HP 20b Business Consultant Financial Calculator Manual For free training, visit www.hp.com/go/calctraining HP part number: F2219-90201 First edition: August 2008 Legal Notices Legal Notices This manual and any examples contained herein are provided “as is” and are subject to change without notice. Hewlett-Packard Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability, non-infringement and fitness for a particular purpose. Hewlett-Packard Company shall not be liable for any errors or for incidental or consequential damages in connection with the furnishing, performance, or use of this manual or the examples contained herein. Copyright © 2008 Hewlett-Packard Development Company, L.P. Reproduction, adaptation, or translation of this manual is prohibited without prior written permission of Hewlett-Packard Company, except as allowed under the copyright laws. Hewlett-Packard Company 16399 West Bernardo Drive MS 8-600 San Diego, CA 92127-1899 USA Revision History Revision History Revision Date Edition 1, v. 12 August 7, 2008 2 Contents Contents Legal Notices Revision History..................................................................................................................2 HP 20b Business Consultant Keyboard Keyboard Map Legend .......................................................................................................6 1 Basic Features Welcome to the HP 20b Financial Calculator .....................................................................7 Turning the Calculator On and Off......................................................................................7 Selecting a Language .........................................................................................................7 Adjusting the Display Contrast............................................................................................7 Cursor .................................................................................................................................7 Two Line Display ................................................................................................................8 The Mode Menu: Setting Preferences ................................................................................8 Changing the Calculation Mode........................................................................................10 Key Presses and the Secondary Function : Key ..........................................................11 Annunciators.....................................................................................................................11 The I Key ..................................................................................................................12 The = Key ......................................................................................................................12 Using the I and = Keys ..........................................................................................12 Editing and Clearing Entries .............................................................................................13 The On/CE O Key ..........................................................................................................13 The Reset :x Menu ....................................................................................................13 Notes about Special Menus..............................................................................................13 Memory and the Memory Menu........................................................................................13 Accessing Menus and Menu Maps...................................................................................14 2 Mathematical Calculations Mathematical Functions....................................................................................................16 Number Entry and Display................................................................................................16 Chain Mode ......................................................................................................................17 Algebraic Mode.................................................................................................................17 Reverse Polish Notation (RPN) Mode ..............................................................................18 The RPN Stack .................................................................................................................18 Last Number .....................................................................................................................19 One-Number Functions and the Math Menu ....................................................................22 The Math :s Menu.....................................................................................................23 The Probability Sub-menu ................................................................................................25 3 Contents Two-Number Functions ....................................................................................................26 Storing and Recalling Numbers ........................................................................................27 Recall Arithmetic...............................................................................................................28 Storing and Recalling with Time Value of Money (TVM) Keys .........................................28 Recalling a Menu Item Value in a Menu ...........................................................................28 Rounding Numbers...........................................................................................................28 Percentages......................................................................................................................28 3 Time Value of Money Time Value of Money (TVM) Keys....................................................................................30 Calculating Payments on a Loan ................................................................................32 Amortization......................................................................................................................33 Creating an Amortization Schedule ............................................................................34 Interest Conversion Menu.................................................................................................35 Using the Interest Conversion Menu...........................................................................35 Canadian Mortgages: TVM Canada .................................................................................36 Canadian Mortgage Example .....................................................................................38 4 Cash Flows Cash Flow Example..........................................................................................................40 Analyzing Cash Flows.................................................................................................42 Editing Cash Flows .....................................................................................................44 Sample Cash Flow Diagrams ...........................................................................................45 5 Bonds The Bond Menu ................................................................................................................46 Bond Calculation Example ..........................................................................................47 6 Date Calculation The Date Calculation Menu ..............................................................................................49 Date Calculation Example...........................................................................................49 7 Break-even The Break-even Menu ......................................................................................................51 Break-even Example...................................................................................................51 8 Business Problems The Percent Calculation Menu .........................................................................................53 Percent Calculation Examples ....................................................................................54 9 Depreciation The Depreciation Menu ....................................................................................................56 Depreciation Example .................................................................................................58 10 Statistical Operations The Data and Stats Menus ...............................................................................................61 4 Contents Statistics Example.......................................................................................................63 11 Errors Error Messages and Calculator Status .............................................................................65 12 Warranty, Regulatory, and Contact Information Replacing the Batteries.....................................................................................................67 HP Limited Hardware Warranty and Customer Care........................................................67 Customer Care .................................................................................................................68 Product Regulatory & Environment Information ...............................................................71 Index 5 HP 20b Business Consultant Keyboard HP 20b Business Consultant Keyboard Keyboard Map Legend No. Feature Chapter(s) No. Feature 1 Time Value of Money keys 3 16 Annunciator display area 2 Cash Flows, IRR, and NPV 4 15 Amortization and Depreciation menus 3 Data and Statistics menus Chapter(s) 1 3,8 menus 9 14 % key and Percent 2,6 Calculation menu 4 Input key 1 13 Store and Recall 2 5 Memory menu 1 12 Break-even menu 6 6 Up/Insert and Down/Delete 1 11 Backspace key and Reset 1 keys menu 7 Secondary function key 1 10 Math Menu 2 8 On/Off and clear entry key 1 9 Mathematical function keys 2 6 Basic Features 1 Basic Features Welcome to the HP 20b Financial Calculator This manual is designed to familiarize you with the many features of your new 20b Financial Calculator. It includes menu maps, example problems and solutions with key presses, screen shots, and examples of cash flow diagrams. There are also sections which list the error messages and explain how RPN works. Refer to the section titled, Contents for quick access to various topics. If you need more information about your calculator, or about calculator operation and features, please refer to the training materials available at: www.hp.com/go/calctraining. Turning the Calculator On and Off To turn on your calculator, press O. To turn it off, press :a. Turning the calculator off does not erase any data. The calculator automatically turns itself off after approximately five minutes to conserve energy. If you see the low battery symbol () in the display, replace the batteries. See Chapter 12, Warranty, Regulatory, and Contact Information for instructions on replacing the batteries. Selecting a Language English is the default language for messages displayed on the screen. To select a language other than English: :u to access the Mode menu. FIX displays on the top line of the screen. Press < repeatedly until English displays on the screen. Press I until the desired language is displayed. The displayed language is the active setting. Press O to return to the default calculator screen. 1. Press 2. 3. 4. For more information on accessing menus and changing calculator settings, refer to the sections below titled, The Mode Menu: Setting Preferences, and Accessing Menus and Menu Maps. Adjusting the Display Contrast To adjust the contrast of the display, press and hold O while pressing the + or - keys. Each press of the + or - keys slightly increases or decreases the contrast of the display. Cursor When you enter a number, the cursor (_) blinks in the display and indicates you are in number entry mode. 7 Basic Features Two Line Display There are two lines in the display screen as shown in Figure 1. Figure 1 Display Screen The top line of the screen displays operation status, operator symbols, annunciators, and abbreviations of the registers, variables, and menu names. Throughout this manual, this line is referred to as the top line. In Figure 1, SIN is on the top line. The bottom line displays numbers you have entered, or results. Throughout this manual, this line is referred to as the bottom line. When no operations have been entered and no operations are pending, the bottom line of the screen displays 0.00. This state of the calculator is referred to as the default calculator screen. The Mode Menu: Setting Preferences The Mode menu allows you to customize the calculator. To access the Mode menu, press :u. Press < or > repeatedly to scroll through the menu starting with FIX=2 (the number of digits displayed to the right of the decimal point). Once an item is displayed, press I to cycle through the other options for that setting. To exit the Mode menu, press O. Table 1-1 lists the items in the Mode menu. 8 Basic Features Table 1-1 Mode Menu Settings Setting (top line) Description FIX= 2 Display precision (number of digits displayed to the right of the decimal point). Default is 2. Key in the number of digits you want and press I, or press = until the number of digits you want is displayed. The display precision can be any number from 0-11. If you specify -1, the calculator displays numbers with the most appropriate number of digits after the decimal point. If you find you need to change the FIX setting often, use the following shortcut: : and release it. Check that the secondary function indicator is displayed. Press : again, and, without releasing it, press a key, 0 through 9 that corresponds 1 Press 2 to the desired FIX setting. FIX settings for 10 and 11 are not available using this shortcut. If you press Degree or Radian . instead of a numbered key, FIX=-1 is selected. Angular mode in degrees or radians for trigonometric functions. Default is Degree. Pressing I toggles between these options. Date: Format for dates. December 3, 2010 is entered as 12.032010 in mm.ddyyyy format, or 3.122010 in mm.ddyyyy or dd.mmyyyy format. Note the (.) in both formats separating the first and second groups. dd.mmyyyy Default is mm.ddyyyy format. Pressing I toggles between these options. Note that when a date is displayed, a number between 1 and 7 also displays at the right of the screen. This number indicates the day of the week corresponding to that date. Monday is 1, and Sunday is 7. Note: in 360-day calendar mode (Cal.360), days of the week are displayed only if the date is valid. 1.23 or 1,23 Selects point or comma as decimal separator. Default is decimal point, 1.23 Pressing I toggles between these options. 1000.00, 1,000.00, Selects thousands separator. 1000,00 or 1.000,00 Default is none, 1000.00 Pressing I toggles between these options. Note: the 1000.00 and 1,000.00 options are only available if the decimal separator is set for point (.); 1000,00 and 1.000,00 are available only if the decimal separator is set for comma (,). Chain, Algebraic, or RPN Calculation mode. For more information, refer to Chapter 2, Mathematical Calculations. Pressing I cycles through these options. 9 Basic Features Table 1-1 Mode Menu Settings Setting (top line) Description English, Français, Language setting for the messages displayed on the screen. Deutch, or Español Default is English. Pressing I cycles through these options. Actual or Calendar options for bonds and date calculations. Cal.360 Default is Actual. Pressing Annual or Semiannual I toggles between these options. Bond type. Default is Annual. Pressing I toggles between these options. TVM Standard or TVM Activate or deactivate the compounding per year (C/YR) option in time value of money (TVM) Canada calculations. This option is primarily used for Canadian mortgage calculations. For more information, refer to the section titled, Canadian Mortgages: TVM Canada in Chapter 3. Pressing I toggles between these options. Changing the Calculation Mode After viewing the default settings, suppose you want to change the calculation mode from Chain to RPN. See Table 1-2. Table 1-2 Changing the Calculation Mode Keys Display Description :u Opens the Mode menu, starting with first setting option, FIX, the number of digits displayed to the right of the decimal point. <<<< < Scrolls to the current setting for the calculation mode, Chain. (Press five times) II Selects RPN as the active setting. Note the small RPN annunciator to the right. (Press two times) O Exits the Mode menu and returns you to the default calculator screen. 10 Basic Features Key Presses and the Secondary Function : Key To execute the function associated with a key, press and release the desired key. Most of the 20b's keys have two functions: the primary function and the secondary function. The primary function is printed on the top of the key. The secondary function is printed on the bevel of the key. See Figure 2. Primary Function R Secondary (shifted) Function Figure 2 Primary and Secondary Key Functions : followed by the key with the desired secondary function printed on the bevel. Unlike the shift key on a typewriter or computer keyboard, it is not necessary to press and hold : To activate the secondary function of a key, press and release while pressing another key. : is active, the down arrow annunciator appears on screen, indicating that the next key pressed will execute the secondary function of the key. To cancel an accidental press of :, simply press : a second time. In this manual, commands using the secondary key functions are represented by the secondary function key symbol, :, followed by the key with the secondary function. For example, to execute sine, press :p. Note how the SIN portion of When the key is highlighted, while the 7 is grayed out. This highlighting focuses on the function of the key that will be activated in a given command, and it is used throughout the manual to make the examples easier to follow. Key commands for example problems are provided throughout the text and in tables. Key symbols are placed in the order they are to be pressed, from left to right. Annunciators Annunciators are symbols that appear in the display as messages, or after certain keys or key combinations have been pressed. Annunciators are special symbols indicating a specific status in the calculator. Figure 3 illustrates the annunciator symbols in the display. 11 Basic Features Figure 3 Annunciator Symbols in the Screen Display The I Key The I key is used to input values for variables and execute menu items. The I key is also used in Reverse Polish Notation (RPN) mode to enter a number on the stack or duplicate it. The = Key The = key is used at the end of a mathematical operation to calculate the final result. For example, 1+2= returns a final result of 3. The = key, when pressed outside of a mathematical operation, also allows you to request a calculation for the value of an item. This request only applies to items that can be calculated. Using the I and = Keys Suppose you wanted to calculate the effective interest rate for a 12% nominal interest rate with 12 payments per year in the Interest Conversion (IConv) menu. To open the IConv menu, press :&. Nom %= displays on the top line, and the current value assigned to the nominal interest rate is displayed on the bottom line. With this screen displayed, press 12I to input a new value for the nominal rate. Press < followed by = to calculate the value for the effective rate. See Figure 4. Figure 4 12 Basic Features When an item for which the = key is valid displays, the small annunciator (=) is displayed on the top line at the right of the screen. Do not confuse this small annunciator (=) with the larger annunciator When an item for which the (=) found to the right of a variable. I key is valid displays, the INPUT annunciator is displayed on the top line at the right of the screen. Editing and Clearing Entries The On/CE O Key Pressing O one time cancels current number entries, mathematical operations, or a menu selection, in that order. Pressing O repeatedly when performing multiple operations cancels one operation at a time, from the latest to the earliest. The Reset :x Menu The Reset menu allows you to reset some, or all, of the menu items, variables, and registers to their default values. :x. TVM displays on the top line. Press < or > repeatedly to scroll to a specific item. To validate a choice and reset the selected items, press I. Press O to cancel. If you select the To open the Reset menu, press command to reset the cash flow (Cash Flow ), statistics (Stats ), or all values (All ) items, you will be prompted to confirm your choice. At the Del. All?, Del. Data?, and Del. CF? prompts, press While working within a specific menu, pressing I again to confirm the reset, or O to cancel. :x takes you directly to the item of the Reset menu that allows you to reset that specific menu. For example, if you are working in the Bond menu and you wish to reset all your entries in the Bond menu, with any item of the Bond menu displayed, press :x. Bond displays on screen. At this prompt, pressing I resets the Bond menu and returns you to the last item you were working with in the Bond menu. Notes about Special Menus The Mode, Memory, Math and Reset menus are special menus; if you were working in a menu prior to entering one of these special menus, pressing O to exit them returns you to your previous menu,. This feature allows you to work in two or more menus simultaneously without having to exit a menu. Memory and the Memory Menu The Memory menu contains the following items: memories 1-9 ( Mem 1-9 ) and 0 (Mem 0 ), Cash Flow, Statistics (Stats), and Memory. To enter the menu, press :t. Press < or > repeatedly to scroll through the items starting with memory 1 (Mem 1 ). When a memory item is displayed, you can enter a new number and modify the value of the memory by pressing 13 I. Basic Features For more information about storing and recalling numbers, refer to the section titled, Storing and Recalling Numbers in Chapter 2. The Cash Flow and Statistics menus share the same memory and are limited to a combined total of 50 memory slots. The number displayed with Memory refers to the number of remaining memory slots. When the cash flow or statistics items are displayed, a number also appears on the bottom line. This number indicates the number of memory slots used by the menu. Pressing I with this number displayed resets the memory of the displayed menu item and erases all entered data. Since entering data in these menus can represent a significant amount of work, you will be asked to confirm your choice. At the Del.Data? or Del.CF? prompts, press I to confirm, or O to cancel. Accessing Menus and Menu Maps Many of the calculator's functions are located within menus. To access a menu, press the key, or secondary-function-keycombination, for the menu in which you wish to work. To exit a menu, press O. :!. Once opened, you can scroll through the items in the menu by pressing <or> repeatedly. When you arrive at the last item in a menu, pressing < returns you to the first item. Similarly, pressing > one time on the first menu item scrolls to the last item in the menu. For example, to access the Break-even menu, press Most items consist of two parts: a name and an associated number. For example, the Fixed item in the Break-even menu (Figure 7) displays as shown in Figure 5. Figure 5 The large (=) annunciator shows that the value assigned to Fixed is 120,000. If you perform a calculation with this item displayed by pressing 1+2= for example, Fixed is still selected as the current item, but the large (=) annunciator is now turned off, indicating the 3 is not the value assigned to Fixed (see Figure 6). Figure 6 At this point, to return to the display of the Fixed menu item shown in Figure 5, press Some menus have sub-menus. If an item represents a sub-menu, pressing sub-menu. 14 O. I with that menu item displayed opens the Basic Features In this manual, diagrams called Menu Maps are included at the beginning of each section to assist you with navigating through the menus used for that section. For an example of a menu map, see Figure 7. Figure 7 The Menu Map for the Break-even Menu There are four types of menu items: 1. Read/write. Read/write menu items, such as Fixed in the Break-even menu shown above, are easily recognizable, because when they are selected, both the INPUT and small (=) annunciators are lit. When lit, these annunciators indicate that entering a number and pressing Pressing I will store the entered number in the displayed menu item. = (outside of a mathematical operation) calculates the value for that item based on available data. 2. Read-only. Read-only items such as Internal Rate of Return (IRR% ) in the IRR menu are display-only; they are calculated values computed internally by the calculator. 3. Write-only. Write-only items, such as investment interest rate (Inv. I% ) in the Net Present Value (NPV) menu, are similar to read/write items in that the INPUT annunciator is lit when these items are selected, indicating that entering a number and pressing I stores that number in that menu item. However, the = key does not calculate a value for that item. 4. Special items. Special items, such as the Degree/Radian option in the Mode menu, the items of the Reset menu, and the items of the Percent Calculation (%calc ) menu perform an action when I is pressed. Depending on the menu, this action can be the selection of a sub-menu (%calc menu), changing a mode or setting (Mode menu), or erasing data (Reset menu). 15 Mathematical Calculations 2 Mathematical Calculations Mathematical Functions Mathematical functions are located: +-*/, etc. On keys, such as, On shifted, or secondary functions, such as, In the Math menu, :p :s Number Entry and Display Numbers are entered by pressing: 0- 9 Numbered keys, The decimal point The } The :w keys . key To correct a number entry, press the backspace key, {. Each press of { erases the last digit or symbol you entered. To enter a number in the display, press the number digits successively. A number can have up to 12 digits. To change the sign of a number from positive to negative, press }. Use scientific notation to enter very large and very small numbers. For example, to enter the number 1.23 10 127 notation, first enter the mantissa (1.23 ) and then press in scientific :w and enter the number (127 ) representing the exponent. The exponent must have a value between -499 and +499. Figure 1 Scientific Notation in FIX=2 Mode 16 Mathematical Calculations Chain Mode Calculations in Chain mode are interpreted in the order in which they are entered. For example, entering the following numbers and operations as written from left to right 1+2*3= returns 9. See Figure 2. Figure 2 Calculation in Chain Mode Note: if you press an operator key, +-*/, after =, the calculation is continued using the currently displayed value. In Chain mode, if you wish to override the left to right order of entry, use parentheses For example, to calculate () to prioritize operations. 1 2 3 , you may enter the problem as written from left to right, with parentheses to prioritize the multiplication operation. See Table 2-1 below. Table 2-1 Simple Arithmetic Calculations in Chain Mode Keys Display Description 1+ (2*3) Sets operational priority, inputs numbers, and = Adds 1 to 6 and returns 7.00 on the bottom line as multiplies 2 and 3. the final result. Algebraic Mode To set the calculator in Algebraic mode, refer to the section titled, The Mode Menu: Setting Preferences in Chapter 1. In Algebraic mode, multiplication and division have a higher priority than addition and subtraction. For example, in Algebraic mode, pressing 1+2*3= returns a result of 7.00. In Chain mode, the same key presses return a result of 9.00. In Algebraic mode, operations between two numbers have the following priority: Highest priority: the power function (yx) Second priority: combinations and permutations Third priority: multiplication and division Lowest priority: addition and subtraction 17 Mathematical Calculations For example, key in 1+ 2 x 5 nPr22 in Algebraic mode by pressing: 1+2*5:b2:m=. The result is 241. Note: the calculator is limited to 12 pending operations. An operation is pending when it is waiting for the input of a number or the result of an operation of higher priority. Reverse Polish Notation (RPN) Mode To set the calculator in RPN mode, refer to the section titled, The Mode Menu: Setting Preferences in Chapter 1. In RPN mode, numbers are entered first, separated by pressing Note: pressing I or =, followed by an operation key. I or = is optional after entering a number, if the next key pressed is an operation. Each time you press an operation or function key in RPN, the answer is calculated immediately and displayed. For example, suppose you wanted to add two numbers in RPN, 1 and 2. Press 1I2+. The result, 3.00, is calculated and displayed immediately on the bottom line along with the (+) symbol on the top line. Note: in RPN mode, when you are in a menu for which I or = are valid, pressing these keys enters the number, but it also performs the action associated with the key for the menu item, which is generally saving the number in the variable or calculating the item's value. The RPN Stack RPN works by placing numbers in storage registers called the stack. The RPN stack has four levels numbered 1-4. The levels are stacked on top of one another. See Figure 3. Stack Level 4 -15 Stack Level 3 12 Stack Level 2 41 Stack Level 1 23 Figure 3 The RPN Stack In Figure 3, the stack contains four numbers, 23, 41, 12, and -15. Each level (1-4) contains one number. When a number is typed and entered into the stack by pressing I, this new number is "pushed" into level one of the stack, and each number already in the stack moves up one level. The number in Level 4, -15, is pushed out and is lost. 18 Mathematical Calculations When an operation is performed on the stack, addition (+) for instance, the calculator "pops" or moves the two numbers from the bottom levels (Levels 1 and 2) out of the stack, performs the operation, and "pushes" the results back into the stack. With the numbers entered into the stack as shown in Figure 3, pressing + changes the stack as shown in Figure 4. Note that when the numbers are "popped" out to add 23 and 41, Level 4 of the stack remains unchanged. -15 -15 12 64 Figure 4 The RPN Stack of Figure 3 after the Addition Operation Last Number Each time you perform a mathematical operation, the content of Level 1 of the stack is saved. Pressing :d recalls that number. This functionality can be used to undo an erroneous key press, or if you want to reuse a number, such as 56.123 in the expression: 1.23 56.123 56.123 See Table 2-2 for an example using the last number function. Table 2-2 Last Number Keys Display Description :u3I Sets FIX= to 3.000 <<<<< II Selects RPN as the operating mode. O1c23 I56c1 23 Inputs 1.23 and 56.123 19 Mathematical Calculations Table 2-2 Last Number Keys Display Description +:d/ Adds 1.23 and 56.123, then divides the sum by the last number, 56.123. Returns results in the selected display format. For more complex problems requiring two or more operations, you do not need to enter parentheses to set operational priority. Key in numbers and operations inside the parentheses first, followed by those outside of the parentheses. If a problem has more than one set of parentheses, start by working with the operations and numbers in the innermost parentheses and work out. For example, calculate: 3 4 5 6 One way to calculate this problem is to key in the numbers and operations within the parentheses first, followed by the operation outside of the parentheses. See Table 2-3. Table 2-3 Simple Arithmetic Calculations in RPN Mode Keys Display Description RPN Stack Inputs the numbers and the 3I4+ operation in the first set of Previous Value parentheses. Intermediate results are displayed. Note Previous Value the (+) and (RPN) annunciators. Previous Value 7 5I6+ Inputs the numbers and the operation in the second set of parentheses. Intermediate results are displayed. Note the (+) annunciator. 20 Mathematical Calculations Table 2-3 Simple Arithmetic Calculations in RPN Mode Keys Display Description * RPN Stack Finishes the operation and displays the results. I or = when you are not entering a number duplicates the number on Level 1. That is, the number on Level 1 is pushed on the stack, making Levels 1 and 2 equal. In the example above, pressing I after * duplicates Pressing 77 on the stack, making Levels 1 and 2 equal. See Figure 5. Previous Value Previous Value 77 77 Figure 5 Duplicating a Number on the Stack In RPN, the parentheses keys () manipulate the stack. Pressing ( performs a roll down of the stack. A roll down causes the stack to roll towards the bottom of the stack, during which the number in Level 2 moves down to Level 1, the number in Level 3 moves down to Level 2, the number in Level 4 moves down to Level 3, and the number in Level 1 moves ( key has a small down arrow on it as a reminder of the roll down feature. With the numbers entered into the stack shown in the left column in Figure 6, pressing ( performs the roll down of the stack shown in the right up to Level 4. The column. 21 Mathematical Calculations Figure 6 The RPN Stack and the Roll Down Operation Pressing ) performs a swap. A swap operation exchanges the numbers on Levels 1 and 2 of the stack. The ) key has a small symbol on it as a reminder of the swap feature. With the numbers entered into the stack shown in the left column in Figure 7, pressing ) performs a swap to the stack as shown in the right column. Figure 7 The RPN Stack and the Swap Operation Note: when no menu is selected, the < key performs the same function as the ( key. The > key performs the inverse operation called, roll up. One-Number Functions and the Math Menu The key presses for the one-number mathematical functions listed in Table 2-4 below apply to all modes, Chain, Algebraic, and RPN. To execute one-number functions, with a number displayed, press the key or key combination corresponding to the operation you wish to execute. The result is displayed on the bottom line. 22 Mathematical Calculations For example, to calculate 6 , press 6:n. The result of 2.45 is calculated immediately and displayed on the bottom line. The square root symbol ( ) appears on the top line. Note: before doing any trigonometric calculations in the Math menu, check whether the angle mode is set for degrees (Degrees) or radians (Radians). You will need to change the setting if the active mode is not what your problem requires. For more information on the Mode menu and calculator settings, refer to the section titled, The Mode Menu: Setting Preferences in Chapter 1. Table 2-4 lists one-number functions along with their corresponding keys. Table 2-4 Shifted Function Mathematical Operations Keys Description :p Calculates sine. :q Calculates cosine. :r Calculates tangent. :k Calculates natural log. :l Calculates natural exponent to the power of x. :m Calculates square of x. :n Calculates square root. :f Executes the Random function. Returns a random number in the range 0 < x <1. :g Calculates factorial of x (where -253 < x ≤ 253). The Gamma function is used to calculate x! for :h Calculates y to the x power. :i Calculates the reciprocal. :d In Chain or Algebraic mode, recalls the result of the last operation. In RPN mode, returns the :e Rounds x internally to the number specified by the display format. non-integers or negative numbers. content of the Last Number variable. The Math :s Menu There are additional functions available in the Math menu. To open the Math menu, press menu map of the Math menu. 23 :s. See Figure 8 for the Mathematical Calculations Figure 8 The Menu Map for the Math Menu < to scroll through the menu items, starting with Trigonometry. The Trigonometry, Hyperbolic, and Probability items have sub-menus. Press I with these items displayed to access the functions within the sub menus. Press Press O to cancel the Math menu and return to current work. Press :s to return to the top of the Math menu. For an example using the math menu to calculate Sin -1 (0.5), see Table 2-5. 24 Mathematical Calculations Table 2-5 Math Menu Example Keys Display Description .5I :s Enters 0.5 and opens the Math menu starting with I< Selects the Trigonometry sub-menu and scrolls to Sin-1. Trigonometry. Note the value for Sin-1 is calculated immediately and displayed. I or = Validates the result. In the Math menu, PI does not perform calculations; it enters PI for calculations. You may start an operation, use the Math menu to execute a function, and continue calculating with your original operation without losing your work. The Probability Sub-menu Lower Tail Normal Distribution (LTND) calculates the probability for a normally distributed, random variable to be less than the input. Inverse Lower Tail Normal Distribution (LTND-1) is the inverse function for LTND; it calculates the value (V) for which the probability of a normally distributed, random variable to be less than V is the given input. Student, Inverse Student, Chi 2, Inverse Chi2, F-Distribution and Inverse F-Distribution perform similar operations for Student, Chi 2, and F-Distributions. Student, Chi2, and F-Distribution and their inverse operations are special cases, as they require more than one number as input. Student and Chi2 require (N), the number of degrees of freedom, and F-Distribution requires (N1) and (N2), two degrees of freedom. To perform Student and Chi2 operations or their inverse: 1. Enter the number of degree(s) of freedom by typing the number and pressing I or =. 2. Type the number for which you want to calculate the probability, or, for the inverse, the probability for which you want the number. 3. Navigate to the appropriate function in the Probability sub-menu of the Math menu. To perform F-Distribution operations or their inverse: 1. Enter the two degrees of freedom by typing each number followed by 25 I or =. Mathematical Calculations 2. Type the number for which you want to calculate the probability, or, for the inverse, the probability for which you want the number. 3. Navigate to the appropriate function in the Probability sub-menu of the Math menu. Table 2-6 Probability Example Keys Display Description 10I 8I :s Enters 10 degrees of freedom and the number for which <<I <<<< Selects the Probability menu item and scrolls to Chi2. I or = Validates the result. probability is to be calculated. Opens the Math menu. Table 2-7 Inverse Probability Example Keys Display Description 10I 0.37 12I :s Enters 10 degrees of freedom and the probability. Opens <<I <<<< < Selects the Probability menu item. Scrolls to Chi2-1. I or = Validates the result. the Math menu. Two-Number Functions Apart from +-*/, the three additional two-number functions accessible on the keyboard are: Yx 26 Mathematical Calculations nCr nPr Y x is the power function, nCr stands for the number of combinations of n items taken r at a time, and nPr stands for the number of permutations of n items taken r at a time. Combination= n! r!n r ! Permutation= n! n r ! Perform calculations with these functions in the same way you would perform calculations with but press +-/ and *, : to access the secondary function key. For example, to calculate 153 : 1. Press 15. 2. Press :h. 3. Press 3=. The results are shown Figure 9. Figure 9 I, then press the function key. For example, for the power function example above, in RPN press: 15I3:h. In RPN mode, key in the numbers first, followed by Storing and Recalling Numbers The calculator has ten memories available for use during calculations. These memories are numbered from 1-9 and 0. To store a number in a memory, press stored in a memory, press :$, followed by the key representing the memory number. To recall a number L followed by the key representing the memory number. You can use the store and recall functions for these memories any time a number is displayed, or when you wish to enter a number. For example, to store 15 in memory 1, press To recall the number in memory 1, press 15:$1. L1. 5:$2 to store 5 in memory 2. To add 12 to the value of memory 2, press 12:$+2. Later on, during a calculation, you can You can also perform operations to numbers stored in memories. For example, press 27 Mathematical Calculations press L2 to recall memory 2. Note how the new current value stored in memory 2 is 17, (5 +12). +-* and / are valid mathematical operations for memories. To view the stored values in memories 1-9 and 0, press :t, followed by < or > repeatedly to scroll through each memory starting with memory 1 (Mem 1 ). Note that in the Memory menu, you can change the value of any memory by selecting the memory and typing a number followed by the t key. Recall Arithmetic 12L+2 adds the value of memory 2 to the first level of the stack, but it will not modify the stored value of memory 2. This is useful, as it "saves" one stack level. You can also use -* and / after L. In RPN, typing To perform the same operation in Algebraic and Chain modes, press 12+L2=. Storing and Recalling with Time Value of Money (TVM) Keys To store the current number in the Time Value of Money (TVM) variables, press To recall the stored value of a TVM variable, press :$ followed by the desired TVM key. L followed by the key of the desired TVM variable. Note: pressing L does not calculate the variable; it recalls the current value. Recalling a Menu Item Value in a Menu In a menu, you can recall the current value of a menu item. For example, open the Interest Conversion menu (IConv) by pressing :&. With Nom.% displayed, pressing 2*L= recalls the nominal rate. This feature is useful when you need to insert the contents of a menu item into an algebraic operation. Rounding Numbers All calculations are performed internally with 15-digit precision and are rounded to 12 digits when returning the results. In certain instances, calculations are performed internally with greater than 15-digit precision. When displayed, a number is further rounded to the number of digits after the decimal point set by the FIX item in the Mode menu. The default setting is two digits to the right of the decimal point. For more information, refer to the section titled, The Mode Menu: Setting Preferences in Chapter 1. Note: the FIX setting only affects the display; it does not affect the actual numbers. Percentages In Algebraic or Chain modes, pressing % divides a number by 100. For example, pressing 25% returns 0.25. 28 Mathematical Calculations To find a percentage of a given number, enter the number and multiply it by the desired percentage, followed by =. For 200*25%= to return a result of 50. To add or subtract a percentage of a number, enter the first number, followed by + or - and the percentage followed by %. Finish your calculation with =. For example, to add 10% to 50, press 50+10%= to example, to find 25% of 200, press return a result of 55. In RPN mode, the % key calculates x % of the number on Level 2 of the stack, when x is the number on Level 1 of the stack. It does not modify the number on Level 2 of the stack, and thus allows you to perform addition or subtraction after pressing % to add or subtract x % from the number. For example, 200I25% returns 50, but 200 is still on Level 2 of the stack, and pressing - returns 150, or 200-25%. 29 Time Value of Money 3 Time Value of Money The examples in the following sections are calculated with the Mode menu preferences in their default settings, unless otherwise noted. For more information about basic features and setting preferences, see Chapter 1 , Basic Features. Time Value of Money (TVM) Keys Cash flow diagrams are useful tools for analyzing financial situations, as they help you identify the TVM functions needed to resolve your problem. A cash flow diagram is a drawing with a set of vertical arrows arranged on a horizontal line. The horizontal line represents the period of time from the beginning of the financing to the end. The vertical arrows represent the money or cash flows at certain times throughout the period. The arrows' length is proportional to the cash flow amount each arrow represents; a longer arrow indicates a larger amount, a shorter arrow, a smaller amount. Each arrow's position on the line represents the time at which the cash flow occurs. The orientation of the arrow, up or down, represents the "direction" of the cash flow: up for money received, down for money paid out. See Figure 1. 30 Time Value of Money Figure 1 Cash Flow Diagram Example with Corresponding TVM Keys The TVM functions of the calculator can solve problems with at least one cash flow, and problems in which all the cash flows, except the first and last, are of the same value. To solve other types of cash flows, refer to the section below titled, Canadian Mortgages: TVM Canada, or Chapter 4, Cash Flows. Figure 1 illustrates a cash flow diagram and how the data in the diagram corresponds to the TVM keys. For a complete list of keys used for TVM problems, along with their descriptions, see Table 3-1. 31 Time Value of Money To save values for the TVM variables, enter the desired number, followed by the corresponding TVM key. To calculate an unknown value, enter all known values and press the key of the item you want solved. Table 3-1 TVM Keys Keys Description N Stores or calculates the number of payments or compounding periods. ^ Multiplies a value by the number of payments per year and stores as N. Y Stores or calculates the nominal, annual interest rate. V Stores or calculates the present value (PV). To a lender or borrower, PV is the amount of a loan; M Stores or calculates the amount of each periodic payment. [ Stores the number of payments or compounding periods per year. F Stores or calculates the future value (FV), a final cash flow. FV always occurs at the end of the ? Sets Begin mode (Beg). Payments occur at the beginning of each compounding period. ] Sets End mode (End). Payments occur at the end of each compounding period. to an investor, PV is the initial investment. PV always occurs at the beginning of the first period. last compounding period. Calculating Payments on a Loan You borrow 140,000.00 for 30 years (360 months) at 6.5% annual interest, compounded monthly. What is your monthly payment to the lender? Note: at the end of the 30 years, you expect to have a zero balance (FV=0). Table 3-2 TVM Example Keys Display Description 12:[ Inputs 12 as the number of payments per year, or 360 N Inputs 360 as the number of payments over 30 years. 6.5 Y Inputs 6.5% as the nominal interest rate percentage per year. 1400 00V Inputs the present value of the loan at the time of the first 0F Inputs 0 as the future value of the loan (the remaining compounding periods per year. payment. This value is positive (+); it is money you receive. balance). 32 Time Value of Money Table 3-2 TVM Example Keys Display Description M Returns the monthly payment. This result is negative (-); it is money you pay out. To reset the TVM variables to their default values, with any TVM variable displayed press repeatedly until TVM displays. Press :x. Press < or > I to reset the TVM values, or press O to cancel. Amortization Refer to Figure 2 for a menu map of the Amortization menu (Amort). Table 3-3 lists the keys and variables of the Amortization A. The Amortization menu calculations are based on values stored in the following TVM registers: N, Y, V, M and [. menu. To open the menu, press To enter values for the TVM variables, enter a number followed by the corresponding key. For an amortization example, see Table 3-4. Figure 2 The Menu Map for the Amortization Menu Table 3-3 Amortization Menu Items Menu Item/Key Description A Opens the Amortization menu. Nb Period Number of periods to group together in the amortization calculation. The default value is the number of payments per year defined by the Start [ key. Period on which to start amortization. Default is 1. If you want to amortize for the second year with 12 payments per year, enter 13 (the second year starts at the 13th payment with 12 payments per year). Balance The loan balance at the end of the assigned amortized period. Principal Amount of the loan payment applied to the principal at the end of the amortized period. Interest Amount of the loan payment applied to the interest at the end of the amortized period. 33 Time Value of Money Enter the values for the TVM keys for the example below. Press A followed by < or > to view the amortization schedule. Creating an Amortization Schedule You borrow 140,000.00 for 360 months at 10% interest. Create an amortization schedule for the loan. How much interest did you pay for the first year? What is the balance of your loan after the first year? See Table 3-4. The example below is shown with RPN as the active operating mode. Table 3-4 Amortization Example Keys Display Description 12: [ Inputs 12 as the number of payments per year. 30: ^ Inputs 360 (30 times 12 payments per year) as the number of 10Y Inputs 10 as the interest rate percentage per year. 1400 00V Inputs the value of the loan at the time of the first payment. 0F Inputs 0 as the future value of the loan (zero balance). M Calculates the monthly payment. A Displays the number of periods to group together in the < Displays the first period of the group of periods to amortize. < Displays the current balance remaining after the first year. < Displays the current amount of the principal applied towards < Displays the amount of interest paid on the loan for the first payments for the 30-year loan. amortization schedule. Default is the current value of P/YR. the loan for the first year. year. The amount of your payments applied towards interest for the first year is about 14,000.00. < Displays the first payment in the next period to amortize (the second year). Note that the calculator automatically updates Start to the next group of periods to amortize. 34 Time Value of Money To reset the menu items to their default values, with any item of the Amortization menu displayed press displayed, press :x. With TVM I. At the TVM Reset prompt, press I to reset, or O to cancel. Interest Conversion Menu Figure 3 The Menu Map for the Interest Conversion Menu To open the Interest Conversion menu (IConv) press :&. Table 3-5 Interest Conversion Menu Items Item Description Nom.% Nominal interest rate: the stated annual interest rate compounded as represented by P/YR, such as 18% compounded monthly (P/YR=12 ). Eff.% Effective annual interest rate taking compounding into account. C/YR Compounding periods per year. Default is 12. Using the Interest Conversion Menu Find the effective rate of a 36.5% nominal rate compounded daily. See Table 3-6. See Figure 3 for help with navigating through the menu. Table 3-6 Interest Rate Conversion Example Keys Display Description :& Opens the IConv menu, starting with the current value of the 36. 5I Inputs 36.5 as the nominal percentage rate. > Scrolls to compounding periods per year, C/YR. Default value nominal percentage rate. is 12. 35 Time Value of Money Table 3-6 Interest Rate Conversion Example Keys Display Description 365 I Inputs 365 as the value for the number of compounding periods per year. >= Scrolls to the variable for the effective rate and calculates it. A 36.5% nominal rate compounded daily equals an effective rate of 44.03%. Note: C/YR is the same number as P/YR in TVM calculations, since most interest calculations are based on the same number of payments and compounding periods per year, and interest rate conversions are commonly linked to a subsequent TVM calculation. This feature is provided for your convenience, but this means modifying one number also modifies the other. If your TVM problem requires different values for P/YR and C/YR, refer to the section below titled, Canadian Mortgages: TVM Canada. The IConv menu permits you to solve for C/YR, but the result is not always a positive integer. TVM calculations, however, require C/YR to be an integer larger than zero. If you attempt to perform a TVM calculation without a valid value for C/YR or P/YR, an invalid P/YR error (ER: Invalid P/YR) will occur. If you set C/YR to 0, the resulting interest conversions are calculated assuming a continuous compounding. As stated above, 0 is not a valid value for P/YR or C/YR when used in TVM calculations, and you will have to reset it to a valid value before performing TVM calculations. To reset the menu items to their default values, with any item of the Interest Conversion menu displayed press With IConv displayed, press :x. I to reset, or O to cancel. To exit the menu, press O once again. Canadian Mortgages: TVM Canada Figure 4 The Menu Map for the P/YR Menu In Canada, interest rates for mortgages are, by law, given as a nominal interest rate, compounded twice yearly. This means that the compounding period for the per-period interest rate calculation differs from the compounding period used to calculate the nominal rate. By default, the HP 20b performs calculations assuming that the number of compounding periods always equals the number of payments per year. You can, however, enable the TVM Canada option in the Mode menu, which enables you to select the number of compounding periods per year. For more information, refer to Chapter 1, Basic Features. 36 Time Value of Money With TVM Canada enabled in the Mode menu, the following TVM features change: :[, now opens a menu with two items, P/YR and C/YR, in which you can specify the number of payments and compounding periods per year. Press < or > to scroll through the menu. See 1. The P/YR key, Figure 4. 2. To change the value of an item, with the item displayed, enter the number desired followed by I. 3. In the Interest Conversion menu, the C/YR item has the same value as the C/YR item in the P/YR menu, and C/YR and no longer affects P/YR. 4. Note, however, if you now change the value of P/YR, the calculator automatically sets C/YR so it equals your new value assigned to P/YR. This means that if you modify P/YR, you also need to modify C/YR, if P/YR and C/YR are different values in your TVM problem. 37 Time Value of Money Canadian Mortgage Example Calculate the monthly payment for a 25-year (N=300) Canadian mortgage valued at 350,000.00, if the nominal interest rate is 6.0%, compounded twice yearly (C/YR=2) with 12 payments per year (P/YR). Table 3-7 Canadian Mortgage Example Keys Display Description :u Opens the Mode menu, starting with the current FIX value >I Scrolls to TVM mode and sets mode to TVM Canada. O Returns to default calculator screen. (number of digits to the right of the decimal point). :[12 I<2 I Opens P/YR menu. Inputs 12 for P/YR and 2 for C/YR. O300N 6Y350 00V Exits menu and inputs values for N, I/YR, and PV. M Calculates the monthly payment as required by the example. :x. With TVM displayed, press I. At the TVM Reset prompt, press I to reset, or O to cancel. To exit the menu, press O once again. With the menu set to its default settings, P/YR and C/YR To reset the menu, press are both set to 12 payments/compounding periods per year. 38 Cash Flows 4 Cash Flows Figure 1 Cash Flow Diagram In the calculator, a cash flow list is a set of numbered pairs, CF(n) and #CF(n), where n is the index of the cash flow list. Each pair represents one or more cash flows in a cash flow diagram. As with TVM problems, it helps to sketch a cash flow diagram as a first step in solving cash flow problems. For some examples of cash flow diagrams, see Figure 3 at the end of this chapter. CF(n) represents the monetary value of the cash flow; #CF(n) represents the number of consecutive occurrences of that cash flow. By default, #CF(n) is equal to 1, as most cash flows occur only once. However, in cases where a cash flow is repeated multiple times, using #CF(n) instead of entering the cash flow value multiple times saves calculation time and memory space in the calculator. To enter a cash flow list, press C to open the cash flow menu. For each cash flow item, first enter the monetary value followed by by I, then enter the number of occurrences followed I. If a cash flow occurs once, you do not need to type 1I. Simply press I or < as 1 is the default. 39 Cash Flows :x. The number of cash flows in the list is displayed on the bottom line, along with Cash Flow=. At this prompt, press I. You will be asked to confirm your choice. Either press I to confirm the reset, or O to cancel. To erase a cash flow list, with any cash flow displayed press Table 4-1 lists the keys used for cash flow problems. For a cash flow example, see Table 4-2. Table 4-1 Cash Flow Keys Key Description C Opens the cash flow list. I Inputs new values for variables in the cash flow list, the Net Present Value (NPV) menu, and the Internal Rate of Return (IRR) menu. >< Scrolls up and down. o Inserts cash flows into a cash flow list. j Removes cash flows from a cash flow list. RP Opens the Internal Rate of Return (IRR) and Net Present Value (NPV) menus. Cash Flow Example After an initial investment of 80,000.00, cash flow (0), you expect returns over the next five years as follows: Cash Flow Number Cash Flow Amount Occurrences 1 5,000.00 1 2 4,500.00 1 3 0.00 1 4 4,000.00 1 5 5,000.00 5 6 115,000.00 1 Given this information, calculate the total of the cash flows and the internal rate of return (IRR) of the investment. Calculate net present value (NPV) and net future value (NFV), assuming an annual investment interest rate of 10.5%. See Figure 1 for the cash flow diagram and Table 4-2 for how to enter the cash flows. The example is shown with RPN as the active operating mode. 40 Cash Flows Table 4-2 Cash Flow Example Keys Display Description C Opens the cash flow list. 8000 0}I Inputs -80000 as the monetary value of the initial I Accepts 1 as the number of occurrences for CF(0). 5000I Inputs 5000 as the monetary value of CF(1). cash flow. Note: the sign of the cash outflow is negative. Displays the current monetary value of CF(1). Displays the current value,1, for the number of times CF(1) occurs. I Accepts 1 as the number of occurrences for CF(1). 4500I Inputs 4500 as the monetary value of CF(2). Displays the current monetary value of CF(2). Displays the current value, 1, for the number of times CF(2) occurs. I Accepts 1 as the number of occurrences for CF(2). I Accepts 0 as the monetary value of CF(3). Displays Displays the current monetary value of CF(3). the current value, 1, for the number of times CF(3) occurs. I Accepts 1 as the number of occurrences for CF(3). 4000I Inputs 4000 as the monetary value of CF(4). Displays the current monetary value of CF(4). Displays the current value, 1, for the number of times CF(4) occurs. I Accepts 1 as the number of occurrences for CF(4). 5000I Inputs 5000 as the monetary value of CF(5). Displays the current monetary value of CF(5). Displays the current value, 1, for the number of times CF(5) occurs. 5I Inputs 5 for the number of occurrences for CF(5). Displays the current monetary value of CF(6). 41 Cash Flows Table 4-2 Cash Flow Example Keys Display Description 115000 I Inputs 115000 as the monetary value of CF(6). I Accepts 1 as the number of occurrences for CF(6). Displays the current value, 1, for the number of times CF(6) occurs. Analyzing Cash Flows The various functions used to analyze cash flows are located in the NPV P and IRR R menus. If you press R or P before entering cash flows, you will be redirected to the cash flow menu to enter values into the cash flow list. The menu maps for the IRR and NPV menus are shown in Figure 2. Table 4-3 describes the items within these menus. Figure 2 The Menu Map for the NPV and IRR Menus 42 Cash Flows Table 4-3 NPV and IRR Menu Items Item Description Inv. I% Investment or discount rate. Enter the investment rate or discount rate for the cash flow followed by Net PV I. Net present value. Shows the value of the cash flows at the time of the initial cash flow, discounting the future cash flows by the value set for Inv. I%. Net FV Net future value. Shows the value of the cash flows at the time of the last cash flow, discounting the earlier cash flows by the value set for Inv. I%. Net US Net uniform series. Shows the per-period payment of a regular, periodic cash flow of equivalent present value to the cash flow list. Payback Payback. Shows the number of periods for the investment to return value. Discounted Payback Discounted Payback. Shows the number of periods required for the investment to return value if the cash flows are discounted using the value set in Inv. I%. Total The sum of all the cash flows, equivalent to NPV if Inv. I% is 0. #CF/Yr The number of cash flows per year. The default is 1. IRR% Internal rate of return. This is the discount rate for the cash flow that returns a Net Present Value of 0. See Table 4-4 for an example of the NPV and IRR functions using the cash flow example in Table 4-2. Table 4-4 NPV and IRR Example Keys Display Description P Opens the NPV menu. 10. 5I Inputs 10.5 for investment rate. < Displays the NPV of the cash flow with the given Inv. I%. < Displays the NFV of the cash flow with the given Inv. I%. < Displays the Net US of the cash flow with the given interest rate. 43 Cash Flows Table 4-4 NPV and IRR Example Keys Display Description < Displays the number of periods required for the cash flow to repay the investment. << Scrolls to the total value of the cash flow. R Displays the IRR for the cash flow. Editing Cash Flows In the cash flow list, you can view and modify the current monetary value of a specific cash flow, or cash flows. Press < or > repeatedly to scroll through the list. To modify the displayed entry, type a new number and press I. For example, to change the current monetary value of the cash flow three, CF(3), in the example in Table 4-2 from 0 to 200, with CF(3)= displayed, press 200 followed by I. You can also modify the number of occurrences of a cash flow in the same manner with #CF(n) displayed. Pressing :j with a cash flow displayed erases the displayed cash flow. Pressing :o inserts a cash flow into the list before the displayed cash flow. 44 Cash Flows Sample Cash Flow Diagrams Figure 3 Sample Cash Flow Diagrams 45 Bonds 5 Bonds DWN B Set.Date DWN Mat.Date CPN% DWN Accrued DWN DWN Call DWN Yield% DWN Price DWN Actual/ DWN Cal.360 Annual/ Semiannual Figure 1 The Menu Map for the Bond Menu The Bond Menu Before you enter the Bond menu, be sure to verify the date format is set appropriately for your problem. The default setting is mm.ddyyyy, but it can be set for dd.mmyyyy. Bond day counts (360/365) and annual or semiannual coupon payment schedules may be set from either the Mode menu or the Bond menu. For more information on setting the preferences in the Mode menu, see the section titled, The Mode Menu: Setting Preferences in Chapter 1. To open the Bond menu, press Press B. < or > repeatedly to scroll through the items shown in Figure 1. I. Once you have entered all known data, press < or > repeatedly to scroll to an unknown item, and press = to calculate it. To change the value of the displayed item, key in a number or a date and press Table 5-1 lists the items in the Bond menu. Table 5-1 Bond Menu Items Variable Description Settlement Date Settlement date. Displays the current settlement date. Note: input only. Maturity Date Maturity date or call date. The call date must coincide with a coupon date. Displays the current maturity. Note: input only. CPN% Coupon rate stored as an annual %. Note: input only. 46 Bonds Table 5-1 Bond Menu Items Variable Description Call Call value. Default is set for a call price per 100.00 face value. A bond at maturity has a call value of 100% of its face value. Note: input only. Yield% Yield% to maturity or yield% to call date for given price. Note: input/output. Price Price per 100.00 face value for a given yield. Note: input/output. Accrued Interest accrued from the last coupon or payment date until the settlement date for a given yield. Note: this item is Read-only. Actual/Cal.360 Actual (365-day calendar) or Cal.360 (30-day month/360-day year calendar). Press Annual/Semiannual I to toggle between these options. Bond coupon (payment) frequency. Press I to toggle between these options. Bond Calculation Example What price should you pay on April 28, 2010 for a 6.75% U.S. Treasury bond maturing on June 4, 2020, if you want a yield of 4.75%? Assume the bond is calculated on a semiannual coupon payment on an actual/actual basis. See Table 52. The example below is shown with RPN as the active operating mode. Table 5-2 Bond Calculation Example Key Display Description B Opens the Bond menu. > Scrolls to bond coupon (payment) frequency. I Selects semiannual coupon payment, as required by the <4.28 2010 I Inputs April 28, 2010 for the settlement date (mm.ddyyyy <6.04 2020 I Inputs June 4, 2020 for the maturity date. <6.75 I Inputs 6.75% for the value for CPN%. example. format). 47 Bonds Table 5-2 Bond Calculation Example Key Display Description < Displays current call value. Default is 100. Note: if Call requires another value, key in the number followed by I. <4.75 I Inputs 4.75% for Yield%. <= Calculates the current value for Price. :$1 Stores 115.89 in memory 1. < Displays the current value for accrued interest. +L1= Returns the result for total price (value of price + value of accrued interest). The net price you should pay for the bond is 118.58. To reset the menu items to their default values, with any item of the Bond menu displayed press displayed, press :x. With Bond I to reset the menu, or O to cancel. Press O again to exit the menu. 48 Date Calculation 6 Date Calculation Figure 1 The Menu Map for the Date Calculation Menu The Date Calculation Menu The Date Calculation menu is used to calculate the number of days between two dates, or a second date given a number of days from an initial, or final date. To open the Date Calculation menu, press :@. Press < or > repeatedly to scroll through the items shown in Figure 1. Before you enter dates, verify the date is set in the format required for your problem. Date and calendar formats may be set in the Mode menu. For more information on setting the preferences in the Mode Menu, see the section titled, The Mode Menu: Setting Preferences in Chapter 1. I. Once you have entered all known data, press < or > repeatedly to scroll to the unknown item and press = to calculate it. To change the value of a displayed item, key in a number or a date and press Date Calculation Example How many days remain in the 2010 fiscal year if today's date is June 4, 2010? Assume the fiscal year ends on October 31st, and you wish to calculate the actual number of days (Actual). Table 6-1 Date Calculation Example Key Display Description :@ Opens the Date Calculation menu. Note: 2 in the right of the display represents the day of the week. 2 represents Tuesday. 6.04 2010 I Inputs the starting date in the selected format. 49 Date Calculation Table 6-1 Date Calculation Example Key Display Description <10.3 12010 I Inputs the ending date in the selected format. <= Calculates the number of actual days between the starting and ending dates. To reset the menu items to their default values, with any item of the Date menu displayed press displayed, press :x. With Date I to reset the menu, or O to cancel. Press O again to exit the menu. 50 Break-even 7 Break-even Figure 1 The Menu Map for the Break-even Menu The Break-even Menu :!. To change the value of the displayed item, key in a number and press I. Once you have entered all known data, press < or > repeatedly to scroll to the unknown item and press = to calculate it. To open the Break-even menu, press The break-even function allows you to study problems involving a profit, when a quantity of items, with a cost to manufacture and a fixed price to develop and market, is sold at a given price. See Figure 1. Break-even Example The sale price of an item is 300.00, the cost is 250.00, and the fixed cost is 150,000.00. How many units would have to be sold to make a profit of 10,000.00? Table 7-1 Break-even Example Keys Display Description :! Opens the Break-even menu starting with the current 1500 00I Inputs 150,000.00 for fixed cost. <250 I Inputs 250.00 for variable cost per unit. <300 I Inputs 300.00 for price. <1000 00I Inputs 10,000.00 for profit. value for fixed costs. 51 Break-even Table 7-1 Break-even Example Keys Display Description <= Calculates the current value for the unknown item. 3200 units would have to be sold to return a profit of 10,000.00. To reset the menu items to their default values, with any item of the Break-even menu displayed press :x. With BrkEven displayed, press I to reset the menu, or O to cancel. Press O again to exit the menu. 52 Business Problems 8 Business Problems Figure 1 The Menu Map for the Percent Calculation (%calc) Menu The Percent Calculation Menu Press :# to open the menu. There are four items in this menu: markup as a percentage of cost ( Mkup. %C ), markup as a percentage of price (Mkup. %P ), part as a percentage of total (Part%Tot. ), and percent change (%Change ). These items allow you to access sub-menus. Press < or > repeatedly to scroll to the desired sub-menu, then press I to open it. See Figure 1. I. Once you have entered all known data, press < or > repeatedly to scroll to the unknown item and press = to calculate it. To change the value of a displayed item, key in a number and press To return to the percent calculation menu, from anywhere within the menu or sub-menus, press To exit the menu, press O 53 :#. Business Problems Note: for business problems, margin is based on price; markup is based on cost. The examples below are shown with RPN as the active operating mode. Percent Calculation Examples See Tables 8-1 through 8-4 for examples of calculations in the %calc menu. 1. Find the markup on an item if the cost price is $15.00 and the selling price is $22.00. See Table 8-1. Table 8-1 Markup Example Keys Display Description :# Opens the %calc menu. I Opens the Mkup.%C sub-menu. 15I Inputs 15 for Cost. <22I Inputs 22 for Price. <= Calculates the value of Mkup.%C for the given data. 2. Find the percent change between 20 and 35 with no compounding. Table 8-2 Percent Change Example Keys Display Description :# Opens the %calc menu. <<< Scrolls to %Change. I Opens the %Change sub-menu. 20I Inputs 20 for Old. <35I Inputs 35 for New. <= Calculates the current value of %Change for the given data. 54 Business Problems Note: although the example in Table 8-2 calls for no compounding, you may specify the number of compounding periods used in calculations with the Nb Period item in the %Change sub-menu. Nb Period is the number of compounding periods used in calculations between the old value and new value. The default is 1, but to change the setting, key in a number with Nb Period displayed, followed by I. After calculating the example above with no compounding, say, for example, you wish to calculate the percent change over six compounding periods: Table 8-3 Percent Change Example with Compounding Keys Display Description The current value of %Change for the given data. <6I Inputs 6 for the number of compounding periods. >= Calculates the percent change between the old value and the new value over six compounding periods. 3. What is 30% of 80? Table 8-4 Part % of Total Example Keys Display Description :# Opens the %calc menu. << Scrolls to the Part %Total menu item. I Opens the Part as %Total sub-menu. 80I Inputs 80 for Total. <30I Inputs 30 for Part. <= Calculates the value of Part%Total for the given data. :x. Press > or < to scroll until %Calc displays and press Ito reset the menu, or O to cancel. Press O to exit the menu. To reset the menu items to their default values, with any item of the %calc menu displayed press 55 Depreciation 9 Depreciation Figure 1 The Menu Map for the Depreciation Menu The Depreciation Menu Press :\ to open the Depreciation menu. To select a depreciation method, press I repeatedly. See Figure 1. Input the values required for the calculation: Asset life Starting date or month of the deprecation Cost and salvage values Declining balance factor (DecBal and DBXover only) The first year for which you want to view the depreciation schedule Scroll through the items of the sub-menu for the selected depreciation method by pressing < or > repeatedly. To I. For the Start item, enter either a number or an actual date, depending on the type of depreciation selected. Press < repeatedly to view the depreciation schedule. change the value of the displayed item, key in a number and press 56 Depreciation Note: pressing < on the last item of a sub-menu returns you to the Year item, not to the top of the sub-menu (see Figure 1). By scrolling through all the items of a sub-menu, you incrementally advance the Year item. This allows you to see the depreciation schedule for the next year without additional entries. Brief descriptions of the methods used to calculate depreciation are provided in Table 9-1. Table 9-2 describes the items found in the depreciation sub-menus. For an example calculating depreciation using the straight-line method, see Table 9-3. Table 9-1 Depreciation Methods Depreciation Method Description Sline Straight line is a method of calculating depreciation presuming an asset loses a certain percentage of its value annually at an amount evenly distributed throughout its useful life. SOYD Sum-of-the-years' digits is an accelerated depreciation method. In SOYD, the depreciation in year Y is (Life-Y+1)/SOY/100% of the asset, where SOY is the sum-of-the-years for the asset, or, for an asset with a 5-year life, 5+4+3+2+1=15. DecBal Declining balance is an accelerated depreciation method that presumes an asset will lose the majority of its value during the first few years of its useful life. DBXover Declining balance crossover is an accelerated depreciation method that presumes an asset will lose the majority of its value in the first few years of its useful life, but that it will revert to a consistent depreciation during the latter part of its life, which is then calculated using the straight line method. French SL Straight line French. This method of depreciation is similar to the Straight line method, except an actual calendar date in the selected format is entered in for Start to indicate when the asset was first placed into service. Amort F French amortization. This method is an accelerated depreciation method with a crossover to the French Straight Line method. Table 9-2 Depreciation Menu Items Item Description Life The expected useful life of the asset in years. Start Start refers to the date or month in which the asset is first placed into service. Depending on the type of depreciation, this can be the month (1-12), or, in the case of French Straight-line and Amort F, the actual date in the selected format. Note: for non-French depreciations, if the asset were placed into service in the middle of March, for example, you would enter 3.5 for Start. Cost The depreciable cost of the asset at acquisition. 57 Depreciation Table 9-2 Depreciation Menu Items Item Description Salvage The salvage value of the asset at the end of its useful life. Factor The declining balance factor as a percentage. This is used for declining balance and declining balance crossover methods only. Year Year for which you want to calculate the depreciation. Depreciation Depreciation in the given year. R.Book Value Remaining book value at the end of the given year. R.Depreciable Value Remaining depreciable value at the end of the given year. Depreciation Example A metalworking machine, purchased for 10,000.00, is to be depreciated over five years. Its salvage value is estimated at 500.00. Using the straight-line method, find the depreciation and remaining depreciable value for each of the first two years of the machine's life. See Table 9-3. Table 9-3 Straight Line Depreciation Example Key Display Description :\ Opens the Depreciation menu starting with the straight <5I Inputs 5 for the useful life. < Displays the current value of Start. 1 (January) is the line method. default value. For this example, this value remains unchanged, since the depreciation of the machine starts January 1st (1.00 ). <1000 0I Inputs 10,000.00 for the cost of the item. <500 I Inputs 500.00 for the salvage value of the item. < Year for which to calculate the depreciation. Year 1 is the default value. To calculate for a year other than 1, type a number and press < I. Depreciation of the asset in year one. 58 Depreciation Table 9-3 Straight Line Depreciation Example Key Display Description < Remaining book value after year one. < Remaining depreciable value after year one. < The next year for which to calculate the depreciation. To calculate for a year other than 2, type a number and press I. < Depreciation of the asset in year two. < Remaining book value after year two. < Remaining depreciable value after year two. To reset the menu items to their default values, with any item of the Depreciation menu displayed press :x. With Depreciation displayed, press I to reset the menu, or O to cancel. Press O to exit the menu. 59 Statistical Operations 10 Statistical Operations Figure 1 The Menu Maps for the Data and Statistics Menus 60 Statistical Operations The Data and Stats Menus Statistics analysis functions are located in the Data and Statistics menus accessible with the :y and :z keys. See Figure 1 for assistance with navigating through the menus. Press :y to open the Data menu. In this menu, enter a list of x values for one-variable statistics, a list of pairs, (x, F) for weighted, one-variable statistics, a list of numbers x for one-variable statistics, or a list of pairs, (x, y) for two-variable statistics. To enter data, key in a number and press I. :z to analyze the data. If you attempt to open the Statistics (Stats) menu before entering data, you will be redirected to the Data menu. When opened, the Stats menu displays 2 Vars for two-variable statistics. Press I Press repeatedly to select the type of statistical operations desired, two-variable, ( 2 Vars ), one-variable, (1 Var ), or one-variable weighted (1 Weight ). After selecting the type of statistical operation you want, select a sub-menu by pressing open it. Once in a sub-menu, press menu, press < or >, and press I to < or > repeatedly to view the results. To return from the sub-menu to the Statistics :z. Note: in one-variable modes, there are no items for y and the Predictions sub-menu is not available. Pressing I with the Predictions sub-menu displayed opens a sub-menu, in which you can choose among six different types of regression lines. See Figure 1. To select a specific type of regression line in the Predictions sub-menu, press I to cycle through the options. Note: if you press =, the calculator automatically selects the curve that is the best fit for your data. Once you select a regression line, press < to see the regression line parameters and perform predictions. 61 Statistical Operations Table 10-1 The Statistics Menu Items Menu Item Description Nb Item Number of items. X Mean Average of X values. Y Mean Average of Y values. X Std. Dev Standard deviation for X: a measure of how dispersed the x data values are about the mean. Y Std. Dev Standard deviation for Y: a measure of how dispersed the y data values are about the mean. X Population Dev Population Standard deviation for X: a measure of how dispersed the X data values are about the mean, assuming the data constitutes a complete set of data. Y Population Dev Population Standard deviation for Y: a measure of how dispersed the y data values are about the mean, assuming the data constitutes a complete set of data. S.E.SamP.X Sample error for X: a measure of how dispersed the X data values are about the mean sample standard deviation, assuming the data is a sampling of a larger, more complete data set. S.E.SamP.Y Sample error for Y: a measure of how dispersed the Y data values are about the mean sample standard deviation, assuming the data is a sampling of a larger, more complete data set. Pred X Predicts X for a given hypothetical value of Y, based upon the model calculated to fit the data. Pred Y Predicts Y for a given hypothetical value of X, based upon the model calculated to fit the data. a The a coefficient for the chosen regression model, which is the slope for a linear model. b The b coefficient for the chosen regression model, which is the y-intercept for a linear model. Correlation The correlation coefficient for the given (x, y) data. The correlation coefficient is a number in the range -1 through 1 that measures how closely the calculated line fits the data. Covariance A measure of how much two variables change in relation to one another. Sigma X The sum of the x values. 62 Statistical Operations Table 10-1 The Statistics Menu Items Menu Item Description Sigma Y The sum of the y values. Sigma X2 The sum of the squares of the x values. Sigma Y2 The sum of the squares for the y values. Sigma XY The sum of the products of the x and y values. Statistics Example Sales for the last five months are represented by the pairs of values shown below, with the month number as x, and the sales values as y. Enter these into the Data menu. Using the Statistics menu for Predictions, predict sales for month seven. What is the linear regression line? What is the sum of all the y values? See Tables 10-2 and 10-3. Table 10-2 Months and Sales Month Sales Values 1 150 2 165 3 160 4 175 5 170 Table 10-3 Statistics Example Keys Display Description :y Opens Data menu. 1I1 50I Inputs values for X(1) and Y(1). 2I1 65I Inputs values for X(2) and Y(2). 3I1 60I Inputs values for X(3) and Y(3). 4I1 75I Inputs values for X(4) and Y(4). 63 Statistical Operations Table 10-3 Statistics Example Keys Display Description 5I1 70I Inputs values for X(5) and Y(5). :z Opens Stats menu. <I Opens Descriptive sub-menu. << Displays average y. :z<< I Opens Predictions sub-menu. Note: this example <7I Inputs 7 as the Prediction X value (month 7). <= Calculates Prediction Y value (sales at month 7). < Displays value for a: the slope of the regression < Displays current value for b: the y-intercept of the < Displays value for Correlation. :z<< <I< Opens Sums sub-menu. Displays the sum of all y performs calculations based on a linear (a*X+b) regression line. line. regression line. values (Sigma Y). To reset the menu items to their default values, with any item of the Data or Statistics menus displayed press the prompt, Stats, press I. Confirm your choice by pressing I. 64 :x. At Errors 11 Errors Error Messages and Calculator Status Table 11-1 Error Messages Error Message Status ER: Underflow The calculation generated an underflow (result of 0). ER: x/0 Division by zero. ER: 0/0 Zero divided by zero. ER: ∞*0 Infinite multiplied by zero. ER: ∞/∞ Infinite divided by infinite. ER: √/ (x<0) Square root of a negative number. ER: LN (0) LN of 0. ER: LN (x<0) LN of a negative number. ER: ATrig(|x|>1) ASIN or ACOS of a number for which the absolute value is > 1. ER: 1^∞ Attempted calculation of 1^+/-Infinite. ER: (x<0)^∞ Attempted calculation of the infinite power of a negative number. ER: ∞^0 Attempted calculation of +/-∞^0. ER: ∞^(Frac) Attempted calculation of +/-∞^ (non-integer y). ER: (x<0)^(Frac) Attempted calculation of (-x) ^ (non-integer y). ER: Out of Bounds Input out of bounds. ER: Invalid P/YR Returned by TVM functions if payments per year are invalid (<0 or non-integer). ER: Invalid Input Returned if arguments are invalid for any reason. ER: Invalid I% Returned by finance functions if I is ≤ 100%. ER: No Solution Returned when there is no solution to the problem. ER: Many or No Solutions Returned if there is no solution, or more than one solution to the problem. 65 Errors Table 11-1 Error Messages Error Message Status ER: Many Solutions Returned when there are many solutions to the problem. ER: Invalid N Returned by TVM/Amort if N is invalid. ER: User Abort Returned by long functions if user stops the calculation prior to completion. ER: ∞ Result Returned if the result is infinite. ER: Insufficient Data Returned by statistics functions if there is insufficient data for analysis. ER: No Payback Returned by payback function if there is no payback on this problem. ER: Unique solution to IRR Not Found Returned if IRR tries to calculate a solution but cannot find it. User should supply a new guess… ER: Stack Stack overflow when performing calculations with more than 12 pending operations. ER: Parenthesis: An error linked to use of parentheses: unmatched, too many, etc. ER: Insufficient Memory Insufficient memory to complete the operation. ER: No Solution Found No solution found. 66 Warranty, Regulatory, and Contact Information 12 Warranty, Regulatory, and Contact Information Replacing the Batteries Use only fresh batteries. Do not use rechargeable batteries. The calculator takes two, 3-volt CR2032 lithium batteries. To install a new battery: 1. With the calculator turned off, slide the back cover off. 2. Remove one of the old batteries and replace it with a new battery with the positive polarity symbol facing outward. 3. Remove the second battery and replace it with a new battery with the positive polarity symbol facing outward. 4. Replace the back cover. Warning! There is danger of explosion if the battery is incorrectly replaced. Replace only with the same or equivalent type recommended by the manufacturer. Dispose of used batteries according to the manufacturer's instructions. Do not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode, releasing hazardous chemicals. HP Limited Hardware Warranty and Customer Care This HP Limited Warranty gives you, the end-user customer, express limited warranty rights from HP, the manufacturer. Please refer to HP’s Web site for an extensive description of your limited warranty entitlements. In addition, you may also have other legal rights under applicable local law or special written agreement with HP. Limited Hardware Warranty Period Duration: 12 months total (may vary by region, please visit www.hp.com/support for latest information) General Terms HP warrants to you, the end-user customer, that HP hardware, accessories and supplies will be free from defects in materials and workmanship after the date of purchase, for the period specified above. If HP receives notice of such defects during the warranty period, HP will, at its option, either repair or replace products which prove to be defective. Replacement products may be either new or like-new. HP warrants to you that HP software will not fail to execute its programming instructions after the date of purchase, for the period specified above, due to defects in material and workmanship when properly installed and used. If HP receives notice of such defects during the warranty period, HP will replace software media which does not execute its programming instructions due to such defects. HP does not warrant that the operation of HP products will be uninterrupted or error free. If HP is unable, within a reasonable time, to repair or replace any product to a condition as warranted, you will be entitled to a refund of the purchase price upon prompt return of the product with proof of purchase. HP products may contain remanufactured parts equivalent to new in performance or may have been subject to incidental use. Warranty does not apply to defects resulting from (a) improper or inadequate maintenance or calibration, (b) software, interfacing, parts or supplies not supplied by HP, (c) unauthorized modification or misuse, (d) operation outside of the published environmental specifications for the product, or (e) improper site preparation or maintenance. HP MAKES NO OTHER EXPRESS WARRANTY OR CONDITION WHETHER WRITTEN OR ORAL. TO THE EXTENT ALLOWED BY LOCAL LAW, ANY IMPLIED WARRANTY OR CONDITION OF MERCHANTABILITY, SATISFACTORY QUALITY, OR FITNESS FOR A PARTICULAR PURPOSE IS LIMITED TO THE DURATION OF THE EXPRESS WARRANTY SET FORTH ABOVE. Some countries, states or provinces do not allow limitations on the duration of an implied warranty, so the above limitation or exclusion might not apply to you. This warranty gives you specific legal rights and you might also have other rights that vary from country to country, state to state, or province to province. TO THE EXTENT ALLOWED BY LOCAL LAW, THE REMEDIES IN THIS WARRANTY STATEMENT ARE YOUR SOLE AND EXCLUSIVE REMEDIES. EXCEPT AS INDICATED ABOVE, IN NO EVENT WILL HP OR ITS SUPPLIERS BE LIABLE FOR LOSS OF DATA OR FOR DIRECT, SPECIAL, INCIDENTAL, CONSEQUENTIAL (INCLUDING LOST PROFIT OR DATA), OR OTHER DAMAGE, WHETHER BASED IN CONTRACT, TORT, OR OTHERWISE. Some countries, States or provinces do not allow the exclusion or limitation of incidental or consequential damages, so the above limitation or exclusion may not apply to you. The only warranties for HP products and services are set forth in the express warranty statements accompanying such products and services. HP shall not be liable for technical or editorial errors or omissions contained herein. FOR CONSUMER TRANSACTIONS IN AUSTRALIA AND NEW ZEALAND: THE WARRANTY TERMS CONTAINED IN THIS STATEMENT, EXCEPT TO THE EXTENT LAWFULLY PERMITTED, DO NOT EXCLUDE, RESTRICT OR MODIFY AND ARE IN ADDITION TO THE MANDATORY STATUTORY RIGHTS APPLICABLE TO THE SALE OF THIS PRODUCT TO YOU. 67 Warranty, Regulatory, and Contact Information Customer Care In addition to the one year hardware warranty your HP calculator also comes with one year of technical support. If you need assistance, HP customer care can be reached by either email or telephone. Before calling please locate the call center nearest you from the list below. Have your proof of purchase and calculator serial number ready when you call. Telephone numbers are subject to change, and local and national telephone rates may apply. For more support information, please visit the web at: www.hp.com/support. Contact Information Table 12-1 Contact Information Country/Region Contact Africa (English) www.hp.com/support Afrique (français) www.hp.com/support Argentina 0-800-555-5000 Australia 1300-551-664 Belgique (français) 02 620 00 85 Belgium (English) 02 620 00 86 Bolivia 800-100-193 Brasil 0-800-709-7751 Canada 800-HP-INVENT Caribbean 1-800-711-2884 Česká republikaik 296 335 612 Chile 800-360-999 China 中国 010-68002397 Colombia 01-8000-51-4746-8368 Costa Rica 0-800-011-0524 Denmark 82 33 28 44 Deutschland 069 9530 7103 Ecuador 800-711-2884 El Salvador 800-6160 España 913753382 France 01 4993 9006 68 Warranty, Regulatory, and Contact Information Table 12-1 Contact Information Country/Region Contact Greece Ελλάδα 210 969 6421 Guatemala 1-800-999-5105 Honduras 800-711-2884 Hong Kong 香港特別行政區 852 2833-1111 India www.hp.com/support/india Indonesia +65 6100 6682 Ireland 01 605 0356 Italia 02 754 19 782 Japan 日本 81-3-6666-9925 Korea 한국 www.hp.com/support/korea Magyarország www.hp.com/support Malaysia +65 6100 6682 México 01-800-474-68368 Middle East International www.hp.com/support Netherland 020 654 5301 New Zealand 0800-551-664 Nicaragua 1-800-711-2884 Norwegen 23500027 Österreich 01 360 277 1203 Panamá 001-800-711-2884 Paraguay (009) 800-541-0006 Perú 0-800-10111 Philippines +65 6100 6682 Polska www.hp.com/support Portugal 021 318 0093 69 Warranty, Regulatory, and Contact Information Table 12-1 Contact Information Country/Region Contact Puerto Rico 1-877 232 0589 Russia Россия 495 228 3050 Schweiz (Deutsch) 01 439 5358 Singapore 6100 6682 South Africa 0800980410 South Korea 한국 2-561-2700 Suisse (français) 022 827 8780 Suomi 09 8171 0281 Sverige 08 5199 2065 Svizzera (italiano) 022 567 5308 Türkiye www.hp.com/support Taiwan 臺灣 +852 28052563 Thailand ไทย +65 6100 6682 United Kingdom 0207 458 0161 United States 800-HP INVENT Uruguay 0004-054-177 Venezuela 0-800-474-68368 Viêt Nam +65 6100 6682 70 Warranty, Regulatory, and Contact Information Product Regulatory & Environment Information Federal Communications Commission Notice This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC Rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference to radio communications. However, there is no guarantee that interference will not occur in a particular installation. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, the user is encouraged to try to correct the interference by one or more of the following measures: Reorient or relocate the receiving antenna. Increase the separation between the equipment and the receiver. Connect the equipment into an outlet on a circuit different from that to which the receiver is connected. Consult the dealer or an experienced radio or television technician for help. Modifications The FCC requires the user to be notified that any changes or modifications made to this device that are not expressly approved by HewlettPackard Company may void the user’s authority to operate the equipment. Declaration of Conformity for products Marked with FCC Logo, United States Only This device complies with Part 15 of the FCC Rules. Operation is subject to the following two conditions: (1) this device may not cause harmful interference, and (2) this device must accept any interference received, including interference that may cause undesired operation. If you have questions about the product that are not related to this declaration, write to Hewlett-Packard Company P.O. Box 692000, Mail Stop 530113 Houston, TX 77269-2000 For questions regarding this FCC declaration, write to Hewlett-Packard Company P.O. Box 692000, Mail Stop 510101 Houston, TX 77269-2000 or call HP at 281-514-3333 To identify your product, refer to the part, series, or model number located on the product. Canadian Notice This Class B digital apparatus meets all requirements of the Canadian Interference-Causing Equipment Regulations. Avis Canadien Cet appareil numérique de la classe B respecte toutes les exigences du Règlement sur le matériel brouilleur du Canada. European Union Regulatory Notice This product complies with the following EU Directives: Low Voltage Directive 2006/95/EC EMC Directive 2004/108/EC Compliance with these directives implies conformity to applicable harmonized European standards (European Norms) which are listed on the EU Declaration of Conformity issued by Hewlett-Packard for this product or product family. 71 Warranty, Regulatory, and Contact Information This compliance is indicated by the following conformity marking placed on the product: xxxx* This marking is valid for non-Telecom products and EU harmonized Telecom products (e.g. Bluetooth). This marking is valid for EU non-harmonized Telecom products . *Notified body number (used only if applicable refer to the product label) Hewlett-Packard GmbH, HQ-TRE, Herrenberger Srasse 140, 71034 Boeblingen, Germany Japanese Notice Perchlorate Material - special handling may apply This calculator's Memory Backup battery may contain perchlorate and may require special handling when recycled or disposed in California. Disposal of Waste Equipment by Users in Private Household in the European Union This symbol on the product or on its packaging indicates that this product just not be disposed of with your other household waste. Instead, it is your responsibility to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste electrical and electronic equipment. The separate collection and recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that it is recycled in a manner that protects human health and the environment. For more information about where you can drop off your waste equipment for recycling, please contact your local city office, your household waste disposal service or the shop where you purchased the product. Chemical Substances HP is committed to providing our customers with information about the chemical substances in our products as needed to comply with legal requirements such as REACH (Regulation EC No 1907/2006 of the European Parliament and the Council). A chemical information report for this product can be found at: http://www.hp.com/go/reach 72 Warranty, Regulatory, and Contact Information 产品中有毒有害物质或元素的名称及含量 根据中国《电子信息产品污染控制管理办法》 有毒有害物质或元素 部件名称 铅 (Pb) 汞 (Hg) 镉 (Cd) 六价铬 (Cr(VI)) 多溴联苯 (PBB) 多溴二苯醚 (PBDE) PCA X O O O O O 外觀殼子/字鍵 O O O O O O O：表示该有毒有害物质在该部件所有均质材料中的含量均在SJ/T11363-2006 标准规定的限量要求以下。 X：表示该有毒有害物质至少在该部件的某一均质材料中的含量超出SJ/T11363-2006 标准规定的限量要求。 表中标有“X” 的所有部件都符合欧盟RoHS法规 “欧洲议会和欧盟理事会2003年1月27日关于电子电器设备中限制使用某些有害物质的2002/95/EC号指令” 注：环保使用期限的参考标识取决于产品正常工作的温度和湿度等条件 73 Index Index ! !: key, 23 % % change, 53 % yield, 47 = =: key, 12 A a: slope, 62 absolute value. See Math menu Algebraic mode, 17 amortization: Amort key, 33; example, 34; menu items, 33 annual: bond, 47 annunciators, 11 ANS. See last number B b: y-intercept, 62 backspace key, 16 balance: amortization, 33 begin mode: Beg key, 32 bond: annual, semiannual, 10; example, 47; key, 46; menu items, 46 bonds, 46 bottom line: display, 8 break-even: BrkEv key, 51; example, 51 business problems, 53; percent calculation examples, 54 C calculation mode: Chain, Algebraic, and RPN, 10 calendar: Actual, Cal.360, 10 call value, 47 Canada TVM example, 38 Canadian TVM, 36 cash flow: example, 40; keys, 40; sample diagrams, 45 cash flows, 39; analyzing, 42; editing, 44; number per year, 43 Chain mode, 17 Chi, 25 clearing. See: Reset menu compounding periods: N key, 32 compounding periods per year: P/YR key, 32 Compounding, per year, 35 contents, 3 contrast, 7 correlation, 61, 62 cosine: COS key, 23 cost: depreciation, 58; fixed. See breakeven; variable per unit. See breakeven coupon rate, 46 covariance, 61, 62 CshFl key. See cash flow cursor, 7 D Data key. See Statistics data menu, 61 date: actual, 47; maturity, 46; settlement, 46 Date 1. See Date calculation Date 2. See Date calculation date calculation: Date key, 49; example, 49 date format, 9 days between. See Date calculation decimal point, 9 decimal separator: point or comma, 9 default calculator screen, 8 degrees, 9 delete: DEL key, 44 delete key, 44 deleting. See Reset menu depreciation, 56; Depr key, 56; example, 58; methods, 56 descriptive: sub menu. See Statistics menu discounted payback, 43 display, 7; two lines, 8 down arrow key. See scroll E EEX key. See scientific notation end mode: End key, 32 error messages, 65 F factor: declining balance. See depreciation factorial: ! key, 23 F-distribution, 25 Fix: display precision. See Mode menu function: one-number, 22 74 functions: two-number, 26 future value: FV key, 32 I IConv key. See interest conversion INPUT: key, 12 insert: INS key, 44 interest: accrued. See bonds; towards loan payment. See amortization interest conversion: example, 35 interest rate: effective, 35; nominal, 35; nominal, I/YR key, 32 inverse tail normal distribution, 25 IRR: key, 42 K key: highlighting, 11; presses, 11; primary function, 11; secondary function, 11 keyboard map, 6 L language: selection, 7 last number, 19; ANS key, 19 life. See depreciation line: regression, 61 log: LN key. See Math menu logarithmic functions, 23 lower tail normal distribution, 25 M markup: as cost, 53; as price, 53 math: Math key, 23 math functions, 16 Math menu: Absolute value, 24; Hyperbolic, 24; Log, 24; Probability, 24; Trigonometry, 24 mean, 61 memory, 13; key, 13 menu: Amortization, 33; Bond, 46; Break-even, 51; Cash Flow, 39; Date Calculation, 49; Depreciation, 56; Interest Conversion, 35; IRR, 42; Math, 22; Memory, 13; Mode, 8; NPV, 42; Payment per year, 36; Percent Calculation, 53; Reset, 13; Statistics, 60; TVM, 30; TVM Canada, 36 menu item value: recalling, 28 menus: items, types of, 15; maps, 14; special, 13; sub-menus, opening, 14 mode menu: key, 7 Index N N key, 32 natural exponent: e to the power of x key, 23 nCr, 27 negative numbers, 16 net future value, 43 net present value, 43 net uniform series, 43 nPr, 27 NPV: key, 42 NPV, IRR: menu items, 43 number entry, 16 number period: compounding, 55 number periods: amortization, 33 numbers: rounding, 28; storing and recalling, 27 O off: calculator off, 7 Off: key, 7 on: calculator on, 7 On: key, 7 P P/YR: key, 32 parentheses: use in Chain mode, 17 parentheses (swap and roll down): keys in RPN, 21 payback, 43 percent calculation: % calc key, 53 percentage: % key, 28 percentage of total, 53 percentages: simple, 28 periodic payment: PMT key, 32 PI. See Math Menu population, 61 power functions, 23 Predictions: sub-menu. See Statistics present value: PV key, 32 price: break-even, 51; face value. See bonds; percent calculation, 54 principal, 33 probability, 25 product: x and y values, 63 profit, 51 Q quantity: break-even, 52 R radians, 9 random function: RAND key, 23 recall arithmetic, 28 recalling numbers: RCL key, 27 reciprocal: 1/x key, 23 regression line, 61 remaining book value, 58 remaining depreciable value, 58 Reset: key, 13 roll down. See RPN rounding numbers: RND key, 23 RPN: Reverse Polish Notation, 18 RPN stack, 18 S S.E. SamP.X and Y, 61 salvage: depreciation, 58 scientific notation: EEX key, 16 scroll: up and down arrow keys, 8 semiannual: bond, 47 Sigma X,Y, 61 sign: positive, negative key, 16 sine: SIN key, 23 slope, 61 square of x: key, 23 square root key, 23 standard deviation, 61 start: amortization period, 33 start date: depreciation, 58 75 statistics: menu items, 62; one-variable, 61; one-variable weighted, 61; Stats key, 61; two-variable, 61 statistics example, 63 stats menu, 61 storing numbers: STO key, 27 student, 25 sums: sub-menu. See Statistics swap. See RPN symbol: battery, 7 T tangent: TAN key, 23 thousands separator, 9 time value of money: keys, 32 top line: display, 8 total: cash flows, 43 TVM: example, 32; storing and recalling numbers, 28 U up arrow key. See scroll X x: Sigma, 62; square of Sigma x, 63; times payment per year, xP/YR key, 32 x mean, 62 x mean sample, 62 x population Std. Dev., 62 x prediction, 62 x standard deviation, 62 Y y: Sigma, 63; square of Sigma y, 63 y mean, 62 y mean sample, 62 y population Std. Dev., 62 y prediction, 62 y standard deviation, 62 y to the x power, 23 y-intercept, 61

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