortgage amount (new PV), and the amount of the fee. Remember the cash flow sign convention: money paid out is negative; money received is positive. Example: APR for a Loan With Fees A borrower is charged two points for the issuance of a mortgage. (One point is equal to 1% of the mortgage amount.) If the mortgage amount is 160,000 for 30 years and the annual interest rate is 8.5% with monthly payments, what APR is the borrower paying? Set to End Mode. Press \¯ if BEGIN annunciator is displayed. Table 13-11 Calculating the annual percentage rate considering fees Keys JG\Í g7VÒ 142 Additional Examples Display Description 12.00 Sets payments per year. 8.50 Stores interest rate. Table 13-11 Calculating the annual percentage rate considering fees Keys Display Description D:\Ú JS::::Ï :É Ì vÏ -AG§Ï Ò 360.00 Stores length of mortgage. 160,000.00 Stores original amount of mortgage. 0.00 The loan will be completely paid off in 30 years. -1,230.26 Calculates payment. 160,000.00 Recalls loan amount. 156,800 8.72 Subtracts points. Calculates APR, considering fees. Example: Interest-Only Loan With Fee A 1,000,000, 10-year, 12% (annual interest) interest-only loan has an origination fee of three points. What is the yield to the lender? Assume that monthly payments of interest are made. Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 13-12 Calculating the annual percentage rate Keys JG\Í JGÒ J:\Ú J:::::: Ï yÉ Ì vÏ AD§Ï Display Description 12.00 Sets payments per year. 12.00 Stores interest rate. 120.00 Stores length of mortgage. 1,000,000.00 Stores original amount of mortgage. -1,000,000.00 Enters amount due at end of term. Payments are interest only so entire loan amount is due. -10,000.00 1,000,000.00 970,000.00 Calculates interest-only payments. Recalls loan amount. Subtracts points. Additional Examples 143 Table 13-12 Calculating the annual percentage rate Keys Display Ò 12.53 Description Calculates APR. Loan With a Partial (Odd) First Period TVM calculations apply to financial transactions where each payment period is the same length. However, situations exist where the first payment period is not the same length as the remaining periods. This first period is sometimes called an odd or partial first period. If interest is applied to an odd first period, it is usually calculated as simple interest. So using the HP 10bII+ to do a payment calculation with an odd first period is a two step process: 1. Calculate the amount of simple interest that accrues during the fractional first period and add it to the loan amount. This is the new PV. You must be able to calculate the length of the odd first period as a fraction of the whole period. (For example, a 15-day odd first period would be 0.5 periods assuming a whole period to be a 30-day month.) 2. Calculate the payment using the new PV, with N equal to the number of full periods. Use Begin mode if the number of days until the first payment is less than 30; otherwise use End mode. Example A 36-month loan for 4,500 has an annual rate of 15%. If the first monthly payment is made in 46 days, what is the monthly payment amount assuming 30-day months? The odd first period in this example is 16 days. Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 13-13 Calculating the monthly payment amount Keys JG\Í JVÒ aJGP JSaD:P YV::\«§4 1YV::Ï DSÙ 144 Additional Examples Display Description 12.00 Sets payments per year. 15.00 Stores interest rate. 1.25 Calculates periodic interest rate. 0.67 Multiplies by fraction of a period. 30.00 Calculates amount of simple interest owed for odd period. 4,530.00 Adds this simple interest to present value. 36.00 Stores term of loan. Table 13-13 Calculating the monthly payment amount Keys Display :É Ì 0.00 -157.03 Description Enters amount left to pay after 36 payments. Calculates the payment amount. Automobile Loan Example You are buying a new 14,000.00 sedan. Your down payment is 1,500 and you are going to finance the remaining 12,500. The car dealer is offering two choices for financing: • A 3-year loan with an annual interest rate of 3.5%. • A 3-year loan with an annual interest rate of 9.5% and a 1,000.00 rebate. With which choice do you pay less for the car? Set to End mode. Press \¯ if BEGIN annunciator is displayed. Calculate the first option: Table 13-14 Calculating the annual interest rate of 3.5% Keys JG\Í DSÙ JGV::Ï :É D7VÒ Ì PvÙ4 Display Description 12.00 Sets payments per year. 36.00 Stores known values. 12,500.00 Stores loan amount. 0.00 3.50 -366.28 -13,185.94 Stores first interest rate. Calculates payment. Calculates total interest and principal. Calculate the second option: Table 13-15 Calculating the annual interest rate of 9.5% Keys JJV::Ï Display 11,500.00 Description Stores loan amount with rebate. Additional Examples 145 Table 13-15 Calculating the annual interest rate of 9.5% Keys d7VÒ Ì PvÙ4 Display Description 9.50 Stores second interest rate. -368.38 Calculates payment. -13,261.64 Calculates total interest and principal. The first option costs slightly less. Canadian Mortgages In Canadian mortgages, the compounding and payment periods are not the same. Interest is compounded semi-annually while payments are made monthly. To use the TVM application in the HP 10bII+, you need to calculate a Canadian mortgage factor (which is an adjusted interest rate) to store in I/YR. For additional information on interest rate conversions, see Interest Rate Conversions in Ch. 6. Example What is the monthly payment required to fully amortize a 30-year, 130,000 Canadian mortgage if the annual interest rate is 12%? Table 13-16 Calculating the monthly payment for Canadian mortgage Keys Display JG\Ó 12.00 G\Í \Ð JG\Í \Ó JD::::Ï :ÉD:\Ú Ì 2.00 146 Additional Examples Description Stores known nominal percentage and number of compounding periods. 12.36 Calculates annual effective rate. 12.00 Sets payments per year. 11.71 Calculates Canadian mortgage factor (adjusted interest rate). 130,000 Stores other known values for mortgage. 360.00 -1,308.30 Calculates monthly payment for Canadian mortgage. What if … TVM Calculations One of the most valuable aspects of the HP 10bII+’s TVM application is the ease with which it handles the question “what if …” in financial calculations. For example, one of the most popular “what if …” questions is, “What if the interest rate changes to …? How will that affect my payment?” To answer this question, once you have calculated a payment based on one interest rate, all you need to do is enter the new interest rate and recalculate PMT. Some of the examples earlier in this manual have included some brief encounters with “what if …” questions, but a more complete example follows. Example You are about to sign on the dotted line for a 30-year, 735,000 mortgage, on a vacation home. The annual interest rate is 11.2%. Part 1 What will your payments be at the end of the month? Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 13-17 Calculating the monthly payment Keys JG\Í jDV:::Ï JJ7GÒ D:\Ú :É Ì Display 12.00 735,000.00 Description Sets payments per year. Stores known values. 11.20 360.00 0.00 -7,110.88 Calculates payment. Part 2 Your company’s regular payroll is generated every other Friday. The bank agrees to automatically draw payments of 3,555.00 out of each paycheck (approximately half of what a monthly payment would be) and adjust the payment period accordingly (26 compounding periods per year). What would be the new term of the loan? Table 13-18 Calculating the number of years required to pay off the loan Keys DVVVyÌ Display -3,555.00 Description Enters new payment. Additional Examples 147 Table 13-18 Calculating the number of years required to pay off the loan Keys Display Description GS\Í Ù v\Ú 26.00 Sets payments per year for every two weeks. 514.82 Calculates number of biweekly payments. 19.80 Displays years required to pay off the loan. Part 3 What if you had monthly payments as in part 1, but chose a 15-year term? What would your new payment be? What would be the total interest paid on the contract? Table 13-19 Calculating the total interest paid on the contract Keys JG\Í JV\Ú Ì PvÙ1 vÏ4 Display 12.00 180.00 -8,446.53 -1,520,374.70 -785,374.70 Description Sets payments per year. Stores new term. Calculates payment for shorter term. Calculates total paid. Displays the total interest paid on the contract. Savings Saving for College Costs Suppose you start saving now to accommodate a future series of cash outflows. An example of this is saving money for college. To determine how much you need to save each period, you must know when you’ll need the money, how much you’ll need, and at what interest rate you can invest your deposits. Example Your oldest daughter will attend college in 12 years and you are starting a fund for her education. She will need 15,000 at the beginning of each year for four years. The fund earns 9% annual interest, compounded monthly, and you plan to make monthly deposits, starting at the end of the current month. The deposits cease when she begins college. How much do you need to deposit each month? This problem is solved in two steps. First calculate the amount you’ll need when she starts college. Start with an interest rate conversion because of the monthly compounding. 148 Additional Examples Figure 20 Cash flow diagram Set to Begin mode. Press \¯ if BEGIN annunciator is not displayed. Table 13-20 Calculating the annual effective rate Keys Display d\Ó JG\Í \Ð Description 9.00 Stores annual nominal rate. 12.00 Stores number of compounding periods used with this nominal rate. 9.38 Calculates annual effective rate. When compounding occurs only once per year, the effective rate and the nominal rate are the same. Ò Set to Begin mode. Press 9.38 Stores effective rate as annual rate. \¯ if BEGIN annunciator is not displayed. Table 13-21 Calculating the amount required at the start Keys J\Í JV::: Ì YÙ :É Ï Display Description 1.00 Sets 1 payment per year. 15,000.00 Stores annual withdrawal. 4.00 Stores number of withdrawals. 0.00 Stores balance at the end of four years. -52,713.28 Calculates the amount required when your daughter starts college. Additional Examples 149 Then use that PV as the FV on the following cash flow diagram, and calculate the PMT. Figure 21 Cash flow diagram (Calculate PMT) Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 13-22 Calculating the monthly deposit required Keys yÉ :Ï JG\Í JYYÙ dÒ Ì Display 52,713.28 Description Stores amount you need. 0.00 Stores amount you are starting with. 12.00 Sets payments per year. 144.00 9.00 -204.54 Stores number of deposits. Stores interest rate. Calculates monthly deposit required. Gains That Go Untaxed Until Withdrawal You can use the TVM application to calculate the future value of a tax-free or tax-deferred account. (Current tax laws and your income determine whether both interest and principal are tax-free. You can solve for either case.) The purchasing power of that future value depends upon the inflation rate and the duration of the account. Example You are considering opening a tax-deferred account with a dividend rate of 8.175%. If you invest 2,000 at the beginning of each year for 35 years, how much will be in the account at retirement? How much will you have paid into the account? How much interest will you have earned? If your post-retirement tax rate is 15%, what will the after tax future value of the 150 Additional Examples account be? Assume that only the interest is taxed (assume the principal was taxed before deposit). What is the purchasing power of that amount, in today’s dollars, assuming a 4% inflation rate? Set to Begin mode. Press \¯ if BEGIN annunciator is not displayed. Table 13-23 Calculating the purchasing power of the amount Keys J\Í DVÙ g7JjVÒ :Ï G:::yÌ É vÌPvÙ4 1vÉ4 PJV§4 y1vÉ4 É YÒ:ÌÏ Display 1.00 35.00 Description Sets 1 payment per year. Stores number of periods and interest rate. 8.18 0.00 -2,000.00 Stores amount you start with. Stores amount of annual payment. 387,640.45 Calculates amount in account at retirement. -70,000.00 Calculates amount you have paid into account by retirement. 317,640.45 Calculates interest account has earned by retirement. 47,646.07 Calculates taxes at 15% of interest. 339,994.39 Calculates after-tax FV. 339,994.39 Stores after-tax future value in FV. -86,159.84 Calculates the present value purchasing power of after-tax FV, assuming a 4% inflation rate. Value of a Taxable Retirement Account This problem uses the TVM application to calculate the future value of a taxable retirement account that receives regular, annual payments beginning today (Begin mode). The annual tax on the interest is paid out of the account. (Assume the deposits have been taxed already.) Additional Examples 151 Example If you invest 3,000 each year for 35 years, with dividends taxed as ordinary income, how much will you have in the account at retirement? Assume an annual dividend rate of 8.175%, a tax rate of 28%, and that payments begin today. What is the purchasing power of that amount in today’s dollars, assuming 4% inflation? Set to Begin mode. Press \¯ if BEGIN annunciator is not displayed. Table 13-24 Calculating the purchasing power, assuming 4% inflation rate Keys J\Í DVÙ g7JjVAGg §4 Ò :Ï D:::yÌ É YÒ:Ì Ï Display Description 1.00 Sets 1 payment per year. 35.00 Stores number of payment periods until retirement. 5.89 Calculates interest rate diminished by tax rate. 5.89 Stores adjusted interest rate. 0.00 Stores amount you are starting with. -3,000.00 Stores amount of annual payment. 345,505.61 Calculates amount in account at retirement. -87,556.47 Calculates present value purchasing power of FV, assuming a 4% inflation rate. Cash Flow Examples Wrap-Around Mortgages A wrap-around mortgage is a combination of refinancing a mortgage and borrowing against real estate equity. Usually the two unknown quantities in the wrapped mortgage are the new payment and the rate of return to the lender. To arrive at a solution, you need to use both the TVM and the cash flow applications. Example You have 82 monthly payments of 754 left on your 8% mortgage, leaving a remaining balance of 47,510.22. You would like to wrap that mortgage and borrow an additional 35,000 for another investment. You find a lender who is willing to “wrap” an 82,510.22 mortgage at 9.5% for 15 years. What are your new payments and what return is the lender getting on this wrap-around mortgage? 152 Additional Examples The payment calculation is a straightforward TVM payment calculation using the new amount as the PV. Set to End mode. Press \¯ if BEGIN annunciator is displayed. Table 13-25 Calculating the payment Keys Display ]OJ JG\Í gGVJ:7GG Ï d7VÒ :É JV\Ú Ì Description 0.00 Clears TVM registers. 12.00 Sets payments per year. 82,510.22 Stores loan amount on which your new payment is calculated. 9.50 Stores interest rate. 0.00 Stores final balance. 180.00 Stores number of monthly payments you will make. -861.59 Calculates your new payment. Then, to calculate the lender’s return, enter cash flows that represent the complete picture of the wrap-around mortgage from the lender’s point of view: Figure 22 Cash flow diagram (Wrap-around mortgage) When you group the above cash flows, you’ll find that: CF0 = 47,510.22 - 82,510.22 = -35,000 CF1 = 861.59 - 754.00 = 107.59 Additional Examples 153 N1 = 82 CF2 = 861.59 N2 = 180 - 82 = 98 Table 13-26 Calculating the annual return Keys Display DV:::y¤ vÌyAjVY ¤ gG\¥ vÌy¤ Jg:AgG\ ¥ \Á CF0 Description Enters 35,000 for loan amount. -35,000.00 CF1 107.59 n1 82.00 CF2 861.59 n2 Enters net payment for first 82 months. Enters number of times payment occurs. Enters net payment for next 98 months. 98.00 Enters number of times payment occurs. 10.16 Calculates annual return. Net Future Value The net future value can be calculated by using the TVM keys to slide the net present value (NPV) forward on the cash flow diagram. Example: Value of a Fund You have made the following deposits over the past two years into a money market fund earning 8.8%. What is the current balance of the account? Figure 23 Cash flow diagram 154 Additional Examples Appendix A: Batteries and Answers to Common Questions Power and Batteries The calculator is powered by two 3-volt lithium button-cell batteries, CR2032. When changing batteries, use only fresh button-cell batteries. Both batteries must be changed at the same time. Do not use rechargeable batteries. Low Power Annunciator When the low battery-power annunciator ( ) comes on, you should replace the batteries as soon as possible. If the battery annunciator is on and the display dims, you may lose data. The All Clear message is displayed if data is lost due to low power. Installing Batteries Warning! There is a danger of explosion if batteries are incorrectly replaced. Replace only with the same type of battery or with equivalent batteries (as recommended by the manufacturer). Dispose of used batteries according to the manufacturer’s instructions. • The calculator is powered by two 3-volt CR2032 coin batteries. • When changing batteries, use only fresh coin-cell batteries. Do not use rechargeable batteries. • Do not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode, releasing hazardous chemicals. • Do not use new and old batteries together, and do not mix batteries of different types. 1. Have two fresh CR2032 batteries at hand. Only touch the batteries by their edges. Wipe each battery with a lint-free cloth to remove dirt and oil. 2. Make sure the calculator is off. When changing the batteries, change the batteries one at a time to avoid clearing the memory. As a back-up, write down any data that you have stored and might need for later use. 3. Turn the calculator over and pry off the battery cover. Accessing the battery compartment 4. Gently remove one battery. 5. Insert the new battery, making sure that the positive sign (+) battery is facing outward. 6. Gently remove the other battery. Appendix A: Batteries and Answers to Common Questions I 7. Insert the other new battery, making sure that the positive sign (+) battery is facing outward. 8. Replace the battery-compartment lid. 9. Press =. If the calculator does not turn on, follow the procedures below. Determining if the Calculator Requires Service Use these guidelines to determine if the calculator requires service. If these procedures confirm that the calculator is not functioning properly, refer to the Warranty, Environmental, and Contact Information located on the product CD. The calculator won’t turn on: This condition most likely indicates that the batteries have run out. Install new batteries. If the calculator still does not turn on when you press O: 1. Reset the calculator (see below) and, if necessary, 2. Erase the memory (see below). The All Clear message should now be displayed. If this is not the case, the calculator requires service. Resetting the calculator: 1. Turn the calculator over and remove the battery cover. 2. Insert the end of a paper clip into the small, round hole located between the batteries. Insert the clip gently as far as it will go. Hold for one second and then remove the clip. 3. Press =. 4. If the calculator is still not responding, erase the memory (see below) and repeat steps 1 to 3 above one more time. Erasing the calculator’s memory: 1. 2. = key. Press and hold down the Ù and then the É key so all three keys are pressed Press and hold down the simultaneously. 3. Release all three keys. Memory is cleared and All Clear should be displayed. The calculator doesn’t respond to keystrokes: 1. Reset the calculator (see above) and, if necessary, 2. Erase the memory (see above). The All Clear message should now be displayed. If this is not the case, the calculator requires service. II Appendix A: Batteries and Answers to Common Questions The calculator responds to keystrokes, but you suspect that it is malfunctioning: 1. It is likely that you’ve made a mistake in operating the calculator. Try rereading portions of the manual, and check Answers to Common Questions below. 2. Contact the Calculator Support department. The contact information is listed on the product CD. Answers to Common Questions Hewlett-Packard is committed to providing you with ongoing support. For more information on calculators and calculator learning products, visit www.hp.com/calculators. You also may contact HP Customer Support. Contact information and phone numbers are available on the product CD included in the package along with your calculator. Please read Answers to Common Questions before contacting us. Our experience has shown that many of our customers have similar questions about our products. If you don’t find an answer to your question, you can contact us using the contact information and phone numbers listed on the product CD. Q: I’m not sure if the calculator is malfunctioning, or if I’m doing something incorrectly. How can I determine if the calculator is operating properly? A: See Determining If the Calculator Requires Service. Q: My numbers contain commas instead of periods as decimal points. How do I restore the periods? A: Press \8 (Ch. 2 Getting Started). Q: How do I change the number of decimal places that the HP 10bII+ displays? A: Press \5 and the number of decimal places that you want (Ch. 2 Getting Started). Q: What does an E in a number (for example, 2.51E–13) mean? A: Exponent of ten. For example, 2.51 × 10–13 (Ch. 2 Getting Started). Q: Why do I get a wrong answer or the No Solution message when using TVM? A: Be sure to enter a value for four of the five TVM values before you solve for the fifth, even if one of the values is zero. (Don’t forget to store a zero for loan.) Clearing all the TVM registers ( É if you completely pay off a ]OJ) before entering your known values accomplishes the same thing. Check to see that the calculator is in the appropriate payment mode (Begin or End mode) and that P/YR is set correctly. Appendix A: Batteries and Answers to Common Questions III Q: How can I change the sign of a number in a list of cash flows? A: You must edit or replace the cash flow entry (Ch. 8 Cash Flow Calculations). Q: What does PEND in the display mean? A: An arithmetic operation is pending (in progress). Q: What does A:The INPUT in the display mean? Æ key has been pressed (Ch. 2 Getting Started). Q: Why is IRR/YR larger than I expected? A: This is IRR per year. To see a periodic IRR, divide IRR/YR by P/YR. Environmental Limits To maintain product reliability, you should avoid getting the calculator wet and observe the following temperature and humidity limits: • • • IV Operating temperature: 0° to 40°C (32° to 104°F). Storage temperature: -20° to 65°C (-4° to 149°F). Operating and storage humidity: 90% relative humidity at 40°C (104°F) maximum. Appendix A: Batteries and Answers to Common Questions Appendix B: More About Calculations IRR/YR Calculations The calculator determines IRR/YR for a set of cash flows using mathematical formulas that search for the answer. The process finds a solution by estimating an answer and then using that estimate to do another calculation. This is called an iterative process. In most cases, the calculator finds the desired answer, since there is usually only one solution to the calculation. However, calculating IRR/YR for certain sets of cash flows is more complex. There may be more than one (or no) mathematical solution to the problem. Possible Outcomes of Calculating IRR/YR These are the possible outcomes of an IRR/YR calculation: • Case 1. The calculator displays a positive answer. This is the only positive answer. However, one or more negative answers may exist. • Case 2. The calculator displays a negative answer and no message.This is the only answer. • Case 3. The calculator displays: No Solution. There is no answer. This situation might be the result of an error, such as a mistake in keying in the cash flows. A common mistake that results in this message is putting the wrong sign on a cash flow. A valid cash-flow series for an IRR/YR calculation must have at least one positive and one negative cash flow. Range of Numbers The largest positive and negative numbers available on the calculator are ± 9.99999999999 × 10499; the smallest positive and negative numbers available are ±1 × 10–499. Underflow briefly displays UFLO and then displays zero. Refer to the messages OFLO and UFLO in Appendix C. Equations Business Percentages and Break-even Calculations PRC – COST MAR = ⎛ ----------------------------------⎞ × 100 ⎝ ⎠ PRC NEW – OLD %CHG = ⎛ --------------------------------⎞ × 100 ⎝ Probability OLD ⎠ PRC – COST MU = ⎛ ----------------------------------⎞ × 100 ⎝ COST ⎠ PROFIT = (SP-VC) x UNITS - FC n! P = -----------------( n – r )! n! C = ---------------------( n – r )!r! Appendix B: More About Calculations I Time Value of Money (TVM) Payment Mode Factor: S = 0 for End mode; 1 for Begin mode. I/YR i% = ------------P/YR –N i% ⎞ ⎞ ⎛ 1 – ⎛ 1 + -------⎝ ⎠ ⎟ ⎜ 100 i% × S 0 = PV + ⎛ 1 + ---------------⎞ × PMT × ⎜ --------------------------------------⎟ ⎝ i% 100 ⎠ ⎜ ⎟ -------⎝ ⎠ 100 i% + FV × ⎛ 1 + --------⎞ ⎝ 100⎠ –N Amortization ΣINT = accumulated interest ΣPRN = accumulated principal i = periodic interest rate BAL is initially PV rounded to the current display setting. PMT is initially PMT rounded to the current display setting. I ⁄ YR i = ----------------------------P ⁄ YR × 100 For each payment amortized: INT' = BAL × i (INT' is rounded to the current display setting; INT’ = 0 for period 0 in Begin mode.) INT = INT' (with sign of PMT) PRN = PMT + INT' BALnew = BALold + PRN ΣINTnew = ΣINTold + INT ΣPRNnew = ΣPRNold + PRN Interest Rate Conversions NOM% P ⁄ YR ⎞ EFF% = ⎛ ⎛ 1 + -----------------------------⎞ – 1 × 100 ⎝⎝ ⎠ 100 × P ⁄ YR⎠ II Appendix B: More About Calculations Cash-Flow Calculations i% = periodic interest rate. j = the group number of the cash flow. CFj = amount of the cash flow for group j. nj = number of times the cash flow occurs for group j. k = the group number of the last group of cash flows. Nj = ∑ n l = total number of cash flows prior to group j. 1≤l<j –n i%-⎞ j⎞ ⎛ 1 – ⎛ 1 + ------⎝ ⎜ 100⎠ ⎟ ⎛ i% – n j NPV = CF 0 + ∑ CF j × ⎜ --------------------------------------⎟ × 1 + --------⎞ i%100⎠ ⎜ ⎟ ⎝ ------j=1 ⎝ ⎠ 100 k When NPV = 0, the solution for i% is the periodic internal rate of return. k NFV = NPV x SPFV(i % : N) where N = k TOTAL = ∑ nj j=1 ∑ ( nj × CFj ) j=0 k COUNT = ∑ nj j=0 Appendix B: More About Calculations III Bonds Reference: Lynch, John J. Jr. and Jan Mayle, Stanford Securities Calculation Methods, Securities Industry Association, New York, 1986. A = accrued days, the number of days from beginning of coupon period to settlement date. E = number of days in coupon bracketing settlement date. By convention, E is 180 (or 360) if calendar basis is 30/360. DSC = number of days from settlement date to next coupon date. (DSC= E - A). M = coupon periods per year (1 = annual, 2 = semiannual). N = number of coupon periods between settlement and redemption dates. If N has a fractional part (settlement not on coupon date), then round it to the next higher whole number. Y = annual yield as a decimal fraction, YLD% / 100. For one or fewer coupon period to redemption: Note: coupon (CPN) is a percentage (CPN%) in both cases. CPN CALL + -----------M A CPN PRICE = ------------------------------------- – ⎛ --- × ------------⎞ ⎝ E M ⎠ DSC Y 1 + ⎛ ------------ × ---⎞ ⎝ E Y⎠ For more than one coupon period to redemption: CPN -----------A CPN M ----------------------------------------- – ⎛ --- × ------------⎞ ∑ DSC⎝E M ⎠ K – 1 + ----------E Y-⎞ ⎛ 1 + ---⎝ M⎠ N CALL ---------------------------------------+ DSC ⎛1 + Y ---⎞ ⎝ Y⎠ N – 1 + -----------E The end of month convention is used to determine coupon dates in the following exceptional situations. This affects calculations for YLD%, PRICE, and ACCRU. IV • If the maturity date falls on the last day of the month, then the coupon payments will also fall on the last day of the month. For example, a semiannual bond that matures on September 30 will have coupon payment dates on March 31 and September 30. • If the maturity date of a semiannual bond falls on August 29 or 30, then the February coupon payment dates will fall on the last day of February (28, or 29 in leap years). Appendix B: More About Calculations Depreciation For the given year number (YR) and with Factor (FACT) as a percentage: BASIS – SALV SL = ------------------------------------LIFE BASIS – SALV SOYD = ------------------------------------------------ × ( LIFE – YR + 1 ) ( LIFE + 1 ) LIFE × --------------------------2 FACT ⎛ FACT ---------------⎞ ⎞ BASIS × --------------- ⎛⎜ ⎝ 100 ⎠ ⎟ 100 DB = --------------------------------------- × ⎜ 1 – ---------------------⎟ LIFE LIFE ⎟ ⎜ ⎝ ⎠ ( YR – 1 ) For the last year of depreciation, DB equals the remaining depreciable value for the prior year. Statistics ∑x ∑y ∑ xy x = --------- , y = --------- , x w = ----------n n ∑y 2 (∑ x) ∑ x – --------------n ---------------------------------n–1 2 Sx = 2 (∑ y) ∑ y – --------------n ---------------------------------n–1 2 Sy = 2 (∑ x) x – ∑ --------------n ---------------------------------σy = n 2 σx = 2 (∑ y) y – ∑ --------------n --------------------------------n 2 x∑ y ∑ – -----------------xy ∑ n r = -----------------------------------------------------------------------------------2 2 (∑ x) ⎞ ⎛ (∑ y) ⎞ ⎛ 2 2 ⎜ ∑ x – ----------------⎟ ⎜ ∑ y – ----------------⎟ n ⎠⎝ n ⎠ ⎝ ∑ x∑ y ∑ xy – -----------------n m = -----------------------------------2 ( x ) ∑ 2 ∑ x – --------------n b = y – mx y–b xˆ = ----------m yˆ = mx + b Appendix B: More About Calculations V Forecasting VI Name Fit Best Fit Automatically selects fit Linear m*x+b Logarithm m*ln(x)+b Exponential b*e(m*x) Power b*xm Exponent b*mx Inverse m/x+b Appendix B: More About Calculations Appendix C: Messages Clear Messages Press M or | to clear a message from the display. Table C-1 Messages Message Displayed Description ALL CLEAR Memory has been erased (Ch. 2). COPR HP 2010 Copyright message. Oflo (Overflow). The magnitude of a result is too large for the calculator to handle. Message is displayed for a moment, then the overflow result is returned (±9.99999999999E499). The overflow message is also displayed if an intermediate TVM or cashflow calculation results in an overflow condition. Uflo (Underflow). An intermediate result in TVM is too small for the HP 10bII+ to process. This message is also briefly displayed if any calculation underflows. In this case, it is followed by zero. no Solution No solution exists for values entered (Appendix B). not Found A solution for IRR/YR or I/YR may or may not exist. If you are attempting to solve I/YR, you may be able to perform the calculation using IRR/YR. If you are attempting an IRR/YR calculation, refer to (Appendix B). Error I_Yr Invalid value in I/Yr register or error solving for I/Yr. Error P_Yr Invalid value in P/Yr register or error solving for P/Yr. Error N Invalid value in N register or error solving for N. Error LN An invalid number was entered for the LN function. Error 0 / 0 An attempt was made to divide 0 by 0. Error / 0 An attempt was made to divide by 0. Algebraic Algebraic calculation mode is active. Chain Chain calculation mode is active. Error days An invalid date or range was attempted with the function. ]È Error ddays An invalid date or range was attempted with the function. \Ä CFLOW CLR cashflow memory was cleared. TVM CLR tvm registers were cleared. BR EV CLR breakeven registers were cleared. Appendix C: Messages I Table C-1 Messages Message Displayed Description BOND CLR bond registers were cleared. STAT CLR statistical memory and registers were cleared. Best Fit The calculator selected the best fit regression which is subsequently flashed for 1 second. running Displays if a calculation takes longer than .25 seconds. User Stop An IRR/YR, I/YR, or amortization calculation was interrupted by pressing II Appendix C: Messages M. 17 Warranty, Regulatory, and Contact Information Replacing the Batteries Warning! There is a danger of explosion if batteries are incorrectly replaced. Replace only with the same type of battery or with equivalent batteries (as recommended by the manufacturer). Dispose of used batteries according to the manufacturer’s instructions. Do not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode, releasing hazardous chemicals. •The calculator is powered by two 3-volt CR2032 coin batteries. •When changing batteries, use only fresh coin-cell batteries. Do not use rechargeable batteries. •Do not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode, releasing hazardous chemicals. •Do not use new and old batteries together, and do not mix batteries of different types. 1. 8. Have two fresh CR2032 batteries at hand. Only touch the batteries by their edges. Wipe each battery with a lint-free cloth to remove dirt and oil. Make sure the calculator is off. When changing the batteries, change the batteries one at a time to avoid clearing the memory. As a back-up, write down any data that you have stored and might need for later use. Turn the calculator over and pry off the battery cover. Gently remove one battery. Insert the new battery, making sure that the positive sign (+) battery is facing outward. Gently remove the other battery. Insert the other new battery, making sure that the positive sign (+) battery is facing outward. Replace the battery-compartment lid. 9. Press 2. 3. 4. 5. 6. 7. =. 10. If the calculator does not turn on, follow the procedures in the section titled, Determining if the Calculator Requires Service in Appendix A of the HP 10bII+ Financial Calculator User’s Guide. HP Limited Hardware Warranty and Customer Care This HP Limited Warranty gives you, the end-user customer, express limited warranty rights from HP, the manufacturer. Please refer to HP's Web site for an extensive description of your limited warranty entitlements. In addition, you may also have other legal rights under applicable local law or special written agreement with HP. Limited Hardware Warranty Period Duration: 12 months total (may vary by region, please visit www.hp.com/support for latest information). Warranty, Regulatory, and Contact Information 1 General Terms EXCEPT FOR THE WARRANTIES SPECIFICALLY PROVIDED FOR IN SUBSEQUENT PARAGRAPHS OF THIS SECTION, HP MAKES NO OTHER EXPRESS WARRANTY OR CONDITION WHETHER WRITTEN OR ORAL. TO THE EXTENT ALLOWED BY LOCAL LAW, ANY IMPLIED WARRANTY OR CONDITION OF MERCHANTABILITY, SATISFACTORY QUALITY, OR FITNESS FOR A PARTICULAR PURPOSE IS LIMITED TO THE DURATION OF THE EXPRESS WARRANTY SET FORTH IN THE SUBSEQUENT PARAGRAPHS OF THIS SECTION. Some countries, states or provinces do not allow limitations on the duration of an implied warranty, so the above limitation or exclusion might not apply to you. This warranty gives you specific legal rights and you might also have other rights that vary from country to country, state to state, or province to province. TO THE EXTENT ALLOWED BY LOCAL LAW, THE REMEDIES IN THIS WARRANTY STATEMENT ARE YOUR SOLE AND EXCLUSIVE REMEDIES. EXCEPT AS INDICATED ABOVE, IN NO EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR DIRECT, SPECIAL, INCIDENTAL, CONSEQUENTIAL (INCLUDING LOST PROFIT OR DATA), OR OTHER DAMAGE, WHETHER BASED IN CONTRACT, TORT, OR OTHERWISE. Some countries, States or provinces do not allow the exclusion or limitation of incidental or consequential damages, so the above limitation or exclusion may not apply to you. FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND NEW ZEALAND: THE WARRANTY TERMS CONTAINED IN THIS STATEMENT, EXCEPT TO THE EXTENT LAWFULLY PERMITTED, DO NOT EXCLUDE, RESTRICT OR MODIFY AND ARE IN ADDITION TO THE MANDATORY STATUTORY RIGHTS APPLICABLE TO THE SALE OF THIS PRODUCT TO YOU. Notwithstanding the above disclaimers, HP expressly warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and workmanship after the date of purchase, for the period specified above. If HP receives notice of such defects during the warranty period, HP will, at its option, either repair or replace products which prove to be defective. Replacement products may be either new or like-new. HP also expressly warrants to you that HP software will not fail to execute its programming instructions after the date of purchase, for the period specified above, due to defects in material and workmanship when properly installed and used. If HP receives notice of such defects during the warranty period, HP will replace software media which does not execute its programming instructions due to such defects. Exclusions HP does not warrant that the operation of HP products will be uninterrupted or error free. If HP is unable, within a reasonable time, to repair or replace any product to a condition as warranted, you will be entitled to a refund of the purchase price upon prompt return of the product with proof of purchase. HP products may contain remanufactured parts equivalent to new in performance or may have been subject to incidental use. Warranty does not apply to defects resulting from (a) improper or inadequate maintenance or calibration, (b) software, interfacing, parts or supplies not supplied by HP, (c) unauthorized modification or misuse, (d) operation outside of the published environmental specifications for the product, or (e) improper site preparation or maintenance. HP MAKES NO OTHER EXPRESS WARRANTY 2 Warranty, Regulatory, and Contact Information OR CONDITION WHETHER WRITTEN OR ORAL. TO THE EXTENT ALLOWED BY LOCAL LAW, ANY IMPLIED WARRANTY OR CONDITION OF MERCHANTABILITY, SATISFACTORY QUALITY, OR FITNESS FOR A PARTICULAR PURPOSE IS LIMITED TO THE DURATION OF THE EXPRESS WARRANTY SET FORTH ABOVE. Some countries, states or provinces do not allow limitations on the duration of an implied warranty, so the above limitation or exclusion might not apply to you. This warranty gives you specific legal rights and you might also have other rights that vary from country to country, state to state, or province to province. TO THE EXTENT ALLOWED BY LOCAL LAW, THE REMEDIES IN THIS WARRANTY STATEMENT ARE YOUR SOLE AND EXCLUSIVE REMEDIES. EXCEPT AS INDICATED ABOVE, IN NO EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR DIRECT, SPECIAL, INCIDENTAL, CONSEQUENTIAL (INCLUDING LOST PROFIT OR DATA), OR OTHER DAMAGE, WHETHER BASED IN CONTRACT, TORT, OR OTHERWISE. Some countries, States or provinces do not allow the exclusion or limitation of incidental or consequential damages, so the above limitation or exclusion may not apply to you. The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services. HP shall not be liable for technical or editorial errors or omissions contained herein. FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND NEW ZEALAND: THE WARRANTY TERMS CONTAINED IN THIS STATEMENT, EXCEPT TO THE EXTENT LAWFULLY PERMITTED, DO NOT EXCLUDE, RESTRICT OR MODIFY AND ARE IN ADDITION TO THE MANDATORY STATUTORY RIGHTS APPLICABLE TO THE SALE OF THIS PRODUCT TO YOU. Regulatory Information Federal Communications Commission Notice This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC Rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference to radio communications. However, there is no guarantee that interference will not occur in a particular installation. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, the user is encouraged to try to correct the interference by one or more of the following measures: • Reorient or relocate the receiving antenna. • Increase the separation between the equipment and the receiver. • Connect the equipment into an outlet on a circuit different from that to which the receiver is connected. • Consult the dealer or an experienced radio or television technician for help. Modifications The FCC requires the user to be notified that any changes or modifications made to this device that are not expressly approved by Hewlett-Packard Company may void the user's authority to operate the equipment. Warranty, Regulatory, and Contact Information 3 Declaration of Conformity for Products Marked with FCC Logo, United States Only This device complies with Part 15 of the FCC Rules. Operation is subject to the following two conditions: 1. This device may not cause harmful interference 2. This device must accept any interference received, including interference that may cause undesired operation. If you have questions about the product that are not related to this declaration, write to: Hewlett-Packard Company P. O. Box 692000, Mail Stop 530113 Houston, TX 77269-2000 For questions regarding this FCC declaration, write to: Hewlett-Packard Company P. O. Box 692000, Mail Stop 510101 Houston, TX 77269-2000 or call HP at 281-514-3333 To identify your product, refer to the part, series, or model number located on the product. Canadian Notice This Class B digital apparatus meets all requirements of the Canadian Interference-Causing Equipment Regulations. Avis Canadien Cet appareil numérique de la classe B respecte toutes les exigences du Règlement sur le matériel brouilleur du Canada. European Union Regulatory Notice Products bearing the CE marking comply with the following EU Directives: • Low Voltage Directive 2006/95/EC • EMC Directive 2004/108/EC • Ecodesign Directive 2009/125/EC, where applicable CE compliance of this product is valid if powered with the correct CE-marked AC adapter provided by HP. Compliance with these directives implies conformity to applicable harmonized European standards (European Norms) that are listed in the EU Declaration of Conformity issued by HP for this product or product family and available (in English only) either within the product documentation or at the following web site: www.hp.eu/certificates (type the product number in the search field). The compliance is indicated by one of the following conformity markings placed on the product: 4 Warranty, Regulatory, and Contact Information For non-telecommunications products and for EU harmonized telecommunications products, such as Bluetooth® within power class below10mW. For EU non-harmonized telecommunications products (If applicable, a 4-digit notified body number is inserted between CE and !). Please refer to the regulatory label provided on the product. The point of contact for regulatory matters is: Hewlett-Packard GmbH, Dept./MS: HQ-TRE, Herrenberger Strasse 140, 71034 Boeblingen, GERMANY. Japanese Notice Disposal of Waste Equipment by Users in Private Household in the European Union This symbol on the product or on its packaging indicates that this product must not be disposed of with your other household waste. Instead, it is your responsibility to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste electrical and electronic equipment. The separate collection and recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that it is recycled in a manner that protects human health and the environment. For more information about where you can drop off your waste equipment for recycling, please contact your local city office, your household waste disposal service or the shop where you purchased the product. Warranty, Regulatory, and Contact Information 5 Perchlorate Material - special handling may apply This calculator's Memory Backup battery may contain perchlorate and may require special handling when recycled or disposed in California. Customer Care In addition to the one year hardware warranty, your HP calculator also comes with one year of technical support. If you need assistance with warranty, please refer to the warranty information on the product CD. HP customer care can be reached by either email or telephone. Before calling please locate the call center nearest you from the list provided. Have your proof of purchase and calculator serial number ready when you call. Telephone numbers are subject to change, and local and national telephone rates may apply. A complete list is available on the web at: www.hp.com/support. Contact Information Table 17-1 Contact Information Country/ Region 6 Contact Country/ Region Contact Algeria www.hp.com/support Anguila 1-800-711-2884 Antigua 1-800-711-2884 Argentina 0-800-555-5000 Aruba 800-8000; 800-711-2884 Austria Österreich 01 360 277 1203 Bahamas 1-800-711-2884 Barbados 1-800-711-2884 Belgique (Français) 02 620 00 85 Belgium (English) 02 620 00 86 Bermuda 1-800-711-2884 Bolivia 800-100-193 Botswana www.hp.com/support Brazil Brasil 0-800-709-7751 British Virgin 1-800-711-2884 Islands Bulgaria www.hp.com/support Canada 800-HP-INVENT Cayman Island 1-800-711-2884 Chile 800-360-999 China 中国 800-820-9669 Costa Rica 0-800-011-0524 Croatia www.hp.com/support Curacao 001-800-872-2881 + 800-711-2884 Czech Republic Česká republikaik 296 335 612 Denmark 82 33 28 44 Dominica 1-800-711-2884 Dominican Republic 1-800-711-2884 Egypt www.hp.com/support Warranty, Regulatory, and Contact Information Country/ Region Contact Country/ Region Contact El Salvador 800-6160 Equador 1-999-119; 800-711-2884 (Andinatel) 1-800-225-528; 800-711-2884 (Pacifitel) Estonia www.hp.com/support Finland Suomi 09 8171 0281 France 01 4993 9006 French Antilles 0-800-990-011; 800-711-2884 French Guiana 0-800-990-011; 800-711-2884 Germany 069 9530 7103 Deutschland Ghana www.hp.com/support Greece Ελλάδα Grenada 1-800-711-2884 Guadelupe 0-800-990-011; 800-711-2884 210 969 6421 Guatemala 1-800-999-5105 Guyana 159; 800-711-2884 Haiti Honduras 800-0-123; 800-711-2884 Hong Kong 800-933011 香港特別行 政區 Hungary www.hp.com/support India 1-800-114772 Indonesia (21)350-3408 Ireland 01 605 0356 Italy Italia 02 754 19 782 Jamaica 1-800-711-2884 Japan 日本 00531-86-0011 Kazakhstan www.hp.com/support Latvia www.hp.com/support Lebanon Lithuania www.hp.com/support Luxembourg 2730 2146 Malaysia 1800-88-8588 Martinica 0-800-990-011; 877-219-8671 Mauritius www.hp.com/support Mexico México 01-800-474-68368 (800 HP INVENT) Montenegro www.hp.com/support Montserrat 1-800-711-2884 Morocco Namibia www.hp.com/support Netherlands 020 654 5301 183; 800-711-2884 www.hp.com/support www.hp.com/support Netherland 001-800-872-2881; Antilles 800-711-2884 New Zealand 0800-551-664 Nicaragua 1-800-0164; 800-711-2884 Norway Norwegen 23500027 Panama Panamá 001-800-711-2884 Paraguay (009) 800-541-0006 Warranty, Regulatory, and Contact Information 7 Country/ Region 8 Contact Country/ Region Contact Peru Perú 0-800-10111 Philippines (2)-867-3351 Poland Polska www.hp.com/support Portugal 021 318 0093 Puerto Rico 1-877 232 0589 Romania www.hp.com/support Russia Россия 495-228-3050 Saudi Arabia www.hp.com/support Serbia www.hp.com/support Singapore 6272-5300 Slovakia www.hp.com/support South Africa 0800980410 South Korea 00798-862-0305 한국 Spain España 913753382 St Kitts & Nevis 1-800-711-2884 St Lucia 1-800-478-4602 St Marteen 1-800-711-2884 St Vincent 01-800-711-2884 Suriname 156; 800-711-2884 Swaziland www.hp.com/support Sweden Sverige 08 5199 2065 Switzerland 022 827 8780 Switzerland 022 827 8780 (Suisse Français) Switzerland 01 439 5358 (Schweiz Deutsch) Switzerland 022 567 5308 (Svizzeera Italiano) Taiwan 臺灣 00801-86-1047 Thailand ไทย (2)-353-9000 Trinidad & Tobago 1-800-711-2884 Tunisia www.hp.com/support Turkey Türkiye www.hp.com/support Turks & Caicos 01-800-711-2884 UAE www.hp.com/support United Kingdom 0207 458 0161 Uruguay US Virgin Islands 1-800-711-2884 United States 800-HP INVENT Venezuela 0-800-474-68368 (0-800 HP INVENT) Vietnam Viêt Nam +65-6272-5300 Zambia www.hp.com/support Warranty, Regulatory, and Contact Information 0004-054-177 Warranty, Regulatory, and Contact Information 9 10 Warranty, Regulatory, and Contact Information A Chain mode Advance payments 72 Algebraic mode calculations 28 Amortization 74 equations II range of payments 76 single payment 77 TVM keys used 75 Angle format selecting 35 Annuity account 70 Annunciators 30 Arithmetic operators 26 At a Glance Clearing quick reference guide 1 B Balloon payment 65 Batteries I installing I Battery replacing the batteries 1, 6 Bonds 105 clear memory 105 example 106 keys used 105 resetting bond keys 108 Break-even 109 example 16, 110 keys used 109 resetting keys 112 calculations 27 backspace 29 messages in the display 30 Comma interchanging with period 43 Comma separator III Constants using 49 Cursor 29 Customer care and contact information 6 D Date calculations 101 Date format 99 bonds 106 Date keys 99 Decimal specifying display of decimal places 42 Depreciation 83 resetting TVM keys 86 TVM keys used 83 Display full precision 42 Display format 41 E Environmental limits IV Equations amortization II bonds IV cash-flow calculations III depreciation V forecasting V interest rate conversions II margins and markups I statistical V TVM II C Calendar 99 Calendar format 99 Calendar keys 99 Cash flow equations III Cash flows application 87 calculating NPV and NFV 95 clearing memory 88 discounting 91 keys used 88 organizing 91 periods 56 recognizing one 59 signs of 56 storage of 89 storing IRR and NPV 98 viewing and editing 93 Error messages I F Factorial 126 FAQ I, III Frequently Asked Questions I, III H Home mortgage 64 Hyperbolic functions 35 I Individual retirement account 69 1 In-line functions 37 Interest mean of x weighted by y 113 means of x and y 113 MU (markup) 47 N 61 NFV 88 Nj 87 nom% 79 NPV 88 number of days 99 off 23 on 23 one-number functions 33 P/YR 61 parentheses 28 percent 45 period/comma 43 plus, minus, multiply, divide 26 PMT 61 population standard deviation 113 PRC (price business) 47 price (bonds) 105 profit (break-even) 109 PV 61 RAND 127 regression models 113 RND 43 sample standard deviation 113 semi/ann (bonds) 105 setdate (bonds) 105 shift keys 25 SL (straight line) 83 SOYD 83 SP (break-even) 109 statistics 32 STO (store) 52 swap 32 two-number functions 39 units (break-even) 109 VC (break-even) 109 xP/YR 61 YTM (bonds) 105 compound interest 57 interest rates 57 simple interest 56 Interest rate conversions 79 Investments IRR different compounding periods 79 calculating IRR 90 IRR/YR I IRR/YR calculations possible outcomes I K Keyboard iv map legend iv Keys 360/ACT 99 Accint (bonds) 105 advanced probability distributions 128 Alg/Chain 26 Amort 62 backspace 29 basic functions 24 Beg/End 62 boxed key functions 25 business percentages 45 C STAT 113 call (bonds) 105 CFj 87 clear 29 clear all 30 clear memory 29 clearing functions 25 CPN% (bonds) 105 CST (cost business) 47 date 99 DB (declining balance) 83 DISP 42 DMY/MDY 99 E 43 eff% 79 estimation of x 113 estimation of y 113 FC (break-even) 109 FV 61 I/YR 61 input 32 K 49 M 51 MAR (margin) 47 matdate (bonds) 105 2 L Last answer 41 Lease calculations 71 Legal notice ii Loan calculations 62 M Manual conventions 23 Margin 47 Markup 47 Memory clearing II Messages I calculator status 44 list of I Registers M register 51 using numbered registers 51 Modes Regulatory Information 3 Reset II Rounding numbers 43 N S Negative numbers 29 Net future value 95 Net present value 95 Number of days 101 Number storage 49 Numbers display format 41 range of I Savings calculations 67 Scientific notation 43 Screen display iv Service II Statistics TVM begin and end 62 calculations that return two values 119 clearing data 114 entering data 114 keys used 113 linear regression, estimation, and regression modes 121 mean, standard deviation and summation 120 memory and storage 114 one-variable 115 regression models and variables 125 summary of calculations 119 two-variable 115 viewing and editing data 116 weighted mean 115, 124 O One-number functions 33 arithmetic with 39 Operating conditions IV Operating modes 26 P Parentheses use in calculations 28 Percent dividing by 100 45 percent change 46 Percentages business 45 Period interchanging with comma 43 Pi 36 Probability advanced distributions 128 combinations 126 conversions from lower tail 133 inverse normal lower tail 130 inverse Student’s T lower tail 132 keys used 128 normal lower tail 129 permutations 126 Student’s T and inverse 128 Student’s T lower tail 131 Z and inverse 128 Storage registers arithmetic with 49 T Trigonometric functions 35 Troubleshooting II TVM equations II keys 61 recognizing one 58 TVM keys resetting 82 Two number functions 37 Two-number functions arithmetic with 39 W Warranty 1 Q Questions I, III R Random number and seed 127 3

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