HEWLETT-PACKARD Contents Page 10 At a Glance 21 1: Getting Started 31 2: Business Percentages 35 3: Number Storage and Arithmetic 43 4: Picturing Financial Problems 51 5: Time Value of Money Calculations 75 6: Cash Flow Calculations 85 7: Statistical Calculations 95 8: Additional Examples 116 A: Assistance, Batteries, and Service 127 B: More About Calculations 133 Messages 136 Index E] Pacino i E | HEWLETT Printed in Singapore 11/94 у i И РАСКАНО (Р) 00010-90037 N ; q Ne O presos 108 BUSINESS \ 19 HP-10B Business Calculator Owners Manual 12 1. Interest conversion (page 71). 11. On, clear display,cancel 2. Time value of money (page 51). operation (page 21). 12. n through Zxy: statistical summation registers (page 89). 13. Statistical functions (page 28). 14. Backspace (page 23). 3. Cash flows (page 75). 4. Store and recall (page 38). 5. Percent (page 31). 6. Clear all memory (page 23). 15. 3-key memory (page 37). Ky A CKARD 7. Separale two numbers (page 25). 16. Margin and markup (page 33). 8. Change sign (раде 22). 17. Accumulate statistical data Edition 6 9. Constant (page 35). (page 86 and 87). Part Number 00010-90037 10. Shift: activate yellow labeled 18. Amortization (page 66). functions (page 24). 19. Annunciator line (page 24). Notice For warranty and regulatory information for this calculator, see pages 123 and 120. 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 and fitness for a particular purpose. Hewlett-Packard Co. shall not be lable for any crrors or for incidental or consequential damages in connection with the furnishing, performance, or use of this manual or the keystroke programs contained herein. e Hewlett-Packard Co. 1988. All rights reserved. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws. The programs that control your calculator are copyrighted and all rights are reserved, Reproduction, adaptation, or translation of those programs without prior written permission of Hewlett-Packard Co. is also prohibited. Corvallis Division 1000 N.E. Circle Blvd. Corvallis, OR 97330, U.S.A. Printing History Edition 1 October 1988 Edition 2 June 1989 Edition 3 June 1990 Edition 4 August 1992 Edition 6 November 1994 Welcome to the HP-10B Your HP-10B reflects the superior quality and attention to detail in engineering and manufacturing that have distinguished Hewlett-Packard products for 50 years. Hewlett-Packard stands behind this calculator — we offer expertise to support its use (sce inside the back cover) and world- wide scrvice. Hewlett-Packard Quality Our calculators are made to excel and to be easy to use. ® This calculator is designed to withstand the drops, vibrations, pollu- tants (smog, ozone), temperature extremes, and humidity variations that it may encounter in everyday work life. ® The calculator and its manual have been designed and tested for case of use. We added many examples to highlight the varied uses of the calculator. Advanced materials and permanent, molded key lettering provide a long keyboard life and a positive fecl to the keyboard. m CMOS (low-power) electronics and a liquid-crystal display allow data to be retained indefinitely and the batteries to last a long time. m The microprocessor has been optimized for fast and reliable compu- tations using 15 digits internally for precise results, m Extensive research has created a design that has minimized the adverse clfects of static electricity, a potential cause of malfunctions and data loss in calculators. Welcome to the HP-10B 3 Featu res The features of the HP-10B and the manual reflect the needs and wishes of many customers: 4 m A large 12-character display. m An At-a-Glance section in the manual for quick reference. m Applications to solve business and financial tasks: = Time Value of Money. Loans, savings, Icases, and amortiza- tion schedules. » Interest Conversion. Nominal and effective rates. = Cash Flows. Net present value and internal rate of return. = Business Percentages. Percent change, markup, and margin calculations. m Statistics. Mcan, standard deviation, correlation coefficient, and linear regression forecasting, plus other statistical calcula- tions. ® Enough memory to store an initial cash flow and 14 cash flow groups, with up to 99 cash flows per group. m Filtecn numbered storage registers. mM Easy access to functions saves keystrokes and adds convenience. ® Auto-increment capability for amortization schedules. wm Labels for amortization and cash (lows. ® Automatic constant. m 3-key memory. ® Many examples are included in the manual so you can combine them for your specific needs. Welcome to the HP-10B Contents 10 Ata Glance... 10 Basics 11 Percentages 12 Memory Keys 13 Time Value of Money (TVM) 14 TVM What if. .. 15 Amortization 16 Interest Rate Conversion 17 IRR/YR and NPV 19 Statistics 21 Getting Started 21 Power On and Off 21 Adjusting the Display Contrast 21 Simple Arithmetic Calculations 23 Understanding the Display and Keyboard 23 Cursor 23 Clearing the Calculator 23 Clearing Memory 24 Annunciators 24 Shift Key 25 INPUT Key 25 SWAP Key 25 Math Functions 26 Display Format of Numbers 27 Specifying Displayed Decimal Places 27 Scientific Notation 28 Displaying the Full Precision of Numbers Contents 51 Time Value of Money Calculations 28 Interchanging the Period and Comma 28 Rounding Numbers 29 Messages 29 Picturing Memory 2 31 Business Percentages 31 Percent Key 31 Finding a Percent 32 Adding or Subtracting a Percent 32 Percent Change 33 Margin and Markup Calculations 33 Margin Calculations 34 Markup on Cost Calculations 34 Using Margin and Markup Together 3 35 Number Storage and Arithmetic 35 Using Stored Numbers in Calculations 35 Using Constants 37 Using the M Register 38 Using Numbered Registers 39 Doing Arithmetic Inside Registers 40 Doing Arithmetic 41 Power Operator 41 Using Parentheses in Calculations 4 43 Picturing Financial Problems 43 Howto Approach a Financial Problem 44 Signs of Cash Flows 45 Periods and Cash Flows 45 Simple and Compound Interest 45 Simple Interest 46 Compound Interest 47 Interest Rates 47 Two Types of Financial Problems 47 Recognizing a TVM Problem 49 Recognizing a Cash Flow Problem 6 Contents 51 Using the TVM Application 53 Clearing TVM 53 Begin and End Modes 53 Loan Calculations 58 Savings Calculations 62 Lease Calculations 66 Amortization 71 Interest Rate Conversions 71 Investments With Different Compounding Periods 73 Compounding and Payment Periods Differ 75 Cash Flow Calculations 75 How to Use the Cash Flow Application 77 NPV and IRR/YR: Discounting Cash Flows 77 Organizing Cash Flows 78 Entering Cash Flows 79 Viewing and Replacing Cash Flows 80 Calculating Net Present Value 83 Calculating Internal Rate of Return 84 Automatic Storage of IRR/YR and NPV 85 Statistical Calculations 85 Clearing Statistical Data 86 Entcring Statistical Data 86 One-Variable Statistics 86 Two-Variable Statistics and Weighted Mean 87 Correcting Statistical Data 87 Correcting One-Variable Dala 87 Correcting Two-Variable Data 88 Summary of Statistical Calculations 89 Mean, Standard Deviations, and Summation Statistics 91 Linear Regression and Estimation 94 Weighted Mean Contents 7 8 95 Additional Examples 95 Business Applications 95 Setting a Sales Price 95 Forccasting Based on History 96 Cost of Not Taking a Cash Discount 97 » Loans and Mortgages 97 Simple Annual Interest 98 Continuous Compounding 99 Yicld of a Discounted (or Premium) Mortgage 101 Annual Percentage Rate for a Loan With Fees 102 Loan With a Partial (Odd) First Period 104 Automobile Loan 105 Canadian Mortgages 106 What if... TVM Calculations 107 Savings 107 Saving for College Costs 109 Gains That Go Untaxed Until Withdrawal 111 Value of a Taxable Retirement Account 112 Cash Flow Examples 112 Wrap-Around Mortgages 114 Net Future Value A 116 Assistance, Batteries, and Service 116 Answers 10 Common Questions 117 Environmental Limits 118 Power and Batteries 118 Low Power Annuncialor 119 Installing Batteries 120 Determining if the Calculator Requires Service 121 Confirming Calculator Operation — the Sclf-Test 123 Limited One-Year Warranty 123 What Is Covered 123 What Is Not Covered 124 Consumer Transactions in the United Kingdom 124 [the Calculator Requires Service 124 Obtaining Service 125 Service Charge 8 Contents 125 Shipping Instructions 126 Warranty on Service 126 Service Agreements 126 Regulatory Information 127 More About Calculations 127 IRR/YR Calculations 127 Possible Outcomes of Calculating IRR/YR 128 Halting and Restarting IRR/YR 128 Entering a Guess for IRR/YR 129 Effect of Using E- to Correct Data 129 Range of Numbers 129 Equations 129 Margin and Markup Calculations 130 Time Value of Money (TVM) 130 Amortization 131 Interest Rate Conversions 131 Cash-Flow Calculations 132 Statistics 133 Messages 136 Index Contents At a Glance... This section is designed for you if you're alrcady familiar with calculator operation or financial concepts, You can usc it for quick reference. The rest of the manual is filled with explanations and examples of the concepts presented in this section, —— оннЕЕЕЕ Basics — At a Glance... | EL | loooooa 90900200) ON С) СОСО 35558 esco Keys: Display: Description: [С] 0.00 Turns calculator on. E 0.00 Displays shift annuncia- lor (—). в 0.00 Discontinues shift. 123 [+] 12° Erases last character. 0.00 Clears display. MiCL 7) 0.00 Clears statistics memory. M[CLEAR ALL] 0.00 Clears all memory. RC] Turns calculator off. 10 At a Glance... Percentages — At a Glance... Las — |] 0000001 OC —osecs 00000; DOO ODOOCT} CONC - — Percent. Cost. [PRC] Price. MAR Margin, Markup. Add 15% to $17.50. Keys: Display: Description: 17.50 [+] 17.50 Enters number. 15 (%]) (=) 20.13 Adds 15 %. Find the margin if the cost is $15.00 and selling price 1s $22.00). 15 15.00 Enters cost. 22 [PRC] 22.00 Enters pricc. [MAR] 31.82 Calculates margin, If the cost is $20.00 and the markup is 335¢, what is the selling price? 20 [CST] 20.00 Enters cost. 33 (MU) 33.00 Enters markup, [PRC] 26.60 Calculates price. А! д Glance... 11 Memory Keys — At a Glance. .. 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. Stores a value in a numbered register. Recalls a value from a numbered register. Multiply 17, 22, and 25 by 7, storing “x 7” as à constant operation. 22 (=) 25 [=] Display: Description: 7.00 Stores “X 7” as a constant operation. 119.00 Multiplics 17 х 7. 154.00 Multiplies 22 x 7. 175.00 Multiplies 25 x 7. Store 519 in register 2, then recall it. 519 M (STO) 2 [С] [RCL] 2 519.00 Stores in register 2. 0.00 Clears display. 519.00 Recalls register 2. 12 At a Glance... Time Value of Money (TVM) — At a Glance... [| il | Enter any four of the five values and solve for the filth. A negative sign in the display represents money paid out; money received is positive, Number of payments. 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 (7/YR), what is the monthly payment? Set to End mode. Press M(BEG/END) if BEGIN annunciator is displayed. Keys: 12 BF/YR 360 (N) 10 14000 0 PMT Display: Description: 12.00 Sets payments per year. 360.00 Enters number of payments. 10.00 Enters interest per year. 14,000.00 Enters present value. 0.00 Enters future value. - 122.86 Calculates payment if paid at end of period. At a Glance... 13 TVM What if. ..— At a Glance. . . | ОС; ODOOOC 90000) O oO ЗЕЕ OOD % = = Кеуз: 100 [+7-] [РУ] Display: — 100.00 11,395.08 | | It is not necessary to reenter TVM values for each example. | Using the values you just entered (page 13), how much can особо) you borrow if you want a payment of $100.00? Description: Enters new payment amount. (Money paid out is negative.) Calculates amount you can borrow. How much can you borrow at a 9.5% interest rate? 9.5 [1/YR] [PV] 10 (1/YA) 14000 14 Ata Glance... 9.50 11,892.67 10.00 14,000.00 - 122.86 Enters new interest rate. Calculates new present value for $100.00 pay- ment and 9.5% interest. Reenters original interest rate. Reenters original present value. Calculates original payment. осо 000 ooo oa с OO Amortize the 20th payment of the loan. Keys: 20 W(AMGRT] a [=] =) Amortizc the 1st through 12th loan payments. 1 (INPUT) 12 B(AMORT E =] Display: 20.00 PEr 20- 20 Int -115.61 Prin -7,25 DAL 13,865.83 12 PEr1- 12 Int = 1 ‚396.50 Prin - 77.82 bAL 13,922.18 Amortization — At a Glance... __liI After calculating a payment using Time Value of Moncey cocoeo| (TVM), enter the periods to amortize, then press M[AMORT). Using the previous TVM example (page 13), amortize a single payment and then a range of payments. Description: Enters payment to amortize. Displays payment to amortize. Displays interest. (Moncy paid out is negative.) Displays principal. Displays balance. Enters range of payments to amortize. Displays range of periods (payments). Displays interest. (Money paid out is negative.) Displays principal. Displays balance. At a Glance... 15 Interest Rate Conversion— At a Glance... HNOM%]) Nominal interest percent. B(EFF%) Effective interest percent. M(P/YR] Periods per year. | | To convert between nominal and effective interest rates, coææsoo| enter the known rate and the number of periods per year, = then solve for the unknown rate. Find the annual effective interest rate of 10% nominal interest com- pounded monthly. Keys: 10 BNOM%) 12 M(P/YR] ШЕЕР%) 16 At a Glance... Display: 10.00 12.00 10.47 Description: Enters nominal rate. Enters payments per ycar. Calculates annual effective interest. Боевое IRR/YR and NPV — At a Glance... ¡OTE НОС 4 COS с OOOBC! H[P/YR Number of periods per year (default is 12). [CF] Cash flows, up to 15 (*7” identifies the cash Flow number). MÍN) Number of conscculive times cash flow “7” occurs. B(RA/YR Internal rate of return per year. BNPV) Net present value. l you have an initial cash outflow ofl $- 40,000, followed by monthly cash inflows ol $4,700, $7,000, $7,000, and $23,000, what is thc JRR/YR? What is Lhe ZRR per month? Keys: Display: Description: BICLEAR ALL] 0.00 Clears all memory. 12 B(P/YR] 12.00 Sets payments per year. 40000 [+7] CFO Enters initial outflow. - 40,000.00 4700 [СЕ] CF 1 Enters first cash flow. 4,700.00 7000 CF 2 Enters second cash flow. 7,000.00 2 (№) ne Enters number of con- 2.00 seculive Limes cash (low occurs. At a Glance... 17 23000 [СЕЛ CF 3 23.000.00 B(iRR/YR] 15.96 (=) 12 [=] 1.33 Whal is the NPV if the discount rate 15 10%? 10 10.00 Ш (МУ) 622.85 18 At a Glance... Enters third cash low. Calculates IRR/YR. Calculates IRR per month. Enters //YR. Calculates NPV. Statistics — At a Glance. .. Danone] 000000! ина ВС)! С) в ол ев | |0 вв в в CC) 5656030 1 сос) M[CL 7) number number M[E-] number] (INPUT) number? number] (INPUT) number2 M(E-) Bi: v] BSWAP] Bzw H(Sx.Sy) (СУАР) Bloxoy) H[SWAP) y-value P(X) BSWAP] x-value (Sm) 0 MU.m) MISWAP] Clear statistical registers. Enter one-variable statistical data. Delete one-variablc statistical data. Enter two-variable statistical data. Delete two-variable statistical data. Mean of x and y. Mean of x weighted by y. Sample standard deviation of x and y. Population standard deviation of x and y. Estimate of € and corrclation coefficient, Estimate of y. y-intercept and slope. At a Glance... 19 Using the following data, find the mean of x and y, the sample standard deviation of x and y, and the y-intercept and the slope of the linear regres- sion forecast line. Then, use summation statistics to find n and Ey. Ixdatal 2 | 4 | 6 | y-data | 50 | 90 | 160 Keys: Display: Description: 0.00 Clears statistics registers. 2 50 1.00 Enters first x,y pair. 4 90 2.00 Enters second x,y pair. 6 160 3.00 Enters third x,y pair. 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 (predicted ÿ value forx = 0), 27.50 Displays slope of regres- sion line. 4 3.00 Displays n, number of data points entered. 9 1,420.00 Displays Ex, sum of the products of x- and y-values. 20 Ata Glance... Getting Started Power On and off | "| To turn on your HP-10B, press (€) (the key above the “ON” 900965 label). To turn the calculator off, press the yellow shift key AS (MM), then [C) (also written M(OFF)). 00000 ® 0000) Since the calculator has continuous memory, turning it off ? does not affect the information you've stored. To conserve energy, the calculator turns itself off approximately 10 minutes after you stop using it. The calculator's three alkaline batteries last approximately one year, If you see the low-battery symbol (<3) in the display, replace the batteries. Refer to appendix A for more information. Adjusting the Display Contrast To change the brightness of the display, hold down (C) and ргез$ (+) ог |). Simple Arithmetic Calculations Arithmetic Operators. The following examples demonstrate using the arithmetic operators [+], [=], [x], and [=]. If you press more than one operator consccutively, for example [+] [=] [x] [+], all are ignored except the last one. 1: Getting Started 21 If you make a typing mistake while entcring a number, press [e] to erase the incorrect digits. Keys: Display: Description: 24.71 (+) 62.47 [=] 87.18 Adds 24.71 and 62.47. When a calculation has been completed (by pressing [=]), pressing a number key starts a new calculation. 19 [x] 12.68 [=] 240.92 Calculates 19 x 12.68. If you press an operator key after completing a calculation, the calculation is continued. 115.5 (=) 356.42 Completes calculation of 240.92 + 115.5. You can do chain calculations without using [=] after cach step. 6.9 [x] 5.35 [=] 36.92 Pressing [) displays intermediate result (6.9 x 5.35). 91 [=] 40.57 Completes calculation, Chain calculations are interpreted in the order in which they are entered. Calculate 4 + 9x3. 4 (+) 9 x] 13.00 Adds 4 + 9. 3 [=] 39.00 Multiplies 13 x 3. Negative Numbers. Enter the number and press to change the sign. Calculate -75 = 3. Keys: Display: Description: 75 [+/-] -75_ Changes the sign of 75. [=] 3 =) — 25.00 Calculates result. 22 1: Gotting Started Understanding the Display and Keyboard Cursor The cursor ( _ is visible when you are entering a number. Clearing the Calculator NL. ' When the cursor is on, [+] erases the last digit you entered. 205 oa Otherwise, (+) clears the display and cancels the calculation. —ooce| 90009)! = * & 5 235555 While you are entering a number, pressing [C] clears it to ООО) zero. Otherwise, [€) clears the display of its current contents (e 0009 ——— and cancels the current calculation. Clearing Messages. When the HP-10B is displaying an crror mes- sage, (+) or [C] clears the message and restores the original contents of the display. Refer to “Messages,” on page 133 for a complete list of messages and meanings. Clearing Memory Keys . Description MICLEAR ALL) | Clears all memory. Does not reset modes.* M[CLE Clears statistical memory. * Modes on your HP-10B are number of payments per year (page 52 ), Begin and End (page 53), and the display formats (page 26). 1: Getting Started 23 To clear all memory and reset calculator modes, press and hold down [C], | INPUT Key then press and hold down both [N] and (£+]. When you release all three, all memory is cleared. The ALL CLr message 1s displayed. Annunciators Annunciators are symbols in the display that indicate the status of the calculator. Annunciator Status _+ Shift is active; when a key is pressed, the function labeled in yellow above the key, is executed (below). has been pressed, or two values have been entered or returned (page 25). PEND An arithmetic operator is pending ([+], for exam- ple). BEGIN | Begin mode is active (page 53). = Battery power is low (page 118). Shift Key All of the HP-10B keys have a second or “shifted” function printed in yellow above the key. The yellow shift key (BB) is used to access these functions. | | 00000 900000 ООО! 00000) i) cc) E a a = 206066 When you press ll, the shift annunciator (—2) is displayed 2000 14 indicate that the shifted functions are active. To turn the — annunciator off, press NM again. PP For example, press WM followed by [x?) (also shown M(x?)) to multiply a number in the display by itself. To perform consecutive shifted operations, hold down the shift key while pressing the desired keys. 24 1: Getting Started The [INPUT] key is used to separate two numbers when using two-number functions or two-variable statistics. | il 00000 DOOOOC ша ОИ 9900| The : annunciator is displayed if INPUT] has been pressed. If 99000 a number is in the display, press [C] to erase the : annuncia- 9090000 | : — tor and clear the display. If the cursor or an error message 1s visible in the display, press (C) twice to erase the : annunciator. SWAP Key I — 900006 OOOO Pressing W(SWAP) exchanges the following: m The last two numbers that you entered; for instance, to change the order of division or subtraction. E The results of functions that return two values. The : annunciator indicates that two results have been returned; press [SWAP] to see the hidden result, m The x- and y-values when using statistics. Math Functions | One-Number Functions. Math functions involving one number use the number in the display. 1: Getting Started 25 Keys: Display: Description: 89.25 BE] 9.45 Calculates square root. 3.57 [+] 2.36 M(1/x) 0.42 1/2.36 15 calculated first. [=] 3.99 Adds 3.57 and 1/2.36. - Two-Number Functions. When a function requires two |scocce numbers, the numbers are entered like this: number! SS number2 followed by the operation. Pressing [INPUT] evalu- lo 5050) ates the current expression and displays the : annunciator. = 3559| For example, the following keystrokes calculate the percent = change between 17 and 29. Keys: Display: Description: 17 17.00 Enters number], displays : annunciator. 29 29 Enters number2. B(*CHG) 70.59 Calculates the percent change. Display Format of Numbers Mm | НОО QQ0000 5000 О СС ос O oca © ce When you turn on the HP-10B 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 à 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. Regardless of the current display format, cach number is stored internally as a signed, 12-digit number with a signed, three-digit exponent. 26 1: Getting Started | Specifying Displayed Decimal Places To specify the number of displayed decimal places: 1. Press MDISP). 2. Enter the number of digits (0 through 9) that you wish to appcar after the decimal point. Keys: Display: Description: [С] 0.00 Clears display. M(DISP] 3 0.000 Displays three decimal places. 45.6 [x] .1256 [=] 5.727 | [PERE 5.727360000 Displays nine decimal places. M(DISP]) 2 5.73 Restores two decimal places and rounds number in display. When a number is too large or too small to be displayed in DISP format, it automatically displays in scientific notation, Scientific Notation Scientific notation is used to represent numbers that arc 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 1s 1.00E14, which means “onc times ten to the fourteenth power” or “1.00 with the decimal point moved fourtecn places to the right.” You can enter this number by pressing 1 mE) 14. The E stands for “cxponent of ten.” Exponents can also be negative for very small numbers. The number 0.000000000004 15 displayed as 4.00E - 12, which means “four times ten to the negative twellth power” or “4.0 with the decimal point moved 12 places to the left.” You can enter this number by pressing 4 M(E) (+/-) 12. 1: Getting Started 27 Displaying the Full Precision of Numbers | | ососос нес C0000 К o СЭС) O OOOO e oe Keys: 10 (+) 7 (=) To set your calculator to display numbers as precisely as pos- sible, press M(DISP) [) (trailing zcros are not displayed.) To temporarily view all 12 digits of the number in the display (regardless of the current display format setting), press H(DISP) and hold (=). The number is displayed as long as you continue holding (=). The decimal point is not shown. Start with two decimal places (N(DISP) 2). Display: Description: 1.43 Divides. 142857142857 Displays all 12 digits. BOISP) [=] Interchanging the Period and Comma lbosocel DO0O0O косо а а | не [а | ¡ONDA 2 у J = = To switch betwcen the period and comma (United States and International display) used as the decimal point and digit separator, press M(-/). For example, one million can be displayed as 1,000,000.00 or 1.000.000,00. Rounding Numbers | | coma СОС сев 000900 DOO С) СОС He HO Cao; The calculator stores and calculates using 12 digit numbers. When 12 digit accuracy is not desirable, use (ВКО) 10 round the number to the displayed format before using it in a calcu- lation. Rounding numbers is useful when you want the actual (dollars and cents) monthly payment. 28 1: Getting Started Keys: Display: Description: 9.8/654321 9.87654321 Enters a number with more than two non-zero decimal places. M(DISP) 2 9.88 Displays two decimal places. H(OISP] (=] 987654321000 Displays all digits without the decimal while you press [=]. BAND] 9.88 Rounds to two decimal places (specified by pressing M[DISP) 2). M(DISP]) |=] 988000000000 Shows rounded, stored number. Messages The HP-10B 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 [C] or [+]. Refer to “Messages” on page 133 for a list of meanings. Picturing Memory The available memory in the HP-10B consists of: m Ten business application registers. и А convenient M (memory) register. ® Fifteen registers for storing numbers, cash flows, and summary statistics. 1: Getting Started 29 | P/YR EFF% ir As | | R General Storage R, Summation and Cash Flows Statistics . Ra Numbered Memory Registers You can picture each memory register as a separate box that has a name and can hold onc number at a time. If you store a number in a register, you write over the number that was previously stored there. Notice that 7/YR and NOM% share the same register, and that MAR and MU share the same register. 30 1: Getting Started Business Percentages Y ou can use the HP-10B to calculate simple percent, percent change, Cost, price, margin, and markup. Percent Key !| The (%] key has two functions: finding a percent and adding or subtracting a percent, Finding a Percent The (%] key divides a number by 100 unless it is preceded by an addition or subtraction sign. Example. Find 25% of 200. Keys: Display: Description: 200 [x] 200.00 Enters 200. 25 0.25 Converts 25% to a decimal. [=] 50.00 Multiplies 200 by 25%. 2: Business Percentages 31 Adding or Subtracting a Percent You can add or subtract a percent in one calculation. Example. Decrease 200 by 25%. Keys: Display: Description: 200 (-] 200.00 Enters 200. 25 50.00 Multiplies 200 by 0.25. [=] 150.00 Subtracts 50 from 200. Example. 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? Keys: Display: Description: 1250 [+] 7 87.50 Calculates loan interest. (=) 1,337.50 Adds $87.50 and $1,250.00 to show repay- ment amount. Percent Change oNMNDOO | | 3 then press M(4CHG). Calculate the percent change between two numbers (n, and M», expressed as a percent of ,) by entering ny (INPUT) n3, Example. Calculate the percent change between 291.7 and 316.8. Keys: Display: Description: 291.7 (INPUT 291.70 Enters n,. 316.8 J[%CHG] 8.60 Calculates percent change. 32 2: Business Percentages Example. Calculate the percent change between (12x 5) and (65 + 18). Keys: Display: Description: 12 (x] 5 [INPUT] 60.00 Calculates and enters ny. 65 [+) 18 [% СНС] 38.33 Calculates percent change. Margin and Markup Calculations a The HP-10B can calculate cost, selling price, margin, or markup. Application Keys Description Margin [CST], [PRC], Margin is markup expressed as a percent of price. Markup CST), [PRC], Markup calculations are B{Mu] expressed as a percent of cost. To sec any value used by the Margin and Markup application, press and then the key you wish to sec. For example, to see the value stored as CST), press . Margin and Markup share the same storage register. For example, if you store 20 in [MAR], then press B(MU), you will see 20.00 displayed. Margin Calculations Example. Kilowatt Electronics purchases televisions for $255. The tele- visions are sold for $300. What 1s the margin? Keys: Display: Description: 255 255.00 Stores cost in CST, 300 300.00 Stores sclling price in PRC. 15.00 Calculates margin. 2: Business Percontages 33 Markup on Cost Calculations Example. The standard markup on costume jewelry at Kleiner's Kosmetique 15 60%. They just received a shipment of chokers costing $19.00 each. What is the retail price per choker? Keys: 19 (CST) 60 M(MU) Display: 19.00 60.00 30.40 Description: Stores cost. Stores markup. 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? Keys: 9.6 15 BMY) MAR Display: 9.60 15.00 11.04 13.04 34 2: Business Percentages Description: Stores invoice cost. Storcs markup. Calculates the price on a casc of soup. Calculates margin. J Number Storage and Arithmetic Using Stored Numbers in Calculations Y ou can store numbers, for reuse, in scveral different ways: ® Use [K] (Constant) to store a number and its operator for repetitive operations. 8 Use 3 Key Memory ([+=M], [RM], and (M+]) to store, recall, and sum numbers with a single keystroke. в Use and to store and recall the 15 numbered registers. Using Constants | Use [K] to store a number and arithmetic operator for repeti- tive calculations. Once the constant operation is stored, enter a number and press [=]. The stored operation is performed | on the number in the display. 3: Number Storage and Arithmetic 35 Keys Operation ) number [K] (=) Stores “+ number" as constant. [=] number (К) [=] | Stores “— number” as constant. [x] number [K] [=] Stores “x number" as constant. | & member (K) (=) Stores “+ number" as constant. By) x value (К) >) Stores "y? "aluc” as constant, | [+] number [K] [=] | Stores “+ number %" as constant. [-) number (%] (K) [=] | Stores "— number %" as constant. D) mumber (К) (=) | Stores “x number %'" as constant. [+) mumber (%) [K] [=] | Stores “— mumber %” as constant. Example. Calculate 5 + 2,6 + 2, and 7 + 2. Keys: Display: Description: 5 [+] 2 (K] 2.00 Stores “+ 2" as constant. [=] 7.00 Adds 5 + 2. 6 [=] 8.00 Adds 6 + 2. 7 [=] 9.00 Adds 7 + 2. Example. Calculate 10 + 10%, 11 + 10%, and 25 + 10%. Keys: Display: Description: 10 [+] 10 [%] [K] 1.00 Stores “+ 10%” as con- stant. (=) 11.00 Adds 10% to 10. [=] 12.10 Adds 10% to 11. 25 [=) 27.50 Adds 10% to 25. 35 3: Number Storage and Arithmetic Example. Calculate 2° and 4°. Keys: Display: Description: 2 My") 3 (K] 3.00 Stores “y” as constant. [=] 8.00 Calculates 2°, 4 (=) 64.00 Calculates 4°, Using the M Register | |! The (+>M], [RM], and keys perform memory opcrations DOOGCC/| on a single storage register, called the M register. In most 900000 ‚ © Comeso|| cases, it is unnecessary to clear the M register, since [+M] Io replaces the previous contents. However, you can clear the DCC ein 3 Е : 0000) M register by pressing 0 [+M]. To add a series of numbers = to the M register, use [+M) to store the first number and to add subsequent numbers. To subtract the displaycd number from the number in the M register, press followed by [M+]. Keys Description EN Stores displayed number in the M register. Recalls number from the M register. Adds displayed number to the M register. Example. Use the M register to add 17, 14.25, and 16.95. Then subtract 4.65 and recall the result. Keys: Display: Description: 17 [+M] 17.00 Stores 17 in M register. 14.25 14.25 Adds 14.25 to M register. 16.95 16.95 Adds 16.95 to M register. 3: Number Storago and Arithmetic 37 4.65 - 4,65 Adds - 4.65 to M register, 43.55 Recalls contents of the M register. Using Numbered Registers | || The W(STO] and keys access storage registers Ro MODO | through Rs and R 4 through R 4. (Refer to “Picturing [20000 Memory” on page 29.) The W[STO) key is used to copy the lo HS displayed number to a designated register. The key is | mmol used to copy a number from a register to the display. © ово) To store or recall a number in two steps: 1. Press (ЕТО) ог (ВС). (To cancel this step, press [¢] or [C).) 2. Enter the register number (0 through 9 for registers Ry through Ry or [) 0 through [] 4 for registers R y through R 4). In the following example, two storage registers are used. Calculate the following: 4756. 560.1 + 475.6 39.15 39.15 Keys: Display: Description: 475.6 MISTO] 1 475.60 Stores 475.60 (displayed number) in Ry. [:) 39.15 M(STO) 2 39.15 Stores 39.15 in Rs. =] 12.15 Completes first calculation, 560.1 [+] [RCL] 1 475.60 Recalls R,. =) 2 39.15 Recalls Ro. [=] 26.45 Completes second calculation. You can also use W[STO] and for application registers. For exam- ple, W(STO) (1/YR) stores the number from the display in the [[/YR] regis- ter. (RCL) copies the contents from to the display. 38 3: Number Storage and Arithmetic 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 B(CLEAR ALL). Doing Arithmetic Inside Registers You can do arithmetic inside storage registers Ry through Rg. The result is stored in the register. Keys New Number in Register B(STO] [+] register number | Old contents + displayed number H(STO) (F] register number | Old contents - displayed number | [x] register number B(STO) (=) register number Old contents x displayed number Old contents - displayed number Example. Store 45.7 in Ra, multiply by 2.5, and store the result in Ra. Keys: Display: Description: 45.7 BISTO) 3 45.70 Stores 45.7 in Ra. 2.5 H(STO) (x) 3 2.50 Multiplies 45.7 in R3 by 2.5 and stores result 3 114.25 Displays Rs. 3: Number Storage and Arithmetic 39 Doing Arithmetic — Math functions operate on the number in the display. Example. Calculate 1/4, then calculate Y 20 + 47.2 + 1.1%. Keys: 4 M(17:) 2 47.2 1.1 Ml?) E Display: 0.25 4.47 51.67 1.21 52.88 Description: Calculates the reciprocal of 4. Calculates v/ 20. Calculates V20 + 47.20. Calculates 1.12. Completes the calcula- tion. Example. Calculate natural logarithm (e**). Then calculate 790 + 4! Keys: 2.5 Pe”) BLN) 790 [+] 4 Mini |= Display: 12.18 2.50 24.00 814.00 40 3: Number Storage and Arithmetic Description: Calculates e*>. Calculates natural loga- rithm of the result. Calculates 4 factorial. Completes calculation. == Power Operator The power operator, B[y*], raises the preceding number (y- value) to the power of the following number (x-value). Example. Calculate 125° then find the cube root of 125. Keys: Display: 125 8077 3 (=) 1,953,125.00 125 My) 3 M(1/x) (=) 5.00 Description: Calculates 125°, Calculates cube root of 125, which is the same as 125173, Using Parentheses in Calculations Use parentheses to postpone calculating an intermediate result until you've entered more numbers. For example, suppose you want to calculate 30 If you enter 30 (+) 85 [=], 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 sub- tracted 12 from 85, use parentheses. Closing parentheses at the end of the expression can be omitted. For example, entering “25 — (3 x (9 + 12 =” is equivalent to “25 + (3 x (9 + 12)) =”. 9 3: Number Storage and Arithmetic 41 Keys: Display: 30 (=) M 85 (7) 85.00 12 M0] 73.00 [x] 0.41 9 [=] 3.70 42 3: Number Storage and Arithmetic Description: No calculation yet. Calculates 85 = 12. Calculates 30 = 73. Multiplics the result by 9. Picturing Financial Problems How to Approach a Financial Problem The financial vocabulary of the HP-10B is simplificd to apply to all finan- cial fields. For example, your profession may use the term balance, bal- loon payment, residual, matunty value, or remaining amount to designate a valuc that the HP-10B knows as (future value). The simplified terminology of the HP-10B 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. 4: Picturing Financial Problems 43 Up-arrows represent positive The horizontal line represents time. It 1s divided into regular periods, 5,000.00 1 | 2 | 3 14 Down-arrows represent negative Y - 9000.00 cash flows (money paid out). Y - 6,000.00 - 7,000.00 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. Signs of Cash Flows In cash flow diagrams, money invested is shown as negative and money withdrawn is shown as positive. Cash lowing 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. A4 4: Picturing Financial Problems Periods and Cash Flows In addition to the sign convention (cash flowing out is ncgative, cash flowing in is positive) on cash flow diagrams, there are several more considerations: m 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. m To solve a financial problem with the HP-10B, all cash flows must occur at either the beginning or end of a period. E If more than onc cash flow occurs at the same place on the cash flow diagram, they arc 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). w À 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 carns interest over time. There are two types of interest: simple interest and compound interest. The basis for Time Value of Money and cash flow calculations is compound interest. Simple Interest In simple-interest contracts, interest 15 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 15 10% of 500). Simple interest calculations are donc using the [%) key on your HP-10B. An example of a simple interest calculation is on page 97. 4: Picturing Financlal Problems 45 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 onc compounding period. At the end of cach period the interest carned on cach 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 15 1/,% of 1,000). The second month, the same proccss takes place on the new balance of $1,005.00. The amount of interest paid at the end of the second month 15 1 /5% of $1,005.00, ог $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, 1,005.00 1 1,010.03 -1,000.00 -1,005.00 4 1,025.26 -1,020.16 The word compound in compound interest comes from the idea that interest previously carned or owed is added to the principal. Thus, it can earn more interest. The financial calculation capabilities on the HP-10B are based on compound interest. 46 4: Picturing Financial Problems 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: ® As a periodic rate. This is the rate that is applied to your money from period to period. m As an annual nominal rate. This is the periodic rate multiplied by the number of periods in a year. m As an annual effective rate. This is an annual rate that considers com- pounding. In the previous example of a $1,000.00 savings account, the periodic rate is 1/,% (per month), quoted as an annual nominal rate of 6% (1/2 x 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 arc on pages 71 through 72. — 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 and 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 arc five main keys used to solve a TVM problem. 4: Picturing Financial Problems 47 Number of periods or payments. Annual percentage interest rate (usually the annual nomi- nal rate). Present value (the cash flow at the beginning of the time line). Periodic payment. 38 5 6° = 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. 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, $75,000.00 mortgage, with a pay- ment of $-684.07, at 10.5% annual interest, with a $5,000 balloon pay- ment. PV = 75,000.00 I/YR = 10.5% N = 360 (30 x 12) TTL TTL 8399 3 РМТ = - 684.07 1 2 3 FV = - 5,000.00 | 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. 48 A: Picturing Financial Problems FV = 25 327.38 I/YYR = 8.00% PMT = 0.00 1 2 3 4 5 66 . 57 58 59 60 N = 60 PV = -17,000.00 Y Time value of money calculations are described in the next chapter. Recognizing a Cash Flow Problem A financial problem that docs not have regular, uniform payments (some- times called uneven cash flows) is a cash flow problem rather than a TVM problem. A cash flow diagram for an investment in a mutual fund follows. This is an example of a problem that is solved using cither W(NPV) (Net Present Value) or B(IRR/YR] (Internal Rate of Return per Year). 4: Picturing Financial Problems 49 16,567.20 5,000.00 444444445441 | Time Value of Money Calculations 5,000.00 Using the TVM Application y - 6,000.00 Y The time value of money (TVM) application is used for com- + pound 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. -7,000.00 Y Cash flow problems are described in chapter 6. To use TVM, several prerequisites must be met: m The amount of cach payment must be the same. If the payment amounts vary, usc the procedures described in chapter 6, “Cash Flow Calculations.” @ Payments must occur at regular intervals. m The payment period must coincide with the interest compounding period. (If it does not, convert the interest rate using the H(NOM%), MEFF%), and M(P/YR) keys described on page 71.) m There must be at least one positive and one negative cash flow. 50 4: Picturing Financial Problems 5: Time Value of Money Calculations 51 Key Stores or Calculates Cle aring TVM The number of payments or compoundin periods РОУ P J Press M[CLEAR ALL) to clear the TVM registers, This sets N, 7/YR, PY, PMT, and FV to zero and bricfly displays the current value in P/YR. The annual nominal interest rate. PV The present value of future cash flows. PV is usually an initial investment or loan amount and B egin and End Modes _ always occurs at the beginning of the first period. PMT The amount of periodic payments. All payments are equal, and none are skipped; payments can | | Before you start a TVM calculation, identify whether the occur at the beginning or end of each period. (200000) [irst periodic payment occurs at the beginning or end of the FUI The future value. FV is ekher a final cash flow or ONO first period. If the first payment occurs at the end of the first "y compounded value of a serios of previous cash 0 0000) period, set your HP-10B to End mode; if it occurs at the flows. FV occurs at the end of the last period. LEE beginning of the first period, set your calculator to Begin mode. B(P/YR Stores the number of periods per year. The default Is 12. Reset only when you wish to change. To switch between modes, press M[BEG/END). The BEGIN annunciator is displayed when your calculator is in Begin mode. No annunciator 15 B(xP/YR] Optional shortcut for storing N: Number in display displayed when you are in End mode. is multiplied by the value in P/YR and stores result | | in N. Mortgages and loans typically use End mode. Leases and savings plans typically use Begin mode. HB (BEG/END] Switches between Begin and End mode. In Begin mode, the BEGIN annunciator is displayed. B{AMORT) Calculates an amortization table. В Ш Loan Calculations To verify values, press (RCL) (N), (RCL) (i/YR), (РМ), [PMT), and | Example: A Car Loan. You arc financing a new car with a three year [EV]. Pressing MGF/YA) recalls the total number of payments | loan at 10.5% annual nominal interest, compounded monthly. The price in ycars and B(P/YR] shows you the number of payments per year, of the car is $7,250. Your down payment is $1,500. Recalling these numbers does not change the content of the registers. 5 5 > 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.) 52 5: Time Value of Money Calculations 5: Time Value of Money Calculations 53 PV = 7,250 - 1,500 A I/YR = 10.5% N=3x12 P/YR = 12 РМТ = ? End Mode Set to End mode. Press WM(BEG/END] if BEGIN annunciator is displayed. Keys: Display: Description: 12 MP/YR) 12.00 Sets periods per year. 3 (х) 12 (№ 36.00 Stores number of periods in loan. 10.5 10.50 Stores annual nominal interest rate. 7250 [-] 1500 5,750.00 Stores amount borrowed. О [РУ] 0.00 Stores the amount left to pay after 3 years. - 186.89 Calculates the monthly payment. The negative sign indicates money paid out. Part 2. At a pricc of $7,250.00, what interest rate is necessary to lower your payment by $10.00, to — 176.89? 10 -176.89 Decreases payment from - 186.89. 6.75 Calculates annual interest rate for the reduced payment. 54 5: Time Value of Money Calculations Part 3. If interest 1s 10.5%, what is the maximum you can spend on the car to lower your car payment to $175.00? 10.5 (1/YR 10.50 Stores original interest raic. 175 +7] — 175,00 Stores desired payment, [PV] 5,384.21 Calculates amount of money to finance. 1500 [=] 6,884.21 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 $630.00. You can make a $12,000 down payment, and annual interest rates are currently 11.5%. If you obtain a 30 year mortgage, what is the maximum purchase price you can afford? I/YR = 11.5% N=30x12 P/YR = 12 [= [= [= [==] PMT = - 630.00 End Mode Set to End mode, Press M(BEG/END) if BEGIN annunciator is displayed. Keys: 12 M(P/YR) Display: Description: 12.00 Sets periods per year. 5: Time Value of Money Calculations 55 360.00 Stores the length of the | Set to End mode. Press M(BEG/END) if BEGIN annunciator is displayed. mortgage (30 x 12). K Disnl Descripti eys. 5 . . 0 [FV] 0.00 Pays mortgage off in 30 ye may евепрной years. 12 MP/YR) 12.00 Sets periods per year. 11.5 |! 11.50 Stores interest rate. 25 M(xP/YA) 200.00 Stores length of mortgage 630 [+/-) (РМТ) — 630.00 Stores desired payment (25 x 12 = 300 months). (money paid out is 0 0.00 Stores loan balance after negative). 25 ycars. 63,617.64 Calculates the loan you | 79500 72.500.00 Stores original loan can afford with a $630 balance. payment, : 13.8 (1/YR] 13.80 Stores annual interest 12000 [=] 75,617.64 Adds $12,000 down rate. ayment for the total purchase price. - 861.65 Calculates monthly payment. Example: A Mortgage With a Balloon Payment. You've obtained . a 25 ycar, $72,500 mortgage at 13.8% annual interest. You anticipate that Step 2. Since the payment is at the end of the month, the last payment you will own the house for four years and then sell it, repaying the loan and the balloon payment occur at the samc time. The final payment is the with a balloon payment. What will your balloon payment be? sum of PMT and FV. Solve this problem using (wo steps: PV = 72,500.00 1. Calculate the loan payment using a 25 year term. A 2, Calculate the remaining balance after 4 years. Step 1. First calculate the loan payment using a 25 year term. I/YR = 13.8% № = 4х 12 РМ = 72,500 PTR = 12 A 1 2 3 4 1/YR = 13.8% у № = 25 х 12 P/YR = 12 | as PMT = - 861.65 - > 299 200 End Mode Y PMT = 7 End Mode 56 5: Time Value of Money Calculations 5: Time Value of Money Calculations 57 I Ji The value in PMT should always be rounded to two decimal 000800 fr : . 500000 places when calculating FV or PV to avoid small, accumula icoooom| tive discrepancies between non-rounded numbers and actual boooc ; . == (dollars and cents) payments. If the display is not set to two 5 Sood) decimal places, press W(OISP) 2. Keys: Display: Description: HAND) -861.65 Rounds payment to two decimal places, then stores. 48 [№ 48.00 Stores 4 year term (12 x 4) that you expect to own house. [FV] - 70,725.90 Calculates loan balance after 4 years. [=] - 71,587.55 Calculates total 48th payment (PMT and FV) 10 pay off 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 53,000? 58 5: Time Value of Money Calculations I/YR = 7.2% N =? P/YR = 1 PV = - 2,000.00 ER € РМТ = 0 РУ = 3,000.00 Since this account has no regular payments (PMT = 0), the payment mode (End or Begin) is irrelevant. Keys: M(CLEAR ALL 1 B(P/YA) 2000 (+7-) 3000 7.2 Display: 12 P Yr 0.00 1.00 —2,000.00 3,000.00 7.20 5.83 Description: Displays a temporary message and clears all registers. Sets P/YR to 1 since interest 1s compounded annually. Stores amount paid out for first deposit. Stores the amount you wish to accumulate. Stores annual interest rate. Calculates number of years it takes to reach $3,000. 5: Time Value of Money Calculations 59 Since the calculated value of N is between 5 and 6, 1t 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. 6 [N) 6.00 3,035.28 Sets [N] to 6 ycars. Calculates amount you can withdraw after 6 years. Example: An Individual Retirement Account. You opened an individual retirement account on April 15, 1985, with a deposit of $2,000. Thereafter, you deposit $80.00 to the account at the end of cach half- month, The account pays 8.3% annual interest compounded semimonthly. How much will be in the account on April 15, 2000? FV = 7 I/YR = 8.3% N = 360 (15 years x 24 half-months) P/YR = 24 (Hall-month periods) 360 Y PV = -2,000.00 Set to End mode. Press M[BEG/END) if BEGIN annunciator is displayed. Keys: Display: Description: 24 M(P/YR] 24.00 Sets number of periods per year. 2000 [+/-) (PV) - 2,000.00 Stores initial deposit. 60 5: Time Value of Money Calculations | 80 (57) (РМТ) - 80.00 Stores regular semi- monthly deposits. 8.3 8.30 Stores interest rate. 15 BxP/YR) 360.00 Stores number of deposits. 63,963.84 Calculates balance. Example: An Annuity Account. You opt for an carly retirement after a successful business carcer. You have accumulated a savings of $400,000 that carns an average of 10% 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? РМТ = ? 1 2 599 600 I/YR = 10% РУ = 0 № = 600 (50 х 12) у P/YR = 12 PV = - 400,000.00 Begin Mode Set to Begin mode. Press W(BEG/END) if annunciator is not displayed. Keys: Display: Description: 12 B[P/YR) 12.00 Sets payments per year. 400000 [+/-} -400,000.00 Stores your nest egg as an outgoing deposit. 10 (1/YR) 10.00 Stores annual interest rate vou expect to carn, 5: Time Value of Money Calculations 61 50 B[xP/YR) 600.00 Stores number of withdrawals. 0 0.00 Stores balance of account alter 50 years. 3,328.68 Calculates amount that you can withdraw at the beginning of cach month. Lease Calculations A lcase 1s a loan of valuable property (like real estate, automobiles, or equipment) for a specific amount of time, in exchange for regular pay- ments. 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 TYM application keys can be used in lease calculations. There arc lwo common lease calculations. m Finding the Icase payment necessary to achieve à specified yield. ® Finding the present value (capitalized valuc) of a leasc. 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 14% annually, compounded monthly, what will the payments be? Calcu- late the payments from your (the dealer's) point of view. 62 5: Time Value of Money Calculations FV = 7,500.00 PMT = 7 Money received by lessor is 1 2 35 36 positive. I/YR = 14% N = 36 Money paid out P/YR = 12 by lessor is Y negative. PV = - 13,500.00 Begin Mode Set to Begin mode. Press M[BEG/END) if annunciator is not displayed. Keys: Display: Description: 12 M(P/YR) 12.00 Sets payments per year. 14 14.00 Stores desired annual yield. 13500 -13,500.00 Stores lcasc price. 7500 7,500.00 Stores residual (buy out value). 36 (N) 36.00 Stores length of lease, in months. PMT 289.19 Calculates 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 Polc Barns, plans to lease a forklift for the warehouse. The lease is wrilten for a term of 4 ycars 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. 5: Time Value of Money Calculations 63 If the annual interest rate 1s 18%, what is the capitalized value of the lease? Begin Mode N =? I/YR = 18% N = 48 P/YR = 12 | , | y 1 2 3 4 44 45 46 47 48 Y Y Y Y Y Y PMT = - 2,400.00 | } (48th payment due up front) FV = -15,000.00 This solution requires four steps. 1. Calculate the present value of the 47 monthly payments: (4 х 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 [J[BEG/END] if annunciator is not displayed. Keys: Display: Description: 12 M(P/YR] 12.00 Sets payments per year. 47 [N] 47.00 Stores number of payments. 2400 [+/-) [PMT - 2,400.00 Stores monthly payment, 64 5: Time Value of Money Calculations 0 0.00 Stores FV for step 1. 18 18.00 Stores interest rate. (PV) 81,735.58 Calculates present value of 47 monthly payments. Step 2. Add the additional advance payment to PV. Store the answer. Adds additional advance =] 84,135.58 payment. [+M] 84,135.58 Stores result in M register. Step 3. Find the present value of the buy option. 48 [№ 48.00 Stores month when buy option occurs. 0 0.00 Stores zero payment for this step of solution. 15000 - 15,000.00 Stores value to discount. [РУ] 7,340.43 Calculates present value of last cash flow. Step 4. Add the results of steps 2 and 3. Keys: (+) [RM] [=] Display: Description: 91,476.00 Calculates present (capitalized) value of lease. (Rounding discrepancies are explained on page 58.) 5: Time Value of Money Calculations 65 Amortization 1 "| Amortization is the process of dividing a payment into the 200089 amount that applies to interest and the amount that applies 000000} à a 4 a aca | to principal, Payments ncar the beginning of a loan DOOOO| contribute more interest, and less principal, than payments EEES) near the end of a loan. PAYMENT $ fro THEE HH IH HESS aan ТИ HH el! | PRINCIPAL $ | 3 Hi CHEE HHT SI it TS qi Prin |} HHH HT Hi HHH EAS ИНН 14 A 1 LEPE ME ERE a EJ GH HEE Nd TE TE HEHE EE INU HH AARNE RARER AERA RRR PROFES 11| HR EE HE EERE EE НИНА EEE EEreNIEE| BLYERE HT interest si NE Cri HN HE SRRRRERERRE RARE ERAN Tilt IU ENAAES bpp HT HE TIME — The B{AMORT] key on the HP-10B allows you to calculate. ® The amount applied to interest in a range of payments. m The amount applied to principal in a range of payments. m The /oan balance alter a specified number of payments are made. 66 5: Time Value of Money Calculations The MAMORT) function assumes you have just calculated a payment or you have stored the appropriate amortization values in 7/YR, PV, PMT, and P/YR, 1/YR Annual nominal interest rate. [PV] Starting balance. [PMT] Payment amount (rounded to the display format). BP/YR 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 [INPUT], then press MLAMORT). The HP-10B displays the message PEr followed by the starting and ending payments that will bc amortized. Hold [=] down to display the label of the value that you are about to view. Press (=) to see interest (Int). Press [=] again to see the principal (Prin) and again to sec the balance (DAL). Continue pressing [=] to cycle through the same values again. To amortize a range of payments, enter starting period number [INPUT] ending period number, then press IH[AMORT]. The HP-10B displays the message PEr followed by the starting and ending payments that will be amortized. Then press [=] repeatedly to cycle through interest, principal, and balance. Press MLAMORT) 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. If you store, recall, or perform any other calculations during amortization, pressing [=] will no longer cycle through interest, principal, and balance. To resume amortization with the same set of periods, press MAMORTJ. 5: Time Value of Money Calculations 67 Example: Amortizing a Range of Payments. Calculate the first Amortize the second year: two years of the annual amortization schedule for a 30 year, $80,000 mortgage, at 9.75% annual interest with monthly payments. BAMORT PEr 13-24 Displays next range of | o periods. Set to End mode. Press M[BEG/END) if BEGIN annunciator is displayed. © Int Displays interest paid in Keys: Display: Description: = 1,731.67 second ycar. [=] Prin Displays principal paid in 12 M(P/YR) 12.00 Sets paymenis per year. -516.17 second year, 30 360.00 Stores total number of | (=) bAL Displays loan balance payments. 79,015.41 after 24 payments. 9.75 9.75 Stores interest per year. UNA) AA The amount paid toward interest and principal (7,731.67 + 516,17 = 80000 [PY] 80,000.00 Stores present valuc. 8,247.84) equals the total of 12 monthly payments (12 x 687.32 = 0 (EV) 0.00 Stores future value, 8,247.84). The remaining balance equals the initial mortgage less the PR -687 32 Calculates monthly amount applied toward principal (80,000 - 468.42 - 516.17 = 79,015.41). payment. More money is applied to principal during the second rather than the first year, The succeeding years continue in the same fashion. 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, Example: Amortizing a Single Payment. Amortizc the 1st, 25th, and 54th payments of a five year car lease. The lease amount is $14,250 1 (NFUTI2 12 Enters starting and and the interest rate is 11.5%. Payments are monthly and begin Ш ending periods. immediately, MAMORT) PEr1- 12 Displays range. Set to Begin mode, Press if annunciator is not displayed. [=] int Displays label, then -7,779.42 interest paid the first Keys: Display: Description: year 12 M(P/YR) 12.00 Sets payments per year. [=] Prin Displays label, then 5 MGP7VAI 60.00 . ber of -468.42 principal paid the first Stores number © year. payments, 11.5 11.50 Stores interest per year, 5) DAL Displays label, then loan | 14250 [PY] 14,250.00 Stores present value, 79,531.58 balance after one year. — | 0 (FY) 0.00 Stores the future value. The amount paid toward interest and principal (7,779.42 + 468.42 = ~310.42 Calculates monthly 8,247.84) equals the total of 12 monthly payments (12 x 687.32 = payment. 8,247.84). The remaining balance equals the initial mortgage, less the amount applied toward principal (80,000 - 468.42 = 79,531.58). 68 5: Time Value of Money Calculations | 5: Time Value of Money Calculations 69 Amortize the 1st, 25th, and 54th payments. 1 (INPUT) B(AMORT) E] EJ (=) 25 M(AMORT] E) (=) =) 54 [INPUT] B(AMORT) =) (=) 1.00 РЕГ 1 - 1 Int 0.00 Prin — 310.42 bAL 13,939.58 25.00 PEr 25- 25 Int - 90.21 Prin -220.21 bAL 9,193.28 54.00 PEr 54- 54 Int -20.05 Prin -290.37 bAL 1,801.57 70 5: Time Value of Money Calculations Enters first payment. Displays amortized payment period. Displays interest. Displays first principal payment. Displays loan balance after one payment. Enters payment to amorlize, Displays amortized payment period. Displays interest paid on 25th payment. Displays principal paid on 25th payment. Displays balance after 25th payment. Enters payment to amortize. Displays amortized payment period. Displays interest paid on 54th payment. Displays principal paid on 54th payment. Displays balance after Sáth payment. Interest Rate Conversions | || The Interest Conversion application uses three keys: 888. ООС MNOM%) , Ш ЕРР%] , and M(P/YA) . They convert between 0000| nominal and annual effective interest rates. Nominal and DEE | effective interest rates arc described on page 47. O 0000 сос If you know an annual nominal interest rate and you wish to solve for the corresponding annual eflective rate: 1. Enter the nominal rate and press (№М%). 2. Enter the number of compounding periods and press M(P/YR). 3. Calculate the effective rate by pressing (ЕРР%). To calculate a nominal rate from a known effective rate: 1. Enter the cffective rate and press [J[EFF%). 2. Enter the number of compounding periods and press (Р/УА). 3. Calculate the nominal rate by pressing W(NOM%]). In the TVM application, N(NOM%) and share the same register. Interest conversions are used primarily for two types of problems: m Comparing investments with different compounding periods. m Solving TVM problems where the payment period and the interest period differ. Investments With Different Compounding Periods Example: Comparing Investments. You arc considering opening a savings account in onc of three banks. Which bank has the most favorable interest rate? 5: Time Value of Money Calculations 71 First Bank Second Bank Third Bank First Bank. Keys: 6.7 B(NOM%) 4 MP/YA) MEFF%) Second Bank. 6.65 BNOM%] 12 MIP/YR) B(EFF%] Third Bank. 6.63 H[NOM%] 360 W[PLYR] MEFF%) 0.70% annual interest, compounded quarterly, 6.65% annual interest, compounded monthly. 6.63% annual interest, compounded 360 times per year. Display: 6.70 4.00 6.87 6.65 12.00 6.86 6.63 360.00 6.85 Description: Stores nominal rate. Stores quarterly com- pounding periods. Calculates annual effective rate. Stores nominal rate. Stores monthly com- pounding periods. Calculates annual effective rate. Stores nominal rate. Stores compounding periods. Calculates annual effective rate. First Bank offers a slightly better deal since 6.87 is greater than 6.86 and 6.85. 72 5: Time Value of Money Calculations Compounding and Payment Periods Differ assco| and the payment periods are the same, Some loan install Soooo| ments or savings deposits and withdrawals do not coincide 9999| with the bank's compounding periods. If the payment period 95533 differs from the compounding period, adjust the interest rate 2777) to match the payment period before solving the problem. — y The TVM application assumes that the compounding periods ни To adjust an interest rate when the compounding period differs from the payment period complete the following steps: 1. Enter the nominal rate and press W[NOM%). Enter the number of compounding periods in a year and press J[P/YR). Solve for the effective rate by pressing M[EFF%). 2. Enter the number of payment periods in a ycar and press M[P/YR]. Solve for the adjusted nominal rate by pressing W[NOM%]). 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. Keys: Display: Description: 5 B(NOM%) 5.00 Stores nominal per- cenlage rate. 365 M(P/YR) 365.00 Stores bank's compound- ing periods per year. BEFF%] 5.13 Calculates annual effective rate. 12 (Р/УВ) 12.00 Stores monthly periods. B(NOM%) 5.01 Calculates equivalent nominal percentage rate for monthly compounding. Since NOM % and I/YR share the same register, this value is ready for use in the rest of the problem. 5: Time Value of Money Calculations 73 Step 2. Calculate the future value. Set to Begin mode. Press M(BEG/END] if annunciator is not displayed. 0 (РУ) 0.00 25 -25.00 7 B(xP/YR) 84.00 [FV] 2 519.61 74 5: Time Value of Money Calculations Stores present value. Stores payment, Stores number of pay- ments per year. Calculates balance alter 7 years. Cash Flow Calculations How to Use the Cash Flow Application = i| The cash flow application 15 used to solve problems where овово cash flows occur over regular intervals but are of varying coool amounts. You can also use cash flow calculations to solve ВОС problems with regular, equal, periodic cash flows, but these 2099 situations arc handled more casıly using TVM. + In general, these are the steps for cash flow calculations on the HP-10B. 1. Organize your cash flows on paper —a cash flow diagram 1s uscful. 2. Clear the registers. 3. Enter the number of periods per year. 4. Enter the amount of the initial investment. 5. Enter the amount of the next cash flow. 6. If the amount entered in step 5 occurs more than once consecutively, enter the number of times it occurs. 7. Repeat steps 5 and 6 for each cash [low and group. 8. To calculate net present value, enter the annual interest rate and press (1/YR); then press [№У). Or, to calculate annual internal rate of return, press ВА/УА). Example: 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. 6: Cash Flow Calculations 75 11,765.29 p Keys: M(CLEAR ALLI 12 M(P/YR) 5000 [+/-] (СЕ) 2000 [+/-] (CF) 4000 [+/-] (CFj) 11765.29 B(RR/YR] E) 12 (5) Display: 0.00 12.00 CFO -5,000.00 CF 1 -2,000.00 CF 2 — 4,000.00 CF3 11,765.29 38.98 3.25 76 6: Cash Flow Calculations Y Flows receivad | are positive. Flows paid out are negative, Description: Clears all registers. Stores periods per year, Enters initial cash flow. Displays cash flow group number while you hold down [CF]. Enters next cash [low. Enters next cash flow. Enters final cash flow. Calculates annual nominal yield, Monthly yield. NPV and IRR/YR: Discounting Cash Flows Chapter 4 demonstrates the use of cash flow diagrams to clarify financial problems. This section describes discounted cash flows. The NPV 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 à series of cash flows. The annual nominal interest rate must be known to calculate NPV, The internal rate of return (JRR/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 and IRR/YR calculations follow. Organizing Cash Flows The cash flow series is organized into an initial cash flow (CF 0) and succeeding cash flow groups (up to 14 cash flows). CF 0 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 (lows of zero cach, followed by a group of three $1,000 cash flows. The final group consists of one $10,000 cash flow. 6: Cash Flow Calculations 77 CF 3 = 10,000, №3 = 1 CF 2 = 1,000, N2 = 3 F 1 CF1=0 N1=6 10 CFO = -11,000 Whenever you enter à scries of cash flows, it is important to account for every period on the cash flow diagram, even periods with cash flows of zero. Entering Cash Flows The HP-10B can store an initial cash [low plus 14 additional cash flow groups. Each cash flow group can have up to 99 cash flows. The cash flows arc stored in registers Ro through Ro and R 5 through Ry. Enter cash [lows using the following steps: 1. Press W[CLEAR ALL} to clear the registers. 2. Enter the number of periods per year and press M(P/YR]. 3. Enter the amount of the initial investment, then press (CF). (The de PP 7” stands for the cash flow “number,” 0 through 14.) 4. Enter the amount of the next cash flow and press [CFj]. 5. If the amount entered in step 4 occurs more than once consecutively, enter the number of times il occurs, and press M(Nj). 6. Repeal steps 4 and 5 for cach and BIN) until all cash flows have been entered. 78 6: Cash Flow Calculations Example. Enter the cash flows from the preceding diagram and calcu- late the JRR/YR. Then calculate the effective interest rate, Assume there are 12 periods per year. Keys: Display: Description: M(CLEAR ALL] 0.00 Clears all registers. 12 M(P/YR) 12.00 Sets to 12. 11000 [+/-) [СЕЛ CFO Enters initial cash flow. - 11,000.00 Displays cash flow group number for as long as you hold down (CFj]. 0 [CF] CF 1 Enters first cash flow 0.00 group amount. 6 (№ ni Enters number of 6.00 repetitions. 1000 (СЕ) CF 2 Enters second cash flow 1,000.00 group amount, n2 Enters number of 3.00 repetitions, 10000 (CF1] CF 3 Enters final cash flow. 10,000.00 ВАЛУА) 21.22 Calculates annual nominal yield. Viewing and Replacing Cash Flows To view a cash flow list press the following: 1. [RCL] 0 to see the initial cash flow. 2. [RCL] [CF]) to see the next flow. 3. EN) to sec the number of times the cash flow occurs. Repeat steps 2 and 3 until all cash flows are reviewed. You can also view cash flows individually by pressing [RCL), followed by a register number. Register numbers coincide with cash flow numbers. For example, press 4 to see cash flow 4, then [NJ] to see the number of consecutive occurrences. 6: Cash Flow Calculations 79 To replace a cash flow, enter the new cash flow and press (СТО) followed by the cash flow (register) number. To replace the number of times a particular cash flow occurs, [RCL] the cash flow whose number of occurrences will change. Then, enter the number of times it occurs and press (№). To replace both the cash flow and number of times it occurs, enter the new cash flow, press N(STO) followed by the cash flow (register) number. Then enter the number of times it occurs and press MÍN). Since cash flows cannot be deleted or inserted, use [CLEAR ALL) to start over. Calculating Net Present Value The net present value (NPV) function is used to discount all cash [lows to the front of the time line using an annual nominal interest rate that you supply. These steps describe how to calculate [NPV]: 1. Press J[CLEAR_ALLJ, store number of periods per year in P/YR. 2. Enter the cash flows using [CF]] and (NJ). 3. Store the annual nominal interest rate in //YR and press M(NPV). Example: A Discounted Contract, Uneven Cash Flows. You have an opportunity to purchase a contract with the following cash flows: End Of Month Amount $ 5,000.00 $ 5,000.00 10 $ 5,000.00 15 $ 7,500.00 25 $10,000.00 How much should you pay for the contract if you wish to yield a yearly rate of 15% on your investment? 80 6: Cash Flow Calculations I/YYR = 15% Keys: M(CLEAR ALL) 12 B(P/YR] 0 [CF]] 0 (CF) 3 MND 5000 0 [СЕ] 4 (№ 5000 2 BN] 9 10 Display: 0.00 12.00 CFO 0.00 CF 1 0.00 ni 3.00 CF 2 5,000.00 CF 3 0.00 na 4.00 CF 4 5,000.00 ná 2.00 10,000 25 Description: Clears registers. Sels payments per year. Enters initial cash flow of zero. The cash flow number is displayed as long as you hold down the [CF]) key. Enters first cash flow. Enters number of occurrences. Enters second cash flow. Enters third cash flow. Enters number of occurrences. Enters fourth cash flow. Enters number of occurrences. 6: Cash Flow Calculations Bi 0 CF5 Enters fifth cash flow. 0.00 4 №) nd Enters number of 4.00 Occurrences. 7500 [CF]) CF 6 Enters sixth cash flow. 7,500.00 0 [СЕ] CF 7 Enters seventh cash 0.00 flow, 9 BN] п? Enters number of 9.00 Occurrences. 10000 [CF]) CF8 Enters next cash flow. 10,000.00 The cash flows that describe your prospective investment are now in the calculator. You can press 0, followed by [CF]) and Now that you have entered the cash flows, store the interest rate and calculate the net present value. Keys: Display: Description: 15 15.00 Stores annual interest rate. BNP V 27,199.92 Calculates net present value of stored cash flows. (See rounding example on page 58.) 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 linc. 82 6: Cash Flow Calculations B(Nj), repeatedly to view the cash flows and number of times cach occurs. NPV = 27,189.92 o ev a. = — о 6,224.95 — ZZ 1% = 15% per year Dan 4,415.91 > Das Ä 10,000.00 4471.10 À vtt 7,500.00 e" O ——— 5,000.00 4,757.62 i 3 5 7 9 11 13 15 17 19 21 23 25 Calculating internal Rate of Return 1. Press M[CLEAR ALL), store number of periods per year in P/YR. 2. Enter the cash flows using [CF]) and (Ni). 3. Press MIIRA/YR). When you calculate IRR/YR, you get the annual nominal rate thal gives an NPV of zero. The following example uses the cash flows that were entered in the previous example, More than one JRR/YR can exist. If you get the no Solution message sce Appendix B (page 127). Example. If the seller of the contract in the previous example wants $28,000 and you accept that price, what is your yield? This is an JRR/YR calculation that requires a slight modification to the currently stored cash flows. 6: Cash Flow Calculations 83 10,000 5,000 7,500 4444 | 1 3 668 7 9 11 13 15 17 19 21 23 25 IRR/YR = ? -28,000 Кеуз: Display: Description: 28000 (*/-) M(STO) O -28,000.00 Changes initial cash How. B(RR/YR] 12.49 Calculates annual nomi- nal yicld. More examples that use NPV and IRR/YR calculations arc given in chapter 8, “Additional Examples.” Statistical Calculations Automatic Storage of IRR/YR and NPV When you calculate NPV, the result is stored in PV for your convenience. To recall that result, press [PV]. If you haven't changed the TVM values from the last example using NPV (page 82), when you press the result is 27,199.92. When you calculate IRR/YR, the result is also stored in //YR. For the previous example, press lo display the annualized yield 12.49. 84 6: Cash Flow Calculations ipoooco CCOO | | LF ООО Dammam) С В 99 69 Г) || 0) | coed The and M(E-) keys are used to enter and delete data for onc- and two-variable statistics. Summation data is accumu- lated in registers Ry through Re. The register labels at the lower right of the keys indicate what statistical data 15 stored in each register. Once vou enter the data, you can usc the statistical functions to calculate the following: m Mcan and standard deviation. mM Lincar regression statistics. E Lincar estimation and forccasting, ® Weighted mean, » Summation statistics: n, x, Ex”, Ey, 7, and Exy. Clearing Statistical Data Le... wd] 220000 CODO 20000 Doooc [5 300 (2 SOCIE 0000 Clear the statistical registers before entering new data so that R, through R, arc zero when you begin, If you don’t clear the registers, data currently stored in Rs through Rg is auto- matically included in the summation calculations. To clear the statistical registers, press . The display is also cleared. 7: Statistical Calculations 85 Entering Statistical Data There is no limit to the number of values you can accumulate in the statistical registers. * One-Variable Statistics To enter x data for one-variable statistics complete the following steps: 1. Clear the contents of R¿ through Ro by pressing M[CL E). 2. Enter the first value and press [£+). The HP-10B displays n, the number of items accumulated. 3. Continue accumulating values by entering the numbers and pressing [2+]. The n-value is incremented with cach entry. Two-Variable Statistics and Weighted Mean To enter x,y pairs of statistical data complete these steps: 1. Clear the contents of Ry through Rg by pressing С. 5). 2. Enter the first x-value and press (INPUT). The HP-10B displays the x-value and the : annunciator appears in the display. 3. Enter the corresponding y-value and press (£+]. The HP-10B displays n, the number of pairs of items accumulated. 4. Continue centering x,y pairs. The n-value is incremented with each entry. To enter data for calculating the weighted mean, enter each data valuc as x, and its corresponding weight as y. * If statistical data causes the value of à register to exceed =9.99999999999 x 10%, the HP-10B displays a temporary overflow waming (OFLO). 86 7: Statistical Calculations Correcting Statistical Data Incorrect entries can be deleted using ME-]. If either value of an x.y pair is incorrect, you must delete and reenter both values. Correcting One-Variable Data To delete and reenter statistical data: 1. Key in the x-value to be delcted. 2. Press [E-] to delete the value. The n-value is decreased by onc. 3. Enter the correct value using [£4]. Correcting Two-Variable Data To delete and reenter x,y pairs of statistical data: 1. Key in the x-value, press and then key in the y-value. 2. Press M(E-) to delete the values. The n-value is decrcased by one. 3. Enter the correct x,y pair using (INPUT) and (+). 7: Statistical Calculations 87 Summary of Statistical Calculations Some functions return two values. The : annunciator indicates that two values have been returned. Press N[SWAP] to sec the hidden value. Keys Description MSWAF) to Display JE Arithmetic mean (aver- age) of the x-values. Mean (average) of the y-values if you entered y-data. culated line. | lated line. Шу) Mean of the x-values weighted by the y-values. NSx.5>) Sample standard devia- | Sample standard devia- | tion of the x-values.* tion of the y-values if you | entered y-data.* Eo x,0 y) Population standard devi- | Population standard devi- ation of the x-values.* ation of the y-values if you entered y-data.* y-value Estimate of x for a given | Correlation coefficient. Ш.) | value of y. x-value | Estimate of y fora given | Slope (m) of calculated (Sm) value of x. line. 0 M(P.m) y-intercept (b) of the cal- | Slope (m) of the calcu- * 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 dala con: stitutes the entire population. t The correlation coefficient is à 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. 7: Statistical Calculations N Keys Description 4 (n) На Number of data points entered. 5 (Ex) Sum of the x-values. 6 (Ly) Sum of the y-values. 7 (Ex) Sum of the squares of the x-values. 8 (5) Sum of the squares of the y-values. 9 (59) Sum of the products of the x- and y-values. Mean, Standard Deviations, and Summation Statistics You can calculate the mean (xX), sample standard deviation (S, ), and population standard deviation (0, ), and summation statistics, n, Ex, and Iv? of x-data. For xy data, you can also calculate the mean, sample standard deviation, and popula- | tion standard deviation of the y-data and the summation ) statistics Ey, Ту”, and Ey. Example 1. A yacht captain wants to determinc 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 number 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 Y Xv? /n Keys: Display: Description: BCL 0.00 Clears statistical registers. 7: Statistical Calculations 89 4.5 4 2 3.25 3.5 3.75 Example 2. The coach has four new players on the team with heights of 1.00 2.00 3.00 4.00 5.00 6.00 3.50 0.85 77.13 6.00 3.59 Enters first time. Enters second time. Enters third time. Enters fourth time. Enters fifth time. Enters sixth time. Calculates the mean. Calculates the sample standard deviation, Displays E. Displays m. Calculates the root mean square. The standard deviations calculated by B(Sx,57) and W(Sx,Sy) B[SWAP] are the sample standard deviations. They assume that the data is a sampling of a larger, complete set ol data. If the dala constitutes the entire population, the true popula- tion standard deviations can be calculated by pressing B(ox,0y) and Blox,cy) NSWAP). 193, 182, 177, and 185 centimeters and weights of 90, 81, 83, and 77 kilo- grams. Find the mean and population standard deviation of both their heights and weights, then sum the y-data. Keys: BCL 2) Display: 0.00 193 (INPUT) 90 2+] 1.00 182 81 [Z+] 2.00 90 7: Statistical Calculations Description: Clears statistical registers. Enters height and weight of player 1. Enters height and weight of player 2. | 177 (INPUT) 83 (+) — 3.00 185 [INPUT] 77 2+] — 4.00 EBEN 184.25 B(SWAP] 82.75 Eo x,0 y) 5.80 BISWAP] 4.71 6 331.00 Enters height and weight of player 3. Enters height and weight of player 4., Calculates mean of heights (x). Displays mean of weights 0). Calculates population standard deviation for heights (x). Displays population standard deviation for weights (y). Displays the total of the V's. y-intercept. in three steps. to display m (the slope of the line). Linear Regression and Estimation | Linear regression, is a statistical method for estimation and | forecasting. It is used to find a straight line that best fits a set | of xy data. There must be at least two different x,y pairs. The | straight linc provides a relationship between the x- and y-variables: y = mx + b, where m is the slope and b is the Linear Regression. Calculate m, b, and r (the correlation coefficient), 1. Enter the x,y data using the instructions on page 86. 2. To display b (the y-intercept), press 0 N(P.m). Then press SWAP) 3. Press Bx) BSWAP) to display r, the correlation coefficient. 7: Statistical Calculations 91 Linear Estimation. The straight line calculated by lincar regression can be used to estimate a y-value for a given x-valuc, or vice versa: 1. Enter the xy-data using the instructions on page 86. 2. Enter the known x-valuc or y-valuc. w To cstimate x for the given y, enter the y-value, then press Mi. в To estimate y for the given x, enter the x-value, then press Em). Example: Forecasting. Ali's Azalcas advertises on a local radio sta- tion. 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. Week Minutes of Advertising Sales (x-values) (y-values) Week 1 2 $1,400 Week 2 1 $ 920 Week 3 3 $1,100 Week 4 5 $2,265 Week 5 5 $2,890 Week 6 4 $2,200 What is the y-intercept, the slope, and the correlation coefficient? 92 7: Statistical Calculations 3,000.00 (forecasted) x RA a ” R „” a ”». 2,000.00 Sales in Dollars 1 m = 425.88 1,000.00 b MT * 0 1 2 3 4 5 6 7 B Minutes of Advertising Keys: Display: Description: BCL Z 0.00 Clears statistical registers, 2 1400 1.00 Enters minutes and sales for conseculive weeks. 1 INPUT) 920 2.00 3 1100 3.00 5 2265 [z+ 4.00 5 2890 5.00 4 (INPUT) 2200 6.00 о т) 376.25 Calculates y-intereepl (b). H(SWAP) 425.88 Displays slope. Br) N(SWAP) 0.90 Calculates correlation coefficient. Estimate what the level of sales would be if the business purchased 7 or 8 minutes of advertising, 7: Statistical Calculations 93 7 MU.m) 8 Bm) 3,357.38 3,783.25 Estimates sales if 7 minutes of advertising were purchased. Estimates sales if 8 minutes were purchased. How many minutes of advertising should Ali’s buy to attain salcs of $3,000? 3000 г) 6.16 Weighted Mean The following procedure calculates the weighted mean of data points x, Ma, +» +X, occurring with weights y,, V2,- - - Estimates minutes of advertising required for $3,000 in sales. 1. Use [INPUT] and [2+] to enter xy pairs. The y-values arc the weights of the x- 2. Ргс55 values. Example. A survey of 266 one-bedroom rental apartments reveals that 54 of them rent for $200 per month, 32 for $205, 88 for $210, and 92 for $216. What is the average monthly rent? Keys: Display: BCL: 0.00 200 (INPUT) 54 [+] 1.00 205 (INPUT) 32 (#+] 2.00 210 88 3.00 216 [INPUT] 92 [2+] 4.00 ИУ] 209.44 94 7: Statistical Calculations Description: Clears statistics memory. Enters first rent and its weight, Enters second rent and its weight. Enters third rent and its weight, Enters fourth rent and its weight. Calculates weighted mean. Additional Examples Business Applications Setting a Sales Price Onc 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 cquation calculates unit price based on total cost and rate of return; PRICE = TOTAL COST + NUMBER OF UNITS x (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? Keys: Display: Description: 40000 40,000.00 Enters cost. 2000 [x] 20.00 Calculates unit cost. MO 1 (+) 00 20 (= Calculates unit sales 100 [=] 24.00 price. Forecasting Based on History Onc method of forecasting sales, manufacturing rates, or expenses 15 reviewing historical trends. Once you have historical data, the data are fit Lo a curve that has time on the x-axis and quantity on the y-axis. 8: Additional Examples 95 Example. Given the following sales data, what arc the sales estimates for years six and scven? Year Sales $ 1 10,000 2 11,210 3 13,060 4 16,075 5 20,590 Keys: Display: Description: a 0.00 Clears statistics registers. 1 10000 1.00 Enters first year and sales for that year. 2 [INPUT] 11210 2.00 Enters second year's data. 3 13060 3.00 Conlinucs data entry. 4 16075 4.00 5 20590 5.00 6 B[5,m] 22,000.50 Estimates sales for year six. 7 [9m] 24,605.00 Estimates sales for ycar 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 pay- ment 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 1s calculated as an annual interest rate charged for delaying payment. 96 8: Additional Examples DISC% x 360 x 100 COST = 100 - DISC%) x (TOTAL DAYS - DISC DAYS) DISC 15 the discount percent if the payment is made carly. 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? Keys: Display: Description: 2 [x] 360 [x] 100 [=] 72,000.00 Calculates numerator in equation. ШО №00 100 (-) 2 Parentheses force order HD) 98.00 of calculation. [) BJ 30 (-) 10 [=] 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 requested that you 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: INTEREST = LOAN AMOUNT x INTEREST% x TERM OF LOAN (IN DAYS) 365 8: Additional Examples 97 Keys: Display: Description: 450 [+M)[x) 10 0.10 Stores interest. [x] 60 [=] 365 [=] 7.40 Calculates interest owed. [RM] (=) 457.40 Calculates total owed. Continuous Compounding The cquation for calculating an effective rate for continuous compounding IS: EFF % = (e(WOM® +100) _ 1) x 100 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 applics to your pay- ment period. In the following example, P/YR = 12 so you have to calculate a new NOM% using the interest rate conversion applica- tion 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 cach month, you deposit $250.00 in the account. What will the balance be after 15 years? Keys: Display: Description: 18 0.18 Divides nominal rate by 100. Ble] 1.20 Raiscs e to 0.18 power. (=) 1 [x] 100 [=] 19.72 Calculates annual effective rate. W(EFF%) 19.72 Stores cffective rate. 12 MP/YR) 12.00 Sets payments per year. 98 8: Additional Examples | NNOME) 18.14 Calculates annual nomi- nal rate for a monthly payment period. Set to End Mode. Press W[BÉG/END] if BEGIN annunciator is displayed. 15 MxP/YR) 180.00 Stores number of months. 250 - 250.00 Stores regular payment. 4572.8 [+/-] -4,572.80 Stores current balance as a negative value (like an initial investment). 297,640.27 Calculates account bal- ance 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 РИ). Remember the cash flow sign convention: money paid oul is negalive; moncy received is posilive, Example. An investor wishes to purchase a $100,000 mortgage taken out at 9% for 20 years. Since the mortgage was issucd, 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 yicld 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 W(BEG/END] if BEGIN annunciator is displayed. B: Additional Examples 99 Keys: Display: Description: 12 M(P/YR] 12.00 Sets payments per year. 9 9.00 Stores interest rate. 20 H[xP/YR] 240.00 Stores number of months. 100000 - 100,000.00 Stores original amount of mortgage. 0 (FV] 0.00 Enters amount left to pay after 20 ycars. [PMT] 899.73 Calculates regular payment. Step 2. Enter the new value for N indicating when the balloon occurs, then find FY, the amount of the balloon, Keys: Display: Description: BRAND) 899.73 Rounds payment to two decimal places lor accuracy. 5 M(xP/YR) 60.00 Stores number of pay- ments until balloon. [FV] 88,706.74 Calculates 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. Keys: Display: Description: [RCL] [N) [=] 42 [N] 18.00 Stores remaining number of payments. 79000 (+/-) - 79,000.00 Stores price of mortgage. 20.72 Calculates the return on this discounted mortgage. 100 85: Additional Examples | Annual Percentage Rate for a Loan With Fees The annual percentage rate, APR, incorporates fees usually charged when a mortgage is issued, which cffectively 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 (//YR), the mortgage amount (new PV), and the amount of the fee. Remember the cash flow sign convention: money paid out is negative, moncy 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 15 $60,000 for 30 years and the annual interest rate is 11.5% with monthly payments what APR is the bor- rower paying? Set to End Mode. Press [lI[BEG/END] if BEGIN annunciator is displayed. Keys: Display: Description: 12 M(P/YR) 12.00 Sets payments per ycar. 11.5 11.50 Stores interest rate. 30 H[xP/YR] 360.00 Stores length of mortgage. 60000 [PY] 60,000.00 Stores original amount of mortgage. 0 0.00 The loan will be com- pletely paid off in 30 years. -594.17 Calculates paymenl. [RCL] 60,000.00 Recalls loan amount. [=] 2 58,800.00 Subtracts points. УВ 11.76 Calculates APR, con- sidering fecs. 8: Additional Examples 101 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 M[BEG/END) if BEGIN annunciator is displayed. Keys: Display: Description: 12 M(P/YA] 12.00 Sets payments per year. 12 12.00 Stores interest rate. 10 MxP/YR] 120.00 Stores length of morigage. 1000000 1,000,000.00 Stores original amount of morigage. [*+/-) -1,000,000.00 Enters amount due at end of term. Payments are interest only so entire loan amount is due. PMT - 10,000.00 Calculates interest-only payments. [PV] 1,000,000.00 Recalls loan amount. [=] 3 970,000.00 Subtracts points. 1/ УВ. 12.53 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 pay- ment 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 sim- ple interest. So using the HP-10B to do a payment calculation with an odd first period is a two step process: 102 8: Additional Examples 1. Calculate the amount of simple interest that accrues during the frac- tional first period and add it to the loan amount. This is the new PY. 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 JJ[BEG/END] if BEGIN annunciator is displayed. Keys: Display: Description: 12 MP/YR) 12.00 Sets payments per year. 15 15.00 Stores interest rate. [+] 12 [x] 1.25 Calculates periodic interest rate. 16 [=] 30 [x] 0.67 Multiplies by fraction of a period. 4500 BISWAP) (%] (=) 30.00 Calculates amount of simple interest owed for odd period. 4500 4,530.00 Adds this simple interest to present value. 36 (N) 36.00 Stores term of loan. O [FV] 0.00 Enters amount left to pay alter 36 payments. - 157.03 Calculates payment amount. 8: Additional Examples 103 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; m A 3-year loan with an annual interest rate of 3.5%. E 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 W(BEG/ENO) if BEGIN annunciator is displayed. Calculate the first option: Keys: Display: Description: 12 M(P/YR) 12.00 Sets payments per year. 36 [N] Stores known values. 12500 0 [FV] 0.00 3.5 [I/YR] 3.50 Stores first interest rate. PMT - 366.28 Calculates payment. [x] [N] [=] -13,185.94 Calculates total interest and principal. Calculate the second option: Keys: Display: Description: 11500 11,500.00 Stores loan amount with rebale. 9.5 9.50 Stores second interest rate. PMT - 368.38 Calculates payment. [x] [N] (=) —13,261.64 Calculates total interest and principal. The first option costs slightly less. 104 8: Additional Examples | 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-10B, you need to calculate a Canadian mortgage factor (which is an adjusted interest rate) to store in 7/YR. For additional information on interest rate conversions, sce the section “Interest Rate Conversions” in chapter 5. Example. What 15 the monthly payment required to fully amortize a 30-year, $30,000 Canadian mortgage if the annual interest rate is 12%? Keys: Display: Description: 12 M[NOM%| Stores known nominal 2 M(P/YR)] 2.00 percentage and number of compounding periods. B(EFF%] 12.36 Calculates annual effective rate. 12 B(P/YR] 12.00 Sets payments per year. B(NOM%) 11.71 Calculates Canadian mortgage factor (adjusted interest rate). 30000 Stores other known 0 (FV) values for mortgage. 30 MxP7YR) 360.00 PMT -301.92 Calculates monthly payment for Canadian mortgage. 8: Additional Examples 105 What if ... TVM Calculations One of the most valuable aspects of the HP-10B’s TVM application is the case with which it handles the question “what if ,..” in financial calcula- tions, For example, onc of the most popular “what if...” questions is, “What if the interest rate changes to ...? How will that affect my pay- ment?” 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 carlier in this manual have included some bricf 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 M[BEG/END) if BEGIN annunciator is displayed. Keys: Display: Description: 12 M(P/YR] 12.00 Sets payments per year. 735000 Stores known values. 11.2 30 MxP/YR) 0 [EV) 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? 3565 (*/-) ~ 3,555.00 Enters new payment, 26 B(P/YR] 26.00 Sets payments per year for every two weeks. 106 8: Additional Examples I 514.82 Calculates number of biweekly payments. B(xP/YR) 19.80 Displays years required to pay off 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? Keys: Display: Description: 12 M(P/YR) 12.00 Sets payments per year. 15 B(xP/YR] 180.00 Stores new term. PMT - 8,446.53 Calculates payment for shorter term. [x] [N] -1,520,374.70 Calculates total paid. [=] - 785,374.70 Displays total interest paid on contract. Savings Saving for College Costs Supposc you start saving now to accommedate a futurc 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 begin- ning of each year for four years. The fund earns 9% annual interest, com- pounded 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? 8: Additional Examples 107 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. А $15,000 A I/YYR = 9% Year 1 Year 2 Year 3 Year 4 Keys: Display: Description: 9 BNOM%] 9.00 Stores annual nominal rate, 12 M(P/YR) 12.00 Stores number of com- pounding periods used wilh this nominal rate. B(EFF%] 0.38 Calculates annual effective rate. When compounding occurs only once per year, the effective rate and the nominal rate are the same. (/УВ) 9,38 Stores effective rate as annual rate. Set to Begin mode. Press JI[BEG/END] if BEGIN annunciator is not displayed. 1 MP/YR) 1.00 Sets 1 payment per year. 15000 (РМТ) 15,000.00 Stores annual withdrawal. 4 (N] 4,00 Stores number of with- drawals. 108 8: Additional Examples 0 0.00 Stores balance at end of four years. (PV) -52,713.28 Calculates amount required when your daughter starts college. Then use that PV as the FV on the following cash flow diagram, and cal- culate the PMT. FV from pravious calculation. 142 | 143 | 144 РМТ = ? Set to End mode. Press M(BEG/END] if BEGIN annunciator is displayed. [+/-) [РУ] 52,713.28 Stores amount you need. 0 0.00 Stores amount you arc starting with. 12 M(P/YR) 12.00 Sets payments per year. 144 [N] 144.00 Stores number of deposits. 9 9.00 Stores interest rate. -204,54 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 deter- minc whether both interest and principal arc tax-free. You can solve for either case.) 8: Additional Examples 109 The purchasing power of that future value depends upon the inflation rate and the duration of the account. Example. You arc considering opening a tax-deferred account with a dividend rate of 8.175%. Il you invest $2,000 at the beginning of cach 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 you carncd? If your post-retirement tax rate is 15%, what will the alter-tax future value of the account be? Assume that only the interest 15 taxed (assume the principal was taxed before deposit). What is the purchasing power of that amount, in today’s dollars, assuming an 8% inflation ratc? Set to Begin mode. Press W(BEG/END] if BEGIN annunciator is not displayed. Keys: Display: Description: 1 BIP/YA) 1.00 Scts 1 payment per year. 35 [N] Stores number of periods 8.175 and interest rate. 8.18 0 0.00 Stores amount you start with. 2000 [+/-] - 2,000.00 Stores amount of annual payment. [FV] 387,640.45 Calculates amount in account at retirement, [x] Calculates amount you (ВСС) [№ |] -70,000.00 have paid into account by retirement. [FV] (=] 317,640.45 Calculates interest account has carned by retirement. [>] 15 [%] [=] 47,646.07 Calculates taxes at 15% of interest. +4] [FV] [=] 339,994.39 Calculates after-tax FV. 110 8: Additional Examples | 339,994.39 Stores after-tax future valuc in FV, 8 0 [PMT] [PV] -22,995.36 Calculates present-value purchasing power of after-tax FV, assuming an 8% 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 begin- ning today (Begin mode). The annual tax on the interest is paid out of the account. (Assume the deposits have been taxed already.) Example. Il you invest $3,000 cach year for 35 ycars, with dividends taxed as ordinary income, how much will you have in the account al retire- ment? Assume an annual dividend rate of 8.175%, a tax rate of 28%, and that payments begin today. What is the purchasing power ol that amount in today’s dollars, assuming 8% inflation? Set to Begin mode. Press M[BEG/END) if BEGIN annunciator is nol displayed. Keys: Display: Description: 1 B(P/YRA) 1.00 Sets 1 payment per year. 35 (N] 35.00 Stores number of pay- ment periods until retirement, 8.175 [-] 28 [%] [=] 5.89 Calculates interest rate diminished by tax rate. I/YR 5.89 Stores adjusted interest rate. 0 0.00 Stores amount you arc starting with. 3000 [PMT] - 3,000.00 Stores amount of annual payment, 8: Additional Examples 111 [FV] 345,505.61 Calculates amount in account at retirement. 8 [1/YR] O ~23,368.11 Calculates present-value purchasing power of FV, assuming an 8% 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 quantitics 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% mort- gage, 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 al 9,5% for 15 years. What are your new payments and what return 1s the lender getting on this wrap-around mortgage? The payment calculation is a straightforward TVM payment calculation using the new amount as the PV, Set to End mode. Press [J(BEG/END] ¡f BEGIN annunciator is displayed. Keys: Display: Description: BICLEAR_ALL] 0.00 Clears all registers. 12 MP/YR) 12.00 Sets payments per year. 82510.22 82,510.22 Stores loan amount on which your new payment is calculated. 112 8: Additional Examples 19.5 [1/YR) 9.50 Stores interest rate. 0 [FV] 0.00 Stores final balance. 15 B(xP/YR] 180.00 Stores number of monthly payments you will make. (РМТ) - 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: 47,510.22 861.59 1 2 3 4 82 83 84 180 eee eed) 754.00 "В2,510.22 When you group the above cash flows, you'll find that: CF, = 47,510.22 - 82,510.22 = -35,000.00 CF, = 861.59 - 754,00 = 107,59 N, = 82 CF, = 861.59 N, = 180 - 82 = 98 8: Additional Examples 113 Keys: 35000 (F7) (CFD (RCL) EMT) (4) 5) 754 [CF]) 82 MÍN) (RCL] (PMT) (*/-) (CFI) 180 =) 82 MINT M(RR/YR) Display: CFO -35,000.00 CF1 107.59 ni 82.00 CF2 861.59 n2 98.00 10.16 Net Future Value Description: Enters $35,000 for loan amount. Enters nct payment for first 82 months. Enters number of times payment occurs. Enters net payment for next 98 months. Enters number of times payment occurs, Calculates annual return. 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? 1,2,3,4,5,6,7.8,9.10,11.1213,14 15.16,17,18.19 20,21,22 23 24 -3,000 -12,000 1/YR = 8.8% 114 8: Additional Examples -2,000 -7,500 Current Date Keys: M(CLEAR ALL) 12 M(P/YR] 12000 [CF]) 0 [CF]} 2 a6) 3000 (37) (СЕЛ 3 MN) 0 [CF] 9 MINI) 7500 (+/-) (CFI) 0 (CF)) 3 MINI) 2000 [+/-} [CF] 8.8 (I/YR] B(NPY) Display: 12.00 CFO - 12,000.00 CFA 0.00 n1 2.00 CF2 -3,000.00 n2 3.00 n3a 9.00 CF4 = 7.500. 00 ns 3.00 CF6 -2,000.00 8.80 -29,203.14 0.00 34,800.58 | Set to End mode. Press B(BEG/END] if BEGIN annunciator is displayed. Description: Clears all registers. Sets payments per year. Enters initial cash flow. Enters amount in group 1. Enters number of times payment occurs. Enters amount in group 2. Enters number of times payment occurs. Enters number of times payment occurs. Enters cash [low group 4. Enters number of times payment occurs. Enters cash flow group 6. Stores annual interest rate. Calculates net present value (NPV), automati- cally stored as PY, Stores known values. Calculates net future value, 8: Additional Examples 115 A Assistance, Batteries, and Service We at Hewlett-Packard are committed to providing you with ongoing support. You can obtain answers to questions about using your calculator from our Calculator Support department. 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 address or phone number listed on the inside back cover. Answers to Common Questions Q: Im not sure if the calculator is malfunctioning or if I'm doing some- thing incorrectly. How can I determine if the calculator is operating prop- erly? A: The diagnostic sell-test is described on page 121, Q: My numbers contain commas instcad of periods as decimal points. How do I restore the periods? A: Press M7) (page 28). Q: How do I change the number of decimal places that the HP-10B displays? A: Press N(DISP) and the number of decimal places that you want (page 27). Q: What does an “E” in a number (for example, 2.51E — 13) mcan? 116 A: Assistance, Battorios, and Service A: Exponent of ten (for example, 2.51 x 10°), Refer to “Scientific and Engineering Notation” on page 27. Q: Why do I get a wrong answer or the no Solution message when using TVM? A: Be surc 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 [orget to store a zero for [FV] if you completely pay off a loan.) Clearing all the registers (NICLEAR ALL)) 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 sct correctly. Q: How can I change the sign of a number in a list of cash flows? A: You must replace the cash flow entry. “Viewing and Replacing Cash Flows” is discussed on page 79. Q: What does PEND in the display mean? A: An arithmetic operation is pending (in progress). Q: What does : in the display mean? A: The [INPUT] key has been pressed, or two values have been returned (page 25). Q: Why is 7RR/YR larger than I expected? A: This is IRR per year. To sce a periodic IRR, divide 7RR/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: m Operating temperature: 0° Lo 45°C (32° to 113°F). wm Storage temperature: = 20° to 65°C (— 4° to 149°F). = Operating and storage humidity: 90% relative humidity at 40°C (104°F) maximum. A: Assistance, Battarios, and Servico — 117 Noise Declaration. In thc operator position under normal operation (per ISO 7779): LpA < 70dB. Power and Batteries The calculator is powered by three button cell batteries, Expected battery life depends on how the calculator is used and the chemical content of the battery. Use only fresh button-cell batteries. Do not use rechargeable batteries. Low Power Annunciator When the low battery annunciator (1) comes on, you should replace the battcries as soon as possible. If the battery annunciator is on and the display dims, you may lose data. The ALL CLr message is displayed if data is lost due to low power. Battery Specifications Your HP calculator requires three 1.5-volt, button-cell batteries. We reccommend using either alkaline or silver-oxide (ype batteries. Do not nse rechargeable batteries. Usc batteries from the following list, or usc another manufacturer's cquivalent. Alkaline Silver Oxide o Panasonic SR44 W or SP357 Evercady 357 RAY-O-VAC 357 Varta V357 Toshiba LR44 Panasonic LR44 Evercady A76 Duracell LR44 Varta VI3GA Kodak KA76 118 A: Assistance, Batteries, and Service Installing Batteries 1. Havc three fresh button-cell batteries at hand. Only touch batteries by their edges. Wipe cach battery with a lint-free cloth to remove dirt and oil. 2. Make sure the calculator is off. You will lose memory if the bat- teries are removed when the calculator is on. Do not press [C) again until the entire procedure for changing batterics is completed. 3. Hold the calculator as shown. To remove the battery-compartment door, press down and outward on it until it slides off (away from the center). 4. Turn the calculator over and shake the batteries out. Y Do not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode, releasing hazardous chemicals. Warning 5. Hold the calculator as shown and stack the batteries in the battery compartment. Orient the batteries according to the diagram inside the battery compartment. Be sure the raised and flat ends match the diagram. A: Assistance, Battarles, and Service 119 aD 6. Slide the tab of the battery-compartment door back into the slot in the calculator case. 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, read the section “If the Calculator Requires Service” on page 124. = The calculator won't turn on (nothing is in the display): 1. Reset the calculator. Hold down the [C] key and press at the same time. It may be necessary to repeat the reset keys- trokes several times. 2. Erase memory. Press and hold down [C], then press and hold down both [N) and [24]. Memory is cleared and the ALL CLr message is displayed when you release all three keys. 3. If the calculator fails to respond alter steps 1 or 2, replace the batteries (page 119). 4. If the calculator fails to respond after step 3, remove the batteries (page 119) and lightly press a coin against both calcu- lator battery contacts. Put the batteries back in and turn on the calculator. It should display ALL CLr. If steps 1 through 4 fail to restore calculator operation, it requires service, 120 A: Assistance, Batteries, and Service | в The calculator doesn’t respond to keystrokes (nothing happens when you press the keys): 1. Reset the calculator (see step 1 above). 2. Erase memory (sec step 2 above). 3. If the calculator fails to respond after steps 1 and 2, remove the batteries (page 119) and lightly press a coin against both calcu- lator battery contacts. Put the batteries back in and turn on the calculator. It should display ALL Cr. If steps 1 through 3 fail to restore calculator function, the calculator requires service. u The calculator responds to keystrokes but you suspect that it is malfunctioning: 1. Do the self-test (described below). If the calculator fails the self test, it requires service. 2. If the calculator passes the self-test, 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” on page 116. 3. Contact the Calculator Support department. The address and phone number arc listed on the inside back cover. Confirming Calculator Operation — the Self- Test If the display can be turned on, but it appears that the calculator 1s not operating properly, you can do a diagnostic self-test. To run the self-test: 1. First, hold down the [C] key, then press at the same time. 2. Press any key four times, and watch the display as various patterns are displayed. After pressing the key four times, the calculator displays the copyright message COPr. HP 1987 momentarily, and then the message 01. This indicates the calculator is ready for the key Lest. A: Assistance, Battaries, and Service 121 3. Starting at the upper left corner ([N]) and moving from left to right, press each key in the top row, Then, moving left to right, press each key in the second row, third row, etc., until you've pressed each key. m If you press the keys in the proper order, and they arc function- ing properly, the calculator displays two-digit numbers. (The calculator is counting the keys using hexadecimal basc.) m If you press a key out of order, or if a key isn’t functioning properly, the next keystroke displays 10 - FAIL, followed by a onc-digit number. If you received the message because you pressed a key out of order, you should reset the calculator (hold down (C] and press [PV]) and start the self-test over. If you pressed the keys in order, but got this message, the calculator requires service. 4. When the keyboard test has been completed, the calculator displays a message: m The calculator displays 10 - Good if it passed the sel[-test. ® The calculator displays 10 - FAIL, followed by a one-digit hexa- decimal number 1 through F, if it failed the self-test. If the cal- culator failed the self-test, it requires service (page 124). Include a copy of the fail message with the calculator when you ship it for service, 5. If the calculator failed the self-test, rerun the test to verify the results. 6. To exit the self-test, reset the calculator (hold down [€] and press [PV)). To start a continuous self-test (like the one performed at the factory), hold down [С] (еп press [EV]. This test displays various patterns and the copyright message, then automatically repeats. The test continues until you press (CJ. 122 A: Assistance, Battaries, and Service Limited One-Year Warranty What Is Covered The calculator (except for the batteries, or damage caused by the bat- terics) is warranted by Hewlett-Packard against defects in materials and workmanship for one year from the date of original purchase. If you sell your unit or give it as a gift, the warranty is automatically transferred to the new owner and remains in cffect for the original one-year period. During thc warranty period, we will repair or, at our option, replace at no charge a product that proves to be defective, provided you return the product, shipping prepaid, to a Hewlett-Packard service center, (Replace- ment may bc with a newer model of equivalent or better functionality.) This warranty gives you specilic legal rights, and you may also have other rights that vary from state to state, province to province, or country to country. What Is Not Covered Batteries, and damage caused by the batteries, are not covered by the Hewlett-Packard warranty. Check with the battery manufacturer about bat- tery and battery leakage warranties. This warranty does not apply if the product has been damaged by accident or misuse or as the result of service or modification by other than an authorized Hewlett-Packard service center. No other express warranty is given, The repair or replacement of a product is your exclusive remedy. ANY OTHER IMPLIED WAR- RANTY OF MERCHANTABILITY OR FITNESS IS LIMITED TO THE ONE-YEAR DURATION OF THIS WRITTEN WARRANTY. Some states, provinces, or countries do not allow limitations on how long an implied warranty lasts, so the above limitation may not apply to you. IN NO EVENT SHALL HEWLETT-PACKARD COMPANY BE LIABLE FOR CONSEQUENTIAL DAMAGES. Some states, pro- vinces, or countries do not allow the exclusion or limitation of incidental or consequential damages, so the above limitation or exclusion may not apply to you. A: Assistance, Battarios, and Service 123 Products are sold on the basis of specifications applicable at the time of manufacture. Hewlett-Packard shall have no obligation to modily or update products, once sold. Consumer Transactions in the United Kingdom This warranty shall not apply to consumer transactions and shall not affect the statutory rights of à consumer. In relation to such transactions, the rights and obligations of Seller and Buyer shall be determined by statute. If the Calculator Requires Service Hewlett-Packard maintains service centers in many countries. These centers will repair a calculator, or replace it with the same model or one of equal or greater value, whether it is under warranty or not. There is a service charge for service after the warranty period. Calculators normally are serviced and reshipped within five working days. Obtaining Service a In the United States: Send the calculator to the Corvallis Service Center listed on the inside of the back cover. в In Europe: Contact your Hewlett-Packard sales office or dealer, or Hewlett-Packard’s European headquarters for the location of the nearest service center. Do not ship the calculator for service without first contacting a Hewlett-Packard office. Hewlett-Packard S.A. 150, Route du Nant-d'Avril P.O. Box CH 1217 Mcyrin 2 Geneva, Switzerland Telephone: (022) 780 81 11 124 A: Assistance, Battaries, and Service m In other countries: Contact your Hewlett-Packard sales office or dealer or write to the Corvallis Service Center (listed on the inside of the back cover) for the location of other service centers, If local service is unavailable, you can ship the calculator to the Corvallis Service Center for repair. All shipping, reimportation arrangements, and customs costs are your responsibility. Service Charge There is a standard repair charge for out-of-warranty service. The Corvallis Service Center (listed on the inside of the back cover) can tell you how much this charge 15. The full charge 15 subject to the customer's local sales or valuc-added tax wherever applicable. Calculator products damaged by accident or misuse are not covered by the fixed service charges. In these cases, charges are individually deter- mined based on time and material. Shipping Instructions If your calculator requires service, ship it to the nearest authorized service center or collection point. m Include your return address and description of the problem. m Include proof of purchase date if the warranty has not expired. m Include a purchase order, check, or credit card number plus expira- tion date (VISA or MasterCard) to cover the standard repair charge. = Ship the calculator in adequate protective packaging to prevent dam- age. Such damage is not covered by the warranty, so we recommend that you insure the shipment. m Pay the shipping charges for delivery to the Corvallis Service Center, whether or not the calculator is under warranty. A: Assistance, Batteries, and Service 125 Warranty on Service Service 1s warranted against defects in materials and workmanship for 90 days from the date of service. Service Agreements In the U.S, a support agreement is available for repair and service. Reler Lo the form in the front of the manual, For additional information, contact the Corvallis Service Center (sec the inside of the back cover). Regulatory Information U.S.A. The HP-10B generates and uses radio frequency encrgy and may interfere with radio and television reception. The calculator complies with the limits for a Class B computing device as specified in Subpart J of Part 15 of FCC Rules, which provide reasonable protection against such interference in a residential installation. In the unlikely event that there is interference to radio or television reception (which can be determined by turning the HP-10B ofl and on or by removing the batteries), try the following: m Reorienting the receiving antenna. ® Relocating the calculator with respect to the receiver. For more information, consult your dealer, an experienced radio/television technician, or the following booklet, prepared by the Federal Communications Commission: How to Identify and Resolve Radio-TV Interference Problems. This booklet is available from the U.S. Government Printing Office, Washington, D.C. 20402, Stock Number 004-000-00345-4, At the first printing of this manual, the telephone number was (202) 783-3238. West Germany. The HP-10B complics with VFG 1046/84, VDE 0871B, and similar noninterference standards. If vou use equipment that is not authorized by Hewlett-Packard, that system configuration has to com- ply with the requirements of Paragraph 2 of the German Federal Gazetie, Order (VFG) 1046/84, dated December 14, 1984, 126 A: Assistance, Battaries, and Service More About Calculations IRR/YR Calculations The calculator determines JRR/YR for a set of cash flows using mathematical formulas that “scarch” 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 usu- ally only one solution to the calculation, However, calculating JRR/YR for certain sets of cash flows is more complex. There may be more than one (or no) mathematical solution to the problem. In these cases, the calcula- tor displays a message to help you interpret what has happened. Possible Outcomes of Calculating IRR/YR These are the possible outcomes of an IRR /YR calculation: m Case 1. The calculator displays a positive answer. This is the only positive answer. However, one or more negative answers may exist. m Case 2. The calculator finds a negative answer but a single positive answer also exists, It displays: POS Irr ALSO. To see the negative answer, press [+] to clear the message. To search for the positive answer, you must input a guess. (Refer to “Entering a Guess for IRR /YR,” below). There might also be additional negative answers. = Case 3. The calculator displays a negative answer and no message. This is the only answer. m Case 4. The calculator displays the message: Error - Soin, This indicates that the calculation is very complex. It might involve more than one positive or negative answer, or there may be no solution, To continue the calculation, you must store a guess (see below). B: More About Calculations 127 = Case 5. 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 mes- sage 1s putting the wrong sign on a cash flow. A valid cash-flow series for an /RR/YR calculation must have at least onc positive and one negative cash flow. Halting and Restarting IRR/YR The scarch for /RR/YR may take a relatively long time. You can halt the calculation at any time by pressing the [C] key. The message IntErruPtEd is displayed, Pressing (+) now displays the current estimate for JRR/YR. You can resume the calculation by: m Pressing B(RR/YR] while the current estimate is displayed in the calculator hne. This continues the calculation from where it left off. s Storing a guess for 7RR/YR, discussed below. Entering a Guess for IRR/YR To enter a guess, key in an estimate of 7RR/YR and then press B(RR/YR]. You can enter a guess for JRR/YR at these times: m Before beginning the calculation. A fairly accurate guess can reduce the time required to calculate an answer and reduce the chance of the calculator solving for an undesirable negative solution. m After you've interrupted the calculation. m Alter the calculator has halted the calculation due to any of the aforementioned cases. However, for cases 3 and 5, no other solutions will be found. When calculating JRR/YR using a guess, the calculation halts when it finds an answer. However, there may be additional positive or negative answers, or no true solution at all. You can continue searching for another solution by halting the calculation and entering a different guess. Onc way to obtain a good guess for 7RR/YR is to calculate the NPV for various interest rates. Since /RR/YR is the interest rate at which NPV equals zero, the best estimate of JRR/YR is the interest rate that yields the value for NPV closest to zero. 128 B: More About Calculations Effect of Using >— to Correct Data The HP-10B stores the statistical numbers in an “accumulated” fashion. It doesn’t store every number that you enter, but rather it performs inter- mediate calculations when you press the key. The ME--) key performs the opposite intermediate calculations to effectively remove a number or pair of numbers from the stored results. When correcting statistical data, M[E-) docs not delete rounding errors that may occur during the intermediate calculations done by [E+]. Thus, subsequent results for corrected data may be different than for data that was entered originally without having to use M(E-). However, the difference will not be serious unless the incorrect data has a very large magnitude compared with the correct valucs; in this case, you may want to clear the statistical registers and re-enter the data, Range of Numbers The largest positive and negative numbers available on the calculator are +9.99999999999 x 10*”; the smallest positive and negative numbers avail- able are +1 x 10-7, Underflow displays a zero. Refer to the message OFLO in “Messages” following this appendix, Equations Margin and Markup Calculations PRC - COS’ PRC PRC - COST COST MAR = | Jo Mu = | | xo B: More About Calculations 129 Time Value of Money (TVM) Payment Mode Factor: $ = 0 for End mode; 1 for Begin mode. > . I/YR 1% = PyR : 97 N° i Yo 1 - |1 + — = 0 = РИ + |1 + Хх | PMT x | 9 100 1% 100 i% | + РИ Xx | + 100 Amortization LINT = accumulated interest LPRN = accumulated principal i = periodic interest rate BAL 1s initially PV rounded to the current display setting. РМТ is mitially PMT rounded to the current display setting. I/YR 7 P/YR x 100 130 B: More About Calculations | For each payment amortized: INT" = BAL Xi (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’ BAL, = BAL, + PRN ENT neu = ENT + INT EPRN e = EPRN oy + PRN interest Rate Conversions | PRR |], _NOM% " 100 x P /YR \ ’ EFF 9% = - 1| х 100 Cash-Flow Calculations 19 = periodic interest rate j = the group number of the cash flow, CF; = amount of the cash flow for group j. n; = number of times the cash flow occurs for group j. К = the group number of the last group of cash Mows. Nj = 2 mn = total number of cash [lows prior to group j. о - 1 - |1 + = | NPV = CF, + №} СЁ) | > 1%] = + X х |1 + — ’ # 1% 100 100 “ я When NPV = 0, the solution for i% is the periodic internal rate of return. B: More About Calculations 131 Statistics 132 B: More About Calculations Messages Press [C] or [+] to clear a message from the display. ALL CLr (All Clear). Memory has been erased (page 23). bAL (Balance). Balance in an amortization schedule (page 67). CF<j> (Cash Flow j). Cash flow number (page 78). COPr. HP 1987 (Copyright HP 1987). Copyright is displayed during self-test. Error - Func (Error - Function). E Attempt Lo divide by zero. ® Attempt Lo calculate n! with n< 0 or na noninteger. mu Attempt to calculate the logarithm of zero or a negative number, m Attempt to calculate 0° or 0 raised to a negative power. ® Attempt to raise a negative number to a noninteger power. mM Attempt to calculate the square root of a negative number. Error - Full (Error - Full). Attempt to calculate an expression with more than five pending operations or attempt to enter more than 15 cash [low groups. Error - Int (Error - Interest), Periodic interest percent is < - 100%. Error - n (Error - n). Attempt to solve for //YR with N < 0.999909 or > 1E10. Messagos 133 Error-P Yr (Error - Payments per Year). Attempt to solve for P/YR, or storc a number in P/YR that is outside the legal range (1 to 999) or is not an integer. Error - PEr (Error - Period). Attempt (o enter a value in N; that is outside the legal range (1 to 99) or is not an integer. Error - Soln (Error - Solution). A solution for 7RR/YR or 7/YR may or may not exist, If you arc attempting to solve I/YR, you may be able to perform the calcu- lation using 7RR/YR. If you are attempting an JRR/YR calculation, rcler to page 127. Error - StAt (Error - Statistics). mM Attempt to calculate Y, À, Or r with x-data only (all y-values cqual to zero). m Altempt to calculate x, y, r, or m, with all x- values equal. ® Attempt to calculate with n equal to zero. E Allempl to calculate S,, бу, r, orm with n <1, or when a divi- sion by zero or square root of a negative number occurrred in a statis- tics calculation. Also, attempt to calculate X', with Ly = 0. Int (Interest). Interest in an amortization schedule (page 67). IntErruPtEd (Interrupted). An /RR/YR, 1/YR, or amortization calculation was inter- rupted by pressing (C). n <i> (Nj). Number of times a cash flow of the same amount occurs consecu- ively (page 78). no Solution (No Solution). No solution exists for values entered (page 127). 134 Messages | 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 (+ 9,99999999999E 499). The overflow message is also displayed if an intermediate TYVM or cashflow calculation results in an overflow condition. In this casc, the message remains in the display. PEr <P1> - <P?> (Periods starting - ending). Displays beginning and ending paymenis for an amortization schedule (page 67). POS Ir ALSO (Positive Internal Rate of Return Also). An IRR/YR calculation pro- duced a negative solution, A positive solution also exists (page 127). Prin (Principal). Principal in an amortization schedule (page 67). running (Running). A calculation is in process. UFLO (Underflow). An intermediate result in TVM is too small for the HP-10B LO process. <nnn> P Yr (nnn Payments per Year). Temporary message showing number of pay- ments per year. Displaycd for a moment when you press M[CLEAR ALL). 10 - FAIL n (HP-10B Fail). The self-test failed; n 15 the fail code (page 121). 10 - Good (HP-10B Good). The self-test is complete (page 121). Messages 135 Index Special Characters 136 Index [+M], 35, 37 _ 4,24 A, 21, 24, 118 :, 24 A Accumulative discrepancies, 58 Add percent, 31 Adjusted interest rate, 73 Advance payments, 63 ALL CLr, 24, 133 [AMORT], 52 Amortization, 66 equations, 130 interest, 66 loan balance, 66 principal, 66 range of payments, 67 schedule, 68 single payment, 69 Amortization at a glance, 15 Amortize, single payment, 67 Annual percentage rate, 48, 101 Annualized yield, 84 Annuity account, 61 Annunciators, 24 Answers to questions, 116 Application registers, 29 APR, 48, 101 Arithmetic in registers, 39 Arithmetic operators, 21 Aulo increment, 67 Automatic constant, 35 Automobile loan, 104 Average, 88 Backspace, 22 DAL, 67 Balance, 43, 67 Balloon payment, 43, 56 Basics at a glance, 10 Batteries, 118 changing, 118 BEGIN, 24 (BEG/END), 52 Begin, 13 Begin mode, 53 Borrowing equity , 112 Brightness of display, 21 Buy out value, 62 С (C), 21 Canadian mortgage, 105 Capitalized value, 62 Car loan, 53, 104 Cash flow calculations, 75 clearing, 75 diagrams, 43 discount, 77 cntering, 78 cquations, 131 group, 77 mistakes, 79 problems, 47 replacing, 79 viewing, 79 Cash paid out, 44 Cash received, 44 (CF), 78 Chain calculations, 22 Changing batteries, 118 [CHG], 26 Clear display, 10 Clear statistics, 20 Clearing, 23 Clearing messages, 23 [CLEAR ALL), 53 (CL 2), 85 Colon, 24 Comma, 28 Comparing investments, 71 Compound interest, 45, 46 Compounding annual, 60 daily, 72 monthly, 72 periods, 71 quarterly, 72 Constant, 12, 35 Continuous compounding, 98 Continuous memory, 21 Correcting statistics, 87 Correlation coefficient, 88 Cost, 11 Cost of no discount, 96 Cost per unit, 95 (CST), 33 Cursor, 23 D Daily compounding, 72 Decimal point, 26, 28 Digit separator, 28 Digits, 26 Dim display, 21 Discounted contract, 80 Discounted mortgage, 99 (DISP), 27, 58 C), 28 Index 137 Display all digits, 28 Display format, 21 Dot, 28 Down payment, 53, 55 E (e“], 40 E, 27 (E), 27 [EEF%), 51, 71 Effcctive annual rate, 47 rate, 71 Effective rate, 16 End, 13 End mode, 53 Entering a Guess, 127 Equations, 129 amortization, 130 cash Flow, 131 interest rate conversion, 131 margin and markup, 129 statistics, 132 TVM, 130 Equity, borrow against, 112 Erase, 22, 23 Erase memory, 120 Error messages, 133 Estimate for JRR%, 127 Estimate of x, 88 Estimate of y, 88 Exponents, 27 F Factorial, 40 Fees up front, 101 FLA, 20 Forccasting based on history, 95 Format the display, 26 138 Index Future value, 43, 48 [FV], 43, 48, 52 G Grouping cash flows, 77 Guess for IRR/YR, 127 Hclp for questions, 116 History based forecasting, 95 Home mortgage, 55 Individual retirement account, 60 Initial cash flow, 77 (INPUT), 25 Input annunciator, 24 Installing batteries, 118 Int, 67 Interest compound, 45, 52 simple, 45 Interest conversion at a glance, 16 Interest rate conversion, 71 equations, 131 Interest wath fees, 101 Interest-only loan, 102 Intermediate result, 41 Internal precision, 28 Internal rate of relurn, 17, 49, 75, 83 Investment comparisons, 71 IRA, 60 IRR, 49 IRR/YR, 77 [IRR/YR], 49, 75 IRR /YR al a glance, 18 IRR /YR Calculations, 127 (/YR], 48, 52 K, L K], 35 Lease, 62 advance payments, 03 Lincar regression, 85, 91 [LN], 40 Loan, with fees, 101 Loans, 53 interest only, 102 number of payments, 52 odd first payment, 102 [M+], 35, 37 M register, 29, 37, 35 Malfunction, 116 (MAR), 33 Margin, 11, 33 Markup, 11, 33 Maturity value, 43 Mean, 88 weighted, 94 Memory, 29 clearing, 23 Mcmory keys at a glance, 12 Messages, 29, 133 Mortgage Canadian, 105 discounted, 99 premium, 99 wrap-around, 112 [MU], 33 Mutual fund, 48, 49 [ni], 40 [N], 48, 52 n, 85 Natural logarithm, 40 Negative cash flows, 44 numbers, 22 sign, 13 Net future value, 114 Net present value, 17, 49, 80 Netted value, 82 (NJ), 78 [NOM%], 51, 71 Nominal annual rate, 47 rate, 71 Nominal rate, 16 NPV, TT [NPV], 49, 75 NPV at a glance, 18 O Odd first payment, 102 [OFF], 21 [ON], 21 One payment per year, 58 One-number functions, 25 One-variable statistics, 86 Option to buy, 62 P Parentheses, 41 Partial first payment, 102 Payments, 48, 52 PEND, 24 Percent, 11, 31 change, 32 Percent at a glance, 11 Period, 26, 28 Periodic rate, 47 Periods, 48 [PMT], 48, 52 Population standard deviation, 88 Positive cash flows, 44 [PRC], 33 Premium mortgage, 99 index 139 Present value, 48 Price, 11 Prin, 67 Principal, 45, 67 Principal reduction, 66 [PV], 48, 52 (PZYR), 51, 52, 71 Q Questions, 116 Quick reference, 10 R Range of numbers, 129 [RCL], 33, 35, 38 Recall, 38 Recall memory, 52 Reciprocal, 40 Register, 12 Register labels, 85 Registers, 29 Remaining amount, 43 Reset, 24, 120 Residual, 43 value, 62 Retirement account, 111 (ВМ), 35, 37 (RND), 28 Rounding, 28 errors, 58 5 Sample standard deviation, 89 Saving for college, 107 Savings account, 58 Scientific notation, 27 Self-test, 121 Selling price, 33 Service, 124 140 Index Setting a sales price, 95 Shift key, 10, 24 Short term investment, 75 Sign change, 51 convention, 45 Simple interest, 45, 97 Slope, 88 Square root, 26, 40 [Sx,Sy), 88 Statistics, 85 clearing, 85 corrections, 129 equations, 132 forecasting, 91 limit of values, 86 lincar estimation, 85, 91 lincar forecasting, 85 lincar regression, 85, 91 mean, 85, 89 memory, 85 mistakes, 87 one-variable, 85 population standard deviation, 89 .. 00 sample standard deviation, 89 standard deviation, 85 summation , 89 [SWAP], 88 two-variable, 85 weighted mean, 85 Statistics at a glance, 19 Statistics, weighted mean, 94 Status, 24 [STO], 35, 38 Stock investment, 75 Store, 38 Subtract percent, 31 Summation statistics, 85 Summed value, 82 [SWAP], 25 TT Taxable retirement account, 111 Tax-deferred account, 110 Tax-free account, 110 3 Key Memory, 35 Time out, 21 Trailing zeros, 28 Turn off, 21 Turn on, 21 TVM, 14 cquations, 130 problems, 47 TVM at a glance, 13 Two-number functions, 26 Two-variable statistics, 86 uv Uneven cash flows, 80 Value of a fund, 114 Viewing cash Mows, 79 W Warranty, 123 Weighted mcan, 94 What if ..., 14, 106 What if ... al a glance, 14 Won't turn on, 120 Wrap-around mortgage, 112 Y Yellow shift key, 21 Yield, 83 y-intercept, 88 141

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