HP 20b Business Consultant HP 30b Business Professional Financial Calculator User’s Guide HP Part Number: NW238-90001 Edition 1, December 2009 i Legal Notice This manual and any examples contained herein are provided "as is" and are subject to change without notice. Hewlett-Packard Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability, noninfringement and fitness for a particular purpose. In this regard, HP shall not be liable for technical or editorial errors or omissions contained in the manual. Hewlett-Packard Company shall not be liable for any errors or for incidental or consequential damages in connection with the furnishing, performance, or use of this manual or the examples contained herein. Copyright © 2009 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 66M-785 San Diego, CA 92127-1899 USA ii HP 20b Business Consultant iii HP 30b Business Professional iv Keyboard Map Legend Number Feature Number Feature 1 2-line, alphanumeric scrolling display screen 9 Common Mathematical functions and Math (Math) menu 2 Time Value of Money keys (TVM) 10 Program menu* RPN Swap/Close parenthesis 3 Cash Flow, IRR and NPV keys 11 Backspace key/Reset menu 4 Data and Statistics menus 12 Percent/Percent calculation (business) and Date menus 5 Input key and Memory menu 13 Recall and Store 6 Insert and Delete/scroll (up and down) 14 Black-Scholes** and Bond menus 7 Shift key 15 Amortization/Depreciation menus 8 On/Off/Cancel 16 Annunciators * Only applies to HP 30b. **Does not apply to the HP 20b. v vi Table of Contents Legal Notice............................................................................................................. ii HP 20b Business Consultant ...................................................................................... iii HP 30b Business Professional .................................................................................... iv Keyboard Map Legend .............................................................................................. v 1 Basic Features ......................................................................................................... 1 Welcome to your new HP Financial Calculator .............................................................1 Turning the Calculator On and Off..............................................................................1 Selecting a Language ................................................................................................1 Adjusting the Display Contrast ....................................................................................1 Cursor .....................................................................................................................2 Two Line Display.......................................................................................................2 The Mode Menu: Setting Preferences...........................................................................2 Changing the Calculation Mode .................................................................................4 Key Presses, the Shift Key, Secondary, and Tertiary Functions*.......................................4 Annunciators ............................................................................................................6 The Input Key ...........................................................................................................6 The Equals Key .........................................................................................................6 Using the Input and Equals Keys .................................................................................6 Editing and Clearing Entries .......................................................................................7 The On/CE Key........................................................................................................7 The Reset Menu ........................................................................................................7 Notes about Special Menus .......................................................................................8 Memory and the Memory Menu..................................................................................8 Accessing Menus and Menu Maps..............................................................................8 2 Mathematical Calculations ..................................................................................... 11 Mathematical Functions ...........................................................................................11 Number Entry and Display .......................................................................................11 Chain Mode...........................................................................................................12 Algebraic Mode .....................................................................................................12 Reverse Polish Notation (RPN) Mode .........................................................................13 The RPN Stack ........................................................................................................13 Last Number...........................................................................................................14 One-Number Functions and the Math Menu ...............................................................18 Random number .....................................................................................................19 The Math Menu ......................................................................................................19 The Probability Sub-menu .........................................................................................21 Binomial Functions ..................................................................................................23 Two-Number Functions ............................................................................................23 Storing and Recalling Numbers ................................................................................24 Recall Arithmetic .....................................................................................................24 Storing and Recalling with Time Value of Money (TVM) Keys .......................................24 Recalling a Menu Item Value in a Menu.....................................................................25 Recalling and Storing Values in the Data and Cash Flow Menus ...................................25 Rounding Numbers .................................................................................................25 Percentages............................................................................................................25 3 Time Value of Money ............................................................................................. 27 Time Value of Money (TVM) Keys..............................................................................27 i Amortization .......................................................................................................... 29 Interest Conversion Menu ........................................................................................ 33 4 Canadian Mortgages: TVM Canada ........................................................................35 Canadian Mortgage Example .................................................................................. 36 5 Cash Flows ............................................................................................................37 Cash Flow Example ................................................................................................ 38 Sample Cash Flow Diagrams ................................................................................... 46 6 Bonds ....................................................................................................................47 The Bond Menu...................................................................................................... 48 7 Black-Scholes Calculation Menu* ............................................................................51 The Black-Scholes Menu .......................................................................................... 52 8 Date Calculation ....................................................................................................57 The Date Calculation Menu...................................................................................... 57 9 Break-even ............................................................................................................59 The Break-even Menu.............................................................................................. 59 10 Business Problems................................................................................................61 The Percent Calculation Menu .................................................................................. 61 11 Depreciation ........................................................................................................65 The Depreciation Menu ........................................................................................... 66 12 Statistical Operations ...........................................................................................69 The Data and Stats Menus ....................................................................................... 70 13 Programming.......................................................................................................75 Programming the HP 30b ........................................................................................ 75 Key Presses for Program Instructions.......................................................................... 75 Programming Example ............................................................................................ 77 Program Step 0 ...................................................................................................... 78 Reassigning Menu Functions .................................................................................... 79 The Program Menu and Program Editing ................................................................... 80 Tests and Jump Functions ......................................................................................... 81 Long Programs and Battery Life ................................................................................ 82 Sub-Function Call.................................................................................................... 82 Other Programming Functions .................................................................................. 83 Messages .............................................................................................................. 84 Debugging a Program............................................................................................. 85 Saving, Restoring, and Modifying Mode Settings ....................................................... 86 Solve .................................................................................................................... 87 14 Error Messages ....................................................................................................89 Error Messages and Calculator Status ....................................................................... 89 15 Warranty, Regulatory, and Contact Information ....................................................91 Replacing the Batteries ............................................................................................ 91 HP Limited Hardware Warranty and Customer Care................................................... 91 Contact Information ................................................................................................ 95 ii 1 Basic Features Welcome to your new HP Financial Calculator This manual is designed to familiarize you with the many features available on your new HP Business and Financial calculators. It includes menu maps, cash flow diagrams, and example problems and solutions with key presses and screen shots. Also included are sections which list the error messages, a chapter about programming, and an explanation of how Reverse Polish Notation (RPN) works. Refer to the Table of Contents for quick access to various topics. If you need more information about your calculator or calculator operation, please refer to the training materials available at: www.hp.com/calculators. This manual describes in detail the features available on both the HP 20b and the HP 30b calculators. In addition to all of the features found on the HP 20b, the HP 30b includes the Black-Scholes option pricing model, Modified Internal Rate of Return (MIRR), Financial Management Rate of Return (FMRR), and programming capabilities. When features apply only to a particular model, they will be identified throughout the manual with an asterisk*. 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 the Chapter 15, 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: 1. 2. 3. :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 Press active setting. 4. Press O to return to the default calculator screen. 5. For more information on accessing menus and changing calculator settings, refer to the section below titled, The Mode Menu: Setting Preferences. Adjusting the Display Contrast To adjust the contrast of the display, press and hold keys. Each press of the display. O while pressing the + or - + or - keys slightly increases or decreases the contrast of the Basic Features 1 Cursor When you enter a number, the cursor (_) blinks in the display and indicates you are in number entry mode. 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 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, 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. press 2 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. 2. Press : again, and, without releasing it, press a key, 0 through 9 that 1. Press corresponds 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 Date: mm.ddyyyy or dd.mmyyyy I toggles between these options. Format for dates. December 3, 2010 is entered as 12.032010 in mm.ddyyyy format, or 3.122010 in dd.mmyyyy format. Note the (.) in both formats separating the first and second groups. The valid range of dates is October 15, 1582 to December 31, 9999. 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 1000.00, 1,000.00, 1000,00 or 1.000,00 I toggles between these options. Selects thousands separator. 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 English, Français, Deutch, or Español I cycles through these options. Language setting for the messages displayed on the screen. Default is English. Pressing I cycles through these options. Basic Features 3 Table 1-1 Mode Menu Settings Setting (top line) Description Actual or Cal.360 Calendar options for bonds and date calculations. Default is Actual. Pressing Annual or Semiannual I toggles between these options. Bond type. Default is Annual. Pressing TVM Standard or TVM Canada I toggles between these options. Activate or deactivate the compounding per year (C/YR) option in time value of money (TVM) calculations. This option is primarily used for Canadian mortgage calculations. See Chapter 4, Canadian Mortgages: TVM Canada for more information. 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 RPN annunciator to the right. (Press two times) O Exits the Mode menu and returns you to the default calculator screen. Key Presses, the Shift Key, Secondary, and Tertiary Functions* To execute the function associated with a key, press and release the desired key. However, most of the calculators’ keys have more than one function: the first, or primary function, the shifted, or secondary function, and, in some cases, a third, or tertiary function (see Figure 2). * Tertiary functions do not apply to the HP 20b. 4 Basic Features • The primary function is printed on the top of the key. • The secondary function is printed on the bevel of the key. To activate the secondary function of a key, press and release • : followed by the key with the secondary function printed on the bevel. The third, or tertiary functions are printed above specific keys on the keyboard. To activate the tertiary function of a key, press and hold : and simultaneously press the key below the printed function. Release both keys. Black S Tertiary function: (press SHIFT and the function key simultaneously) B Primary Function Shifted (secondary) Function Figure 2 Primary, Secondary, and Tertiary Key Functions In this manual, key symbols of the commands are provided throughout the manual so you can follow along with the examples. • • The primary functions are represented by the key symbol with the primary function. :, followed by the key with the secondary function. For example, to execute sine, press :p. Note how the SIN The secondary key functions are represented by the shift key symbol, portion of 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. • Commands with a tertiary function are represented by the shift key symbol, :, followed by the term (HOLD), followed by the key with the tertiary function. For example, to activate the Black-Scholes feature shown above, press When :(HOLD) B*. : 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. 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. * Does not apply to the HP 20b. Basic Features 5 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. Secondary function active Valid item for the Valid item for Input key the Equals key Low batteries Number recall active Assigned value RPN mode active Begin mode active Radians active 360 day-count calendar active Number storage active Figure 3 Annunciator Symbols in the Screen Display The Input Key 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 the stack or duplicate it. The Equals Key = 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 The a calculation for the value of an item. This request only applies to items that can be calculated. Using the Input and Equals 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 6 Basic Features 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 = 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 (=) found to the right of a variable. I When an item for which the 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 Key O Pressing one time cancels current number entries, mathematical operations, or a menu selection, in that order. O Pressing repeatedly when performing multiple operations cancels one operation at a time, from the latest to the earliest. The Reset 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 To open the Reset menu, press 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 command to reset the cash flow (Cash Flow), statistics (Stats ), programs (Prgm)* or all values (All ) items, you will be prompted to confirm your choice. At the Del. All?, Del. Data?, Del. Prgm?*, and Del. CF? prompts, press again to confirm the reset, or I O to cancel. While working within a specific menu, pressing :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 I on screen. At this prompt, pressing resets the Bond menu and returns you to the last item you were working with in the Bond menu. * Only applies to the HP 30b. Basic Features 7 Notes about Special Menus The Mode, Memory, Math and Reset menus are unique menus; they allow you to work in another menu simultaneously without having to exit. For example, if you were working in the Bond menu prior to entering one of these menus, pressing O to exit returns you to your previous work in the Bond 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), programs (Prgm)*, 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 key in a new number and modify the value of the memory by pressing I. 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 data 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 cash flow or statistical data. 290 bytes are available for programs. The Prgm* menu item displays the number of bytes used. I on the Cash Flow, Statistic, or Prgm* menu item to erase the associated data. Press 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?, Del. Prgm?*, 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, key combination for the menu in which you wish to work. To exit a menu, press O. For example, to access the Break-even menu, press * Only applies to the HP 30b. 8 Basic Features : . < or > repeatedly. In most menus, when you arrive at the last item in a menu, pressing < returns you to the first item. Similarly, pressing > once on the first menu item scrolls to the last Once opened, you can scroll through the items in the menu by pressing item in the menu. Most items consist of two parts: a name and an associated number. For example, the Fixed item in the Break-even menu (Figure 7) is displayed in Figure 5. Figure 5 The large (=) annunciator shows that the value assigned to Fixed is 120,000. For example, if you perform a calculation with the operating mode set to RPN with this item displayed by pressing 1I2+, Fixed is still selected as the current item, but the large (=) annunciator is now turned off, indicating that 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 O. I with that menu item displayed opens the sub-menu. Once the menu sub-menu is open, use > and < to navigate through the items of the sub-menu, unless otherwise directed. Some menus have sub-menus. If an item represents a sub-menu, pressing In this manual, diagrams called Menu Maps are included at the beginning of each section to assist you with navigating through the menus described in that section. For an example of a menu map, see Figure 7 below. Once opened, use the > and < keys to navigate through the menu items of the Break-even menu. The downward arrows in the map indicate you press < to scroll to the next item. If a press of the I key is required to open a sub-menu, the word INPUT appears in the arrow(s). For examples of menu maps with submenus, see chapters 10-12. The return arrows direct you to the next item displayed after the last item in a menu. For example, in Figure 7, pressing < on the last item in the menu returns you to the FIXED item. Basic Features 9 :P Fixed Cost Price DWN Profit Quantity Figure 7 Menu Map of 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 keying in a number and pressing = I will store the entered number in the displayed menu item. Pressing (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 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 keying in 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), changing a mode or setting (Mode menu), or erasing data (Reset menu) 10 Basic Features 2 Mathematical Calculations Mathematical Functions Mathematical functions are located: • • • +-*/, etc. On shifted, or secondary functions, such as, :p In the Math menu, :s On keys, such as, Number Entry and Display Numbers are entered by pressing: • • • • 0–9 The decimal point . The } key The :w keys Numbered keys, To correct a number entry, press the backspace key, digit or symbol you entered. {. Each press of { erases the last 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 1.23x 10127 in scientific notation, first enter the mantissa (1.23) and then press :w and enter the number (127) representing the exponent. The exponent must have a value between –499 and +499. If an expression has more than 12 digits, or if an operation returns a result with more than 12 digits, the calculator automatically displays scientific notation. Figure 1 Scientific Notation in FIX=2 Mode Mathematical Calculations 11 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 +-*/, after =, the calculation is NOTE: if you press an operator key, continued using the currently displayed value. In Chain mode, if you wish to override the left to right order of entry, use parentheses (D to prioritize operations. For example, to calculate 1 + (2 x 3), you may enter the problem as written from left to right, with parentheses to prioritize the multiplication operation. See Table 2-1 below. Table 2-1 Simple Arithmetic Calculations in Chain Mode Keys Display Description Sets operational priority, inputs numbers, and multiplies 2 and 3. 1+ (2*3D Adds 1 to 6 and returns 7.00 on the bottom line as 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: y x) • Highest priority: the power function ( • Second priority: combinations and permutations • Third priority: multiplication and division • Lowest priority: addition and subtraction 12 Mathematical Calculations For example, key in 1 + 2 x 5 nPr 22 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 keyed in first, separated by pressing I or =, followed by an operation key. NOTE: pressing I or = is optional after keying in 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. I = NOTE: in RPN mode, when you are in a menu for which 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 Mathematical Calculations 13 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. + ) for instance, the calculator When an operation is performed on the stack, addition ( "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 Shown 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. 14 Mathematical Calculations Table 2-2 Last Number Keys Display Description Sets FIX= to 3.000 :u3I Selects RPN as the operating mode. <<<< < II Inputs 1.23 and 56.123 O1c23 I56c 1 23 Adds 1.23 and 56.123, then divides the sum by the last number, 56.123. Returns results in the selected display format. +:d/ 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) x (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. Mathematical Calculations 15 Table 2-3 Simple Arithmetic Calculations in RPN Mode Keys Display Description Inputs the numbers and the operation in the first set of parentheses. Intermediate results are displayed. Note the (+) and (RPN) annunciators. 3I4 + RPN Stack Previous Value Previous Value Previous Value 7 Inputs the numbers and the operation in the second set of parentheses. Intermediate results are displayed. Note the (+) annunciator. 5I6 + Previous Value Previous Value 7 11 Finishes the operation and displays the results. * Previous Value Previous Value Previous Value 77 Pressing 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 77 on the stack, making Levels 1 and 2 equal. See Figure 5. 16 Mathematical Calculations Previous Value Previous Value 77 77 Figure 5 Duplicating a Number on the Stack (D ( 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 to moves down to Level 1, the number in Level 3 to moves down to Level 2, the number in Level 4 to moves down to Level 3, and the number of Level 1 to moves ( key has a small down arrow on it to indicate the roll down feature. With the numbers entered into the stack shown in the left column in Figure 6, pressing ( up to Level 4. The performs the roll down of the stack shown in the right column. -15 23 12 -15 41 12 23 41 Figure 6 The RPN Stack and the Roll Down Operation Mathematical Calculations 17 D performs a swap. A swap operation exchanges the numbers on Levels 1 and 2 of the stack. The D key has a small symbol to the right of the parenthesis symbol to indicate Pressing the swap feature. With the numbers entered into the stack shown in the left column in Figure 7, pressing D performs a swap to the stack as shown in the right column. -15 -15 12 -15 41 23 23 41 Figure 7 The RPN Stack and the Swap Operation NOTE: when no menu is selected, the The < key performs the same function as the ( key. > 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. 6:n . The result of 2.45 is calculated For example, to calculate 6 , press immediately and displayed on the bottom line. Note 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 (Degree) or radians (Radian). 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. 18 Mathematical Calculations 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 non-integers or negative numbers. :i Calculates the reciprocal. :d In Chain or Algebraic mode, recalls the result of the last operation. In RPN mode, returns the content of the Last Number variable. :e Rounds x to the number specified by the display format. Random number :f to generate a randomly distributed number between 0 and 1. Type a number and press :$:f to store a new seed for random number Press generation. The Math Menu There are additional functions available in the Math menu. To open the Math menu, press :s. See Figure 8 for the menu map of the Math menu. Mathematical Calculations 19 :s DWN Trigonometry DWN Hyperbolic DWN Probability INPUT INPUT INPUT PI SINH LTND SIN-1 COSH COS-1 TANH DWN ABS (Absolute Value) DWN LOG DWN IP * DWN FP * LTND-1 Student DWN Student-1 TAN -1 SINH-1 DWN Chi 2 COSH-1 DWN Chi 2-1 TANH-1 F—Distribution F-1—Distribution Binomial 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 on any of these items to access the functions within the sub menus. Press < to scroll through the functions. Press * IP and FP functions are not available on the HP 20b. 20 Mathematical Calculations O Press to cancel the Math menu and return to current work. Press to the top of the Math menu. For example, using the math menu calculate Sin –1 :s to return (0.5), see Table 2-5. Table 2-5 Math Menu Example Keys Display .5I :s I< I or = Description Enters 0.5 and opens the Math menu starting with Trigonometry. Selects the Trigonometry sub-menu and scrolls to Sin-1. Note the value for Sin-1 is calculated immediately and displayed. 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, Chi2 ( χ 2), Inverse Chi 2, F-Distribution and Inverse F-Distribution perform similar operations for Student, Chi2, 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 or =. I 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: Mathematical Calculations 21 1. Enter the two degrees of freedom by typing each number followed by =. 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. See Table 2-6. Note: the examples below are calculated with Chain set as the operating mode. Table 2-6 Probability Example Keys Display Description Enters 10 degrees of freedom and the number for which probability is to be calculated. Opens the Math menu. 10I 8I :s Selects the Probability menu item and scrolls to <<I <<<< Chi2.. Validates the result. I or = Table 2-7 Inverse Probability Example Keys 10I 0.37 12I :s <<I <<<< < I or = 22 Mathematical Calculations Display Description Enters 10 degrees of freedom and the probability. Opens the Math menu. Selects the Probability menu item. Scrolls to Chi2-1. Validates the result. Binomial Functions The binomial function calculates the probability of having up to k successes out of n throws, when the probability of success is p. Enter n and p each followed by navigate to the binomial function in the math menu. = and type k and Two-Number Functions +-*/, the three additional two-number functions accessible on Apart from the keyboard are: • yx • nCr • nPr yx 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. n! r! ( n – r )! Combination= ---------------------- n! ( n – r )! Permutation= -----------------Perform calculations with these functions in the same way you would perform calculations with +-/ and *, but press : to access the secondary function key. For example, to calculate 153 : 1. 2. 3. 15. Press :h Press 3= The result is shown in Figure 9. Press . . Figure 9 In RPN mode, key in the numbers first, followed by I, then press the function key. For example, for the power function example above, in RPN press: 15I3:h . Mathematical Calculations 23 Storing and Recalling Numbers The calculator has ten memories available for use during calculations. These memories are :$, followed by the key representing the memory number. To recall a number stored in a memory, press L numbered from 1–9 and 0. To store a number in a memory, press 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. 15:$1. To recall the number in memory 1, press L1. For example, to store 15 in memory 1, press You can also perform operations to numbers stored in memories. For example, press 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 press L2 to recall memory 2. Note how the current value now 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 L+2 In RPN, typing 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. Storing and Recalling with Time Value of Money (TVM) Keys To store the current number in the Time Value of Money (TVM) variables, press followed by the desired TVM key. To recall the stored value of a TVM variable, press TVM variable. Note: pressing :$ L followed by the key of the desired L does not calculate the variable; it recalls the current value. 24 Mathematical Calculations 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== calculates 2 times the nominal rate. This feature is useful when you need to insert the contents of a menu item into an algebraic operation. Recalling and Storing Values in the Data and Cash Flow Menus If you store an index (i) from 0 to 99 in the variable 0, you can then use the store/recall features to store a number in the Data and Cash Flow menus. Press either followed by the CashFlow key :$ or L, C, to either store or recall a number, as desired, in the CF(i/2) (if i is even) or #CF((i-1)/2) if i is odd. In addition, you can store or recall x(i/2+1) if i is even, or y((i+1)/2) if i is odd, as desired, by pressing the Data key :y instead of the CashFlow key, C, as shown above. 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. To find a percentage of a given number, key in the number and multiply it by the desired =. For example, to find 25% of 200, press 200*25%= to return a result of 50. percentage, followed by To add or subtract a percentage of a number, key in 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 return a result of 55. Mathematical Calculations 25 % 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 from the number. % to add or subtract x % 200I25% returns 50, but 200 is still on Level 2 of the stack, and pressing - returns 150, or 200-25%. For example, 26 Mathematical Calculations 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. (PV) Loan amountmoney received is positive (Beg) (End) For payments occurring at the beginning or end of the compounding period Q (P/YR) Payments per year PMT 1 PMT 2 (PMT) Amount paid out in equal payments at regular intervals PMT 3 PMT 4 PMT 5 PMT 6 (N) Number of payments or compounding periods (FV) Final loan value (if any) 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 Chapter 4, Canadian Mortgages: TVM Canada, or Chapter 5, Cash Flows. Time Value of Money 27 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. 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 :^ Y V Stores or calculates the number of payments or compounding periods. M :[ F :? :] Stores or calculates the amount of each periodic payment. Multiplies a value by the number of payments per year and stores as N. Stores or calculates the nominal, annual interest rate. Stores or calculates the present value (PV). To a lender or borrower, PV is the amount of a loan; to an investor, PV is the initial investment. PV always occurs at the beginning of the first period. Stores the number of payments or compounding periods per year. This value is 12 by default, but it maintains its current entered value when TVM Reset is used. Stores or calculates the future value (FV), a final cash flow. FV always occurs at the end of the last compounding period. 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. 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: the following example is calculated with RPN set as the operating mode. At the end of the 30 years, you expect to have a zero balance (FV=0). The example is calculated with RPN set as the operating mode 28 Time Value of Money Table 3-2 TVM Example Keys Display Description 12:[ Inputs 12 as the number of payments per year, or compounding periods per year. 360N Inputs 360 as the number of payments over 30 years. 6.5Y 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 payment. This value is positive (+); it is money you receive. 0F Inputs 0 as the future value of the loan (the remaining balance). M Returns the monthly payment. This result is negative (–); it is money you pay out. :x. Press < or > repeatedly until TVM displays. Press I to reset the TVM values, or press O to To reset the TVM variables to their default values, press cancel. Note: the value for P/YR is not reset; it maintains its current entered value when TVM Reset is used. Amortization Refer to Figure 2 for a menu map of the Amortization menu (Amort). Table 3-3 lists the keys A. The Amortization menu calculations are based on values stored in the following TVM registers: N, Y, V, M and [. and variables of the Amortization 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. Time Value of Money 29 A Nb Per Start Balance DWN Principal Interest Figure 2 The Menu Map for the Amortization Menu Table 3-3 Amortization Menu Items Menu Item/Key Description A Opens the Amortization menu (Amort). 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. Enter the values for the TVM keys for the example below. Press > to view the amortization schedule. 30 Time Value of Money A followed by < or 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 calculated with Chain set as the operating mode, but it can be performed in RPN, Chain, or Algebraic. Table 3-4 Amortization Example Keys Display Description 12:[ Inputs 12 as the number of payments per year. This value is 12 by default, but it maintains its current entered value when TVM Reset is used. 30:^ Inputs 360 (30 times 12 payments per year) as the number of payments for the 30-year loan. 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 amortization schedule. Default is the current value of P/YR. < 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 the loan for the first year. Time Value of Money 31 Table 3-4 Amortization Example Keys Display Description < Displays the amount of interest paid on the loan for the first 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. To reset the menu items to their default values, with any item of the Amortization menu :x. With TVM displayed, press I. At the TVM Reset prompt, press I to reset, or O to cancel. displayed press 32 Time Value of Money Interest Conversion Menu :& Nom.% Eff.% DWN C/YR 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 C/YR, such as 18% compounded monthly (C/YR=12 ). Eff.% Effective annual interest rate taking compounding into account. C/YR Compounding periods per year. Default is 12. Time Value of Money 33 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 nominal percentage rate 36. 5I Inputs 36.5 as the nominal percentage rate. > Scrolls to compounding periods per year, C/YR. Default value is 12. 360 I Inputs 360 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 44.02%. Note: in TVM Standard, 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 when you are calculating in TVM Standard. 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 :x. With IConv displayed, press I to reset, or O to cancel. To exit the menu, press O once again. displayed press 34 Time Value of Money 4 Canadian Mortgages: TVM Canada :[ P/YR DWN C/YR Figure 1 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 when payments are made. By default, the calculator 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. To open the P/YR menu, press Canada enabled: :[. Note the following change in features with TVM 1. The P/YR key 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. See Figure 1. 2. In the Interest Conversion menu, the C/YR item is the same value as the C/YR item in the P/YR menu, and it no longer affects P/YR. However, note how 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. Canadian Mortgages: TVM Canada 35 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). The example is calculated with RPN set as the operating mode. Table 4-1 Canadian Mortgage Example Keys Display Description :u Opens the Mode menu, starting with the current FIX value (number of digits to the right of the decimal point). >I Scrolls to TVM mode and sets mode to TVM Canada. O Returns to default calculator screen. :[12 I<2 I Opens P/YR menu. Inputs 12 for P/YR and 2 for C/YR. O300 N6Y35 0000 V 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 To reset the menu, press again. With the menu in its default settings, P/YR and C/YR are both set to 12 payments/ compounding periods per year. 36 Canadian Mortgages: TVM Canada 5 Cash Flows CF (5) 5,000.00 CF (1) 5,000.00 CF (3) 0.00 1 0 2 10 5 7 8 9 4 3 CF (2) 4,500.00 6 CF (4) 4,000.00 CF (6) 115,000.00 CF (0) -80,000.00 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) is 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 number of occurrences followed by I. If a cash flow occurs once, you do not need to type or I, then enter the 1I. Simply press I < as 1 is the default. Cash Flows 37 To erase a cash flow list, with any cash flow displayed press :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. Table 5-1 lists the keys used for cash flow problems. For a cash flow example, see Table 5-2. Table 5-1 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, CF (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 5-2 for how to enter the cash flows. The example is calculated with RPN as the active operating mode. 38 Cash Flows Table 5-2 Cash Flow Example Keys Display Description C Opens the cash flow list. 8000 0}I Inputs -80000 as the monetary value of the initial cash flow. Note: the sign of the cash outflow is negative. I Accepts 1 as the number of occurrences for CF(0). Displays the current monetary value of CF(1). 5000 I Inputs 5000 as the 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). Displays the current monetary value of CF(2). 4500 I Inputs 4500 as the 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). Displays the current monetary value of CF(3). I Accepts 0 as the monetary value of CF(3). Displays the current value, 1, for the number of times CF(3) occurs. I Accepts 1 as the number of occurrences for CF(3). Displays the current monetary value of CF(4). 4000 I Inputs 4000 as the 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). Displays the current monetary value of CF(5). Cash Flows 39 Table 5-2 Cash Flow Example Keys Display Description 5000 I Inputs 5000 as the 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). 1150 00I Inputs 115000 as the monetary value of CF(6). Displays the current value, 1, for the number of times CF(6) occurs. I Accepts 1 as the number of occurrences for CF(6). 40 Cash Flows Analyzing Cash Flows The various functions used to analyze cash flows are located in the NPV P and IRR R R P or before entering cash flows, you will be redirected to the menus. If you press 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 5-3 describes the items within these menus. The results shown in Table 5-4 are based on the values entered in the cash flows as shown in Table 5-2. Table 5-3 Analyzing Cash Flows Item Description Inv. l% Investment or discount rate. Enter the investment rate or discount rate for the cash flow followed by I. This rate must be entered in both the NPV and IRR menus.* NetPV 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%. NetFV 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%. NetUS 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 that returns a Net Present Value for the entered cash flows. Safe I%* Safe Interest Rate. Enter the safe investment rate followed by I. MIRR* Modified Internal Rate of Return. Used primarily when there is more than one sign change in a series of cash flows to evaluate the overall profitability of an investment. FMRR* Financial Management Rate of Return. Used primarily when there is more than one sign change in a series of cash flows to evaluate the overall profitability of an investment. *Does not apply to the HP 20b. Cash Flows 41 P R Inv. I% IRR % Net PV Inv. I%* Net FV Safe I%* DWN Net US MIRR* DWN Payback FMRR* Discounted Payback #CF/Yr Total #CF/Yr Figure 2 The Menu Maps for the NPV and IRR Menus *Does not apply to the HP 20b. 42 Cash Flows Table 5-4 Keys Display Description P Opens the NPV menu. 10. 5I Inputs 10.5 for investment rate. >1 I (Optional) Verifies one cash flow list per year, as per the example. << 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. < 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. Cash Flows 43 Editing Cash Flows In the cash flow list, you can view and modify the current monetary value of a specific cash < 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 flow, or cash flows. Press monetary value of the cash flow three, CF(3), in the example in Table 5-2 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) :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. displayed. Pressing Note that the values for the number of cash flows occurring for a given year, (#CF/Yr) Investment interest rate, (Inv. I%), and safe interest rate (Safe I%) can be entered in both the NPV and IRR menus*. Key in the desired number or rate followed by I with the item displayed. The other items are then calculated internally. Modified Internal Rate of Return (MIRR) and Financial Management Rate of Return (FMRR)* For the cash flow example you entered in Table 5-2, edit the cash flows using the cash flow amounts and number of occurrences shown in Table 5-5 below. For the initial cash flow, CF(0), enter -1,250,000. In the IRR menu, enter 8% for investment interest rate, and 5% as a safe rate. Verify the number of cash flows per year, #CF/Yr, is set to 1. The results for MIRR and FMRR are shown in Table 5-6. This example was calculated in Algebraic mode. Table 5-5 Cash Flow Number Cash Flow Amount Occurrences 1 -300,000.00 1 2 200,000.00 1 3 450,000.00 1 4 -200,000.00 1 5 700,000.00 1 6 300,000.00 1 7 500,000.00 1 *Does not apply to the HP 20b. 44 Cash Flows Table 5-6 Keys Display Description R Opens the IRR menu. Displays the IRR for the cash flow. >1 I (Optional) Verifies one cash flow list per year, as per the example. <<8 I Inputs 8% for investment rate. <5 I Inputs 5% for the safe investment rate. < Displays MIRR%. < Displays FMRR%. Cash Flows 45 Sample Cash Flow Diagrams Figure 3 Sample Cash Flow Diagrams 46 Cash Flows 6 Bonds B Set.Date Mat.Date CPN% Call Yield% Price Accrued DWN Mod. Duration* Macaulay Duration* Actual/Cal.360 Annual/ Semi-annual Figure 1 The Menu Map for the Bond Menu *Does not apply to the HP 20b. Bonds 47 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. The range of acceptable dates is October 15, 1582 to December 31, 9999. 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. To change the value of the displayed item, key in a number or a date and press Once you have entered all known data, Press unknown item, and press I. < or > repeatedly to scroll to an = to calculate it. Table 6-1 lists the items in the Bond menu. Table 6-1 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. 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. Mod. Duration* Modified duration for the bond. This is a measure of bond price sensitivity to yield changes. Macaulay D.* Macaulay Duration for the bond. This is a measure of bond price sensitivity to yield changes. Actual/Cal.360 Actual (365-day calendar) or Cal.360 (30-day month/360-day year calendar). Press I to toggle between these options. Annual/Semiannual Bond coupon (payment) frequency. Press *Does not apply to the HP 20b. 48 Bonds 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 6-2. The example below is calculated with RPN as the active operating mode. Table 6-2 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 example. <4.2 82010 I Inputs April 28, 2010 for the settlement date (mm.ddyyyy format). <6.0 42020 I Inputs June 4, 2020 for the maturity date. <6.7 5I Inputs 6.75% for the value for CPN%. < Displays current call value. Default is 100. Note: if Call requires another value, key in the number followed by I. <4.7 5I Inputs 4.75% for Yield%. <= Calculates the current value for Price. Bonds 49 Table 6-2 Bond Calculation Example Key Display Description :$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) in RPN mode. If calculating in Chain or Algebraic modes, at this point, press +L1=. 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 :x. With Bond displayed, press I to reset the menu, or O to cancel. Press O again to exit the menu. 50 Bonds 7 Black-Scholes Calculation Menu* :(HOLD)B Stock price Strike price Time to maturity Risk-free % DWN Volatility % Dividend % Call price Put price Figure 1 The Menu Map the Black-Scholes menu *Does not apply to the HP 20b. Black-Scholes Calculation Menu* 51 The Black-Scholes Menu To open the Black-Scholes menu (the Black-Sholes key is : (HOLD) B). To open the menu: 1. Press and hold the 2. Press the : key. B (the Black-Sholes key). 3. Release both keys. In other words, press on the : and B keys simultaneously and hold both keys, just as you would when accessing a shifted-function on a PC keyboard. If you press and release : and then press on the B (Black-Sholes key), you will enter the Date menu. I. Once you have entered all known data, the unknown items are calculated automatically. Press < or > repeatedly to scroll to view the items. To change the value of the displayed item, key in a number and press An option is a contract between two parties giving party A the option to buy or sell an asset from/to party B at a given price. The Black-Scholes model is used to calculate an estimated fair market price for that option, meaning that it calculates the fair price that someone would pay to buy or sell the option to later buy or sell an asset at a given price! The asset or stock that the option refers to is often called the “underlying asset.” The Black-Scholes calculation is based on the contract terms (i.e., the price and date at which the underlying asset can be sold or bought), the quality of the asset itself, its price, volatility and return on investment, and the other available alternatives, such as storing your asset in a safe investment account, for example. Intuitively, if the option is to buy a stock at 10, and the stock is already worth 30 and has little volatility, the value of the option is close to 30-10=20, plus or minus other risk factors. Table 71 lists the Black-Scholes menu items along with their descriptions. 52 Black-Scholes Calculation Menu* Table 7-1 Item Description Stock price (input) Current underlying asset price Strike price (input) Predetermined price at which the option agrees to buy or sell the underlying asset at maturity. Time to maturity (input) Time remaining until expiration of the option in years. Risk free% (input) Current risk-free interest rate (for example, the current US Treasury Bond rate). Volatility % (input) Degree of unpredictable change of the stock price. This is usually approximated by the standard deviation of the variation of the stock price. Dividend % (input) Estimation of the average dividend yield of the stock as a percentage of its price. Call price (output) Estimated fair market value for a call option at expiration (a call option is the right to purchase the asset at a given price). Put price (output) Estimated fair market value for a put option at expiration (a put option is the right to sell the asset at a given price). Note that if you enter a history of the underlying asset price and its yield in the data menu, = key on the Volatility % menu item automatically calculates the standard deviation of the variation of the asset price based on the given data. Pressing = in the pressing the Dividend % menu item automatically calculates the average dividend as a percent of the asset price. Black-Scholes Calculation Menu* 53 Black-Scholes Example The historic prices for an asset and their dividends are listed in Table 7-2 below. Given this data, calculate the call and put prices for the asset. The example is calculated with RPN set as the operating mode. First, enter the historical asset prices and the dividend as ordered pairs in the Data menu. Enter the historical prices for the x values, and the dividend for each y value. For more information about entering data in the Data menu, see Chapter 12, Statistical Operations. Table 7-2 Historical Asset Price (x) Dividend (y) 80 3 85 5 78 1 72 0 < or >, to scroll through the menu. Open the Black-Scholes menu. Use the arrow keys, With the menu item displayed, key in the value in the right column of the table followed by I: Table 7-3 54 Black-Scholes Calculation Menu* Menu item Value Stock Price 74 Strike Price 72 Time to Maturity 0.3 (years) Risk Free% 5 Volatility% 8.21 Dividend% 2.73 Table 7-4 Black-Scholes Example Keys Display Description :y Opens the Data menu. 80I 3I Inputs 80 for x and 3 for y. 85I 5I Inputs 85 for x and 5 for y. 78I 1I Inputs 78 for x and 1 for y. 72I 0I Inputs 72 for x and 0 for y. :(HOLD) B Opens Black-Scholes menu. 74I < Inputs 74 for Stock Price. Scrolls to Strike Price. 72I < Inputs 72 for Strike Price. Scrolls to Time to Maturity. .3 I< Inputs 0.3 years for Time to Maturity. Scrolls to Risk Free%. 5I< Inputs 5 for Risk-Free%. Scrolls to Volatility. Black-Scholes Calculation Menu* 55 Table 7-4 Black-Scholes Example Keys = Press < to scroll to the next item. Display Description Calculates the standard deviation of the price of the underlying asset based on the historical data entered in the Data menu. If you have not entered the historical data, you can enter the standard deviation of the price of the underlying asset directly by typing the number and pressing I. Press < to scroll to the next item. = Press < to scroll to the next item. Calculates the average dividend return as a percentage of the underlying asset cost based on the historical data entered in the Data menu. If you have not entered the historical data, enter the average dividend return as a percentage of the underlying asset cost directly by typing the number and pressing < Scrolls to Call Price. < Scrolls to Put Price. I. To reset the menu items to their default values, with any item of the Black-Scholes menu :x. With Black-Scholes displayed, press I to reset the menu, or O to cancel. Press O again to exit the menu. displayed press 56 Black-Scholes Calculation Menu* 8 Date Calculation :@ Date 1 Date 2 Days Between DWN Actual/ Cal.360 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. The range of acceptable dates is October 15, 1582 to December 31, 9999. For more information on setting the preferences in the Mode Menu, see the section titled, The Mode menu: Setting Preferences in Chapter 1. To change the value of a displayed item, key in a number or a date and press Once you have entered all known data, press unknown item and press I. < or > repeatedly to scroll to the = to calculate it. 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). Date Calculation 57 Table 8-1 Date Calculation Example Key Display Description :@ Opens the Date Calculation menu. 6.04 2010 I Inputs the starting date in the selected format. <10. 3120 10I Inputs the ending date in the selected format. <= Calculates the number of actual days between the starting and ending dates. NOTE: 2 in the right of the display represents the day of the week. 2 represents Tuesday. To reset the menu items to their default values, with any item of the Date menu displayed press :x. With Date displayed, press I to reset the menu, or O to cancel. Press O again to exit the menu. 58 Date Calculation 9 Break-even :P Fixed Cost Price DWN Profit Quantity Figure 1 The Menu Map for the Break-even Menu The Break-even Menu :y. 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? Break-even 59 Table 9-1 Break-even Example Keys Display Description :y Opens the Break-even menu starting with the current value for fixed costs. 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. <100 00I Inputs 10,000.00 for profit. <= 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 :x. With BrkEven displayed, press I to reset the menu, or O to cancel. Press O again to exit the menu. press 60 Break-even 10 Business Problems :# DWN Mkup.%C DWN DWN Mkup.%P DWN Part% Tot. DWN %Change INPUT INPUT INPUT INPUT Cost Cost Total Old Price Price Part New Part% Tot. %Change Mkup.%C DWN Mkup.%P DWN DWN Nb Period Figure 1 The Menu Map for the Percent Calculation (%calc) Menu The Percent Calculation Menu Press 1. 2. 3. 4. :# 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.) Percent change (%Change). These items allow you to access sub-menus. Press desired sub-menu, then press < or > repeatedly to scroll to the I to open it (see Figure 1). To change the value of a displayed item, key in a number and press have entered all known data, press and press I. Once you < or > repeatedly to scroll to the unknown item = to calculate it. Business Problems 61 To return to the percent calculation menu, from anywhere within the menu or sub-menus, press :#. To exit the menu, press O. NOTE: for business problems, margin is based on price; markup is based on cost. The examples below are calculated with RPN as the active operating mode. Percent Calculation Examples See the tables below 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. Table 10-1 Markup Example Keys Display Description :# Opens the %Calc menu. I Opens the Mkup.%C sub-menu. 15I Inputs 15 for Cost. <22 I Inputs 22 for Price. <= Calculates the value of Mkup.%C for the given data. 62 Business Problems 2. Find the percent change between 20 and 35 with no compounding. Table 10-2 Percent Change Example Keys Display Description :# Opens the %Calc menu. <<< Scrolls to %Change. I Opens the %Change sub-menu. 20I Inputs 20 for Old. <35 I Inputs 35 for New. <= Calculates the current value of %Change for the given data. NOTE: although the example in Table 10-2 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: Business Problems 63 Table 10-3 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. 30 is what % of 80? Table 10-4 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. <30 I Inputs 30 for Part. <= Calculates the value of Part%Total for the given data. To reset the menu items to their default values, with any item of the %calc menu displayed :x. With %Calc displayed, press I to reset the menu, or O to cancel. Press O to exit the menu. press 64 Business Problems 11 Depreciation :\ Press I to scroll through the options: Sline SOYD DecBal DBXover French Sl Amort F Life Start Cost Salvage Factor Year (auto-increment) Depreciation DWN R. Book Value R. Depreciable Value Figure 1 The Menu Map for the Depreciation Menu Depreciation 65 The Depreciation Menu :\ to open the Depreciation menu. To select a depreciation method, press I. See Figure 1. Input the values required for the calculation: Press • • • • • Asset life Starting date or month of the depreciation 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 change the value of the displayed item, key in a number and press 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. < NOTE: pressing on the last item of a sub-menu returns you to the Year item and increments it (see Figure 1). Brief descriptions of the methods used to calculate depreciation are provided in Table 11-1. Table 11-2 describes the items found in the depreciation sub-menus. For an example calculating depreciation using the straight-line method, see Table 11-3. Table 11-1 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 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 mm.dd 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. 66 Depreciation Table 11-2 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 was placed into service in the middle of March, for example, enter 3.5 for Start. Cost The depreciable cost of the asset at acquisition. 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 11-3. Table 11-3 Straight Line Depreciation Example Key Display Description :\ Opens the Depreciation menu starting with the straight line method. <5I Inputs 5 for the useful life. < Displays the current value of Start. 1 (January) is the default value. For this example, this value remains unchanged, since the depreciation of the machine starts January 1st (1.00 ). <100 00I Inputs 10,000.00 for the cost of the item. <500 I Inputs 500.00 for the salvage value of the item. Depreciation 67 Table 11-3 Straight Line Depreciation Example Key < Display Description 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. < 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 :x. With Depreciation displayed, press I to reset the menu, or O to cancel. Press O to exit the menu. displayed press 68 Depreciation 12 Statistical Operations :z DWN Descriptive Press DWN I to select: 2 Vars, 1 Var, or 1 Freq. (y items 2 Vars Only) Predictions DWN (2 Vars Only) INPUT INPUT Nb Item Press I to select: y Mean a*x+b a*Ln(x) +b b*e(a*x) b*xa b*ax a/x+b ax2+bx+c* x Std. Dev. Pred x x Mean DWN y Std. Dev. DWN Sums (y items 2 Vars Only) DWN Quartiles* (y items 2 Vars Only) INPUT INPUT Sigma x x Min Sigma y x Q1 Sigma x2 x Median Sigma y2 x Q3 DWN Pred y x Max Sigma xy DWN x Population DWN a y Min y Population b S.E. Samp. x (ax2+bx+c only)* y Median S.E. Samp. y Correlation (Not ax2+bx+c)* y Q3 Covariance (Not ax2+bx+c)* y Max y Q1 C Figure 1 The Menu Map for the Statistics Menu 2 *ax +bx+c and Quartiles do not apply to the HP 20b. Statistical Operations 69 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. :y to open the Data menu. In this menu, enter a list of x values for one-variable Press statistics, a list of pairs, (x, F) for one-variable statistics with frequency, or a list of pairs, (x, y) for two-variable statistics. To enter data, key in a number and press I. :z Press 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 I displays 2 Vars for two-variable statistics. Press repeatedly to select the type of statistical operations desired, two-variable, (2 Vars), one-variable, (1 Var), or one-variable with frequency (1 Freq). After selecting the type of statistical operation you want, select a sub-menu by pressing > I < < > or , and press to open it. Once in a sub-menu, press or repeatedly to view the results. To return from the sub-menu to the Statistics menu, press :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 seven 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 your data. =, the calculator automatically selects the curve that is the best fit for Once you select a regression line, press perform predictions. < to see the regression line parameters and Table 12-1 The Statistics Menu Items Menu Item Description Nb Item Number of items. X Mean Average of Y Mean Average of y values. x Std. Dev Standard deviation for x: a measure of how dispersed the the mean. 70 Statistical Operations x values. x data values are about Table 12-1 The Statistics Menu Items Menu Item Description 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 Standard error for the sample x: a measure of the dispersion of the data is a sampling of a large, more complete data set. S.E.Samp.y Standard error for the sample y: a measure of the dispersion of y mean, assuming the data is a sampling of a large, 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. c The 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. Σx The sum of the Σy The sum of the y values. x mean, assuming c coefficient for the chosen regression model, applies only for ax2+bx+c. x values. x values. Σx 2 The sum of the squares of the Σy 2 The sum of the squares for the y values. x and y values. Σxy The sum of the products of the Quartiles* The boundaries of a given frequency distribution divided into four parts. Median* The middle value in a given frequency distribution. Maximum* The largest value in a given frequency distribution. Minimum* The lowest value in a given frequency distribution. *Does not apply to the HP 20b. Statistical Operations 71 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 Table 12-2 and Table 12-3. Table 12-2 Statistics Example Months and Sales Values 72 Statistical Operations Month Sales Values 1 150 2 165 3 160 4 175 5 170 Table 12-3 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). 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. <7I Inputs 7 as the Prediction x value (month 7). <= Calculates Prediction y value (sales at month 7). NOTE: this example performs calculations based on a linear (a*x+b) regression line. Statistical Operations 73 Table 12-3 Statistics Example Keys Display Description < Displays value for a: the slope of the regression line. < Displays current value for b: the y-intercept of the regression line. < Displays value for Correlation. :z<< Opens Sums sub-menu. Displays the sum of all y values (Sigma y). <I< To reset the menu items to their default values, with any item of the Data or Statistics menus :x. At the prompt, Stats, press I. Confirm your choice by pressing I. displayed press 74 Statistical Operations 13 Programming Programming the HP 30b This chapter applies only to the HP 30b, and explains how to program specifically on the HP 30b. If you are unfamiliar with the basics of programming, you may have trouble understanding some of the following information. Reviewing the material and practicing the concepts illustrated below will help you understand how this feature works on the HP30b. The HP 30b Business Professional is a powerful business calculator, but it may lack a function important to you. The HP 30b programming functions allow you to create up to ten programs to fulfill your needs. In order to keep the calculator keyboard clear and consistent, the programming functions are not written on the keyboard. However, included in the calculator package, you should find an overlay which shows the programming functions. This is designed to be placed on the top surface of the calculator and left in place for the life of the calculator. If you are interested in programming the calculator, you will need to place the overlay on your keyboard before getting started. Key Presses for Program Instructions : followed by E. The instructions specific to programming (illustrated on the overlay) are inserted by pressing : and simultaneously Enter the Program menu by pressing pressing the key with the desired programming instruction. Then release both keys before pressing any additional keys for your program. In the following chapter, this combination is represented in the following manner: (HOLD) This sequence is identical to using the shift key on a computer keyboard to invoke the shiftedfunction. For reference, the table on the following page lists the keys along with their associated programming instructions. Programming 75 Table 13-1 Programming Key Instructions (HOLD) (HOLD) (HOLD) (HOLD) (HOLD) (HOLD) Equal to Not equal to Less than Less than or equal to Greater than or equal to Greater than (HOLD) (HOLD) (HOLD) (HOLD) (HOLD) GOTO GOTO if True GOTO if False Label Stop (HOLD) (HOLD) Display Run/Stop (HOLD) (HOLD) Decrement, Increment, skip if skip if : >or< (HOLD) (HOLD) (HOLD) (HOLD) (HOLD) Debug Call Return Message Solve All programming key combinations listed in the above table require you to press the key and (HOLD) it while simultaneously pressing the desired program instruction. The instructions are described in more detail in the following pages. Almost any function you perform with the calculator can be programmed. A program allows you to repeat an algorithm or sequence of commands without having to retype all the keys each time you want to use that particular function. 76 Programming Programming Example The following programming example, and all examples in this chapter, were written with Chain or Algebraic set as the operating mode. Since a program executes the keys exactly as if you were manually pressing them, the current operating mode affects how the program executes. If you normally operate in RPN, verify your operating mode is set to either Chain or Algebraic before proceeding so you can follow along with the examples below. For more information about setting the operating mode, refer to the section titled, The Mode Menu: Setting Preferences in Chapter 1, Basic Features. 4 3 The volume of a sphere is represented by the equation, --- πr . We will create a program that 3 can calculate the volume of a sphere without having to retype all the keys each time you wish to calculate the volume of a given sphere. Verify your FIX setting is set for three digits to the right of the decimal point. For more information on the FIX setting, refer to the section titled, The Mode Menu: Setting Preferences in Chapter 1, Basic Features. Table 13-2 Keys Display Description :E Enters program mode. The first program is selected. I Starts editing program 0. Note the counter shows your current position in the program. :h3* 4/3* :sI I= :(HOLD) We have entered a program that takes the currently displayed number, raises it to the 3rd power, and multiplies it by 4/3 of PI. The STOP instruction tells the calculator that the program is ending. Note that to enter that special instruction, you need to press and hold the shift key, then press the L key (STOP) before releasing both keys. Programming 77 Keys Display Description Quits program editing mode. Note that program 0 uses 13 bytes and has a checksum of 104. Checksum is a number that verifies the program data is correct. You must be set in FIX 3 or higher to see the full checksum. If your number does not match that shown, verify your FIX setting is set for 3 or higher. If three digits are showing and the number differs from that shown, the program has been keyed in incorrectly. :E Enters the number 5 (the sphere radius) and executes program 0. The result, the volume of the sphere, is 523.6. We press 5== = twice: the first press completes the entry of the 5 (after all, we could have been in the process of entering an equation, such as 5*2). The second press runs the program. Program Step 0 Programs start at step 1, however, if you edit a program by pressing program displayed and press the up key I with the >, you will find there is a step 0. Press any key with step 0 displayed and that key becomes a shortcut for the program. You may also assign any : (HOLD) key combination as well. For example, with the sphere example shown in Table 13-2, after your program has calculated the solution, press :E to open the program menu once again. Prgm 0 is displayed, Figure 1 the program used for the sphere example (Figure 1). Press I, followed by > to :followed by k(assuming you are not interested in using the k key). Exit the program by pressing O, key in a number, 5, and then press :k and you will see the your program was executed with the same results as shown select step 0. Press in the table! 78 Programming :(HOLD) function on that key, the standard function will be executed by pressing the :(HOLD) option of that key. This way If you assign a program to a shift key and there is no you still have the option of using the standard shifted function of the key should you need it. Press O to clear your screen before the next section. Reassigning Menu Functions Often, the best use for a program is to bring a function you use frequently out onto the keyboard. For example, if you use SIN frequently, you may want to have ASIN available directly on the keyboard as well. Having the ability to assign keys permits you to do this easily. Table 13-3 below illustrates how to reassign a menu function to the keyboard. Table 13-3 Reassigning Menu Functions Keys :E >I :sI :(HOLD) < = Display Description Opens Program menu. Scrolls to step 1 of Program 9. Press the keys to enter the steps of the program. Note: to enter the scroll down command as an instruction, you must press and hold : and the < key as shown. :(HOLD) <> :(HOLD) O.5 Scroll to step 0. The ASIN function is now assigned to the SIN key. Exits the program menu, keys in .5, executes the program and returns results for ASIN. :(HOLD) Programming 79 The Program Menu and Program Editing Now that we have been through some short examples, let us look at some of the programming details. The Program menu displays a list of the ten programs that are in the calculator. Use the > < keys to scroll through the program menu. For each program, the number displayed and at the bottom is the memory space used/occupied by the program and a checksum value of that program. For example, program 0 for the sphere uses 13 bytes and has a checksum of 104 (see Figure 2). Figure 2 There are 290 bytes of program space available. :x ) from outside of program To erase all the programs, open the Reset menu (press mode. In the reset menu, select Prgm. The number at the bottom of the display represents the amount of programming steps in use. Press I twice to erase all programs. To erase a specific program, go to the program menu, select the program with the < or > keys, and press :xI to erase that specific program. To execute a program, select the program in the program menu and press =. To edit or modify an existing program, select the program in the program menu and press I: 1. 2. 3. < or > keys. Delete the currently displayed instruction by pressing {. Exit the program by pressing O or :E. Review your program by pressing the 4. Any other key that you press will be inserted as an instruction in the program. >, <,O, or { instruction by pressing : (HOLD) and >, <,O, or {. 5. Insert an Note: you can to a specific label. 80 Programming (HOLD) (HOLD) followed by a label number to go Tests and Jump Functions When creating a program, there is often a need for the conditional execution of an instruction based on a specific condition, as well as the repetition of a set of instructions. This is handled on the HP 30b using the GOTO, LBL (label) and Test instructions. LBL is an instruction that does not do anything by itself, but it acts as a marker for Jump instructions. : and simultaneously press the To enter a label or GOTO instruction, press and hold GOTO, GOTOT, or GOTOF key, then release both keys. 2. Type a number between 00 and 99 (for numbers smaller than 10, you must type the 0 first, such as 03). 1. 3. For example, (HOLD) creates label 03 in your program. You can then use a GOTO 03 instruction to jump to that label from any location in your program to the position of the label. GOTOT (Go To If True) and GOTOF (Go To If False) will only jump if the current displayed number is non-0 (true) for GOTOT or 0 (false) for GOTOF. Used together, these instructions allow you to create programs like the following: 8= LBL 01 DISP 5 - 1= GOTOT 01 STOP Use the following keystrokes to enter the program: (HOLD) 1. 2. (HOLD) (HOLD) 3. 4. (HOLD) . This program has 13 bytes, and the checksum is 234. This program counts from eight to zero displaying each number 1 second. Programming 81 Note: • • • Label numbers must be unique. Only one label with a given number can exist in the calculator. You can jump from one program to another if you know that there is a specific label number in another program. Use the tests ? , ? , ? , ? , ? and ? (the top row of keys) to verify if two numbers are equal, different, and strictly, or not strictly, greater or smaller. These are dual operator-operands and are used in the same way as addition or multiplication ( in Algebraic and Chain modes, number1 ?= number2 =, and in RPN mode, number1 I number2 ?= ) are used, in that they return 0 if false, and 1 if true. Note that in RPN mode, the tests do not remove the arguments from the stack, but do push a 0 or 1. Long Programs and Battery Life Although it is possible to create programs on the HP 30b that can run for a long period of time (calculating PI to 700 decimal places, for example) this is not something that we advise, as it will drain the batteries in less than a day. Programming on the HP 30b was designed to create small programs to perform a function not present in the calculator, or to automate a task requiring many keystrokes and then run relatively quickly. If a program takes more than one second to run, the CPU speed will be reduced in order to preserve battery life. Sub-Function Call It is often useful in a program to have the option to reuse a sub-program from various locations. To avoid having to retype these sub-programs each time they are necessary, you can use the (HOLD) and (HOLD) functions. CALL, followed by a label number, will jump to the specified label, in the same way a GOTO instruction does, but, when the RETURN instruction is encountered, the program will continue execution just after the CALL function. This is equivalent to you temporarily pausing in an activity to answer a phone call, and then returning to your prior activity after the call. Up to four calls can be nested at the same time. Another way to picture this might be going to turn off your stove, while you are answering the doorbell that rang while you were answering your phone, while you were writing an email… it's hard for us, but computers are good at stacking tasks in this way. Enter a call function the same way you enter a GOTO function. 82 Programming Other Programming Functions (HOLD) DISP: takes a number that represents 1/5 of a second. DISP5 is thus one second. (HOLD) STOP: Stops the execution of the program. This instruction should be placed at the end of every program. (HOLD) R/S: Pauses the program execution and returns to the normal system. You can then resume program execution by pressing again. This can be used, for example, when you need to enter a number. (HOLD) DSE ( ) and (HOLD) ISG ( ), followed by 1 digit (0 to 9): Loop control function. Place a number of the form ccccc.eeeii where cccc is the counter, eee is the end value for the counter and ii is the increment in variable 1. For example, DSE 1 will decrement the counter part of the variable by ii (if ii is 0, it decrements by 1) and, if cccc is less or equal to eee, it will skip the next instruction (usually a GOTO). For example, to loop from 0 to 50, incrementing by 3 each loop, use 0.05003 as start the value and the ISG instruction. The following program will loop from 0-50, incrementing by 3 each loop and pause shortly at each loop to show the counter. At the end, it will leave 12 with a blinking cursor. Once in Program mode, select an unused program number and press: .05003:$1 (HOLD) (HOLD) (HOLD) (HOLD) (HOLD) This program has 22 bytes, and the Checksum is 146. Programming 83 Messages The MSG function is used to display messages on screen; it is especially useful when used before halting the program with (HOLD) , as it allows you to display messages on the screen for the user. To enter a message while creating a program: Press :(HOLD) . Release both keys. You can now enter messages. In this mode, you may press > or < to select a character and : (HOLD) > < to jump 10 characters at a time. Once you have found the desired character, press t to validate and move to the next character. Press { to remove the last character. or There are also shortcuts for commonly used characters: • 0-9 selects the corresponding numeric character • . selects ? • = selects = • /*+- are shortcuts for the corresponding mathematical operator signs • } selects space Once the character appears, press t to validate. Press O to exit message entry. If you want to modify a message that has been entered in a program, select the message and press :(HOLD) message mode. As an example using the message mode, let’s return to our sphere calculation program: 1. :EI opens the Program menu, and you are now at step 1 of Program 0. To insert a message at step 1 and push everything else down, simply begin editing at step 1. If you want to delete the current step, press 2. Press 84 Programming :(HOLD) . {. > 3. Press until the letter R appears, and then press screen should display a ?. 4. Press Oto exit. 5. Press : (HOLD) . Then press I. Press . and the Oto exit. 6. Now enter program mode again by pressing :E. The display will show R? in video inverse. Since program 0 has a message as the first command, it is now named R?. The video inverse signifies that it is assigned to a key, in this case 7. k. Press Oto exit. Now press :k. Notice R? appears, and the program pauses to wait for input. 5= Type and press calculates the volume. : (HOLD) to resume. The program continues and Debugging a Program At times, programs do not work as expected. You can debug your programs by pressing the : (HOLD) > or : (HOLD) < keys as follows: Open the Program menu and select the program you want to debug. To execute the first : (HOLD) <. Press this key combination repeatedly to execute your program one instruction at a time. The current instruction is displayed as long as the < instruction, press key is pressed. If you want to see the next instruction without executing it, press : (HOLD) > in the same manner. If you want to let the program continue by itself, press : (HOLD) . If you want to start debugging a program in the middle, place a run/stop (R/S) instruction where you want to start debugging the program, run the program and start debugging using : (HOLD) > or < when the program stops due to the R/S. Programming 85 Saving, Restoring, and Modifying Mode Settings Often, programs are designed to run in a specific mode (for example, FIX 4 or RPN). You can L:u to recall the current mode, save it, modify the settings, either by going in the menu, or using the $:u function and then restoring it. For example: use 1. 2. 3. L:u$1 recalls and stores the current mode settings in Memory 1. :u4IO selects FIX=4. Your program: L1:$:u restores the mode settings to what they were at the beginning of the program. 4. Lu returns a 12 digit number: CactdmrvAOff. See Table 13-4 for a description of each digit. Table 13-4 Digit Description A is “1” for radian mode, “2” for degree mode. a is “1” in Semi-annual mode, “2” in Annual mode. C is “1” in Standard TVM mode, “2” in Canadian TVM mode. c is “1” in Actual day count mode, “2” in 360 day count mode. d is “1” if the decimal separator is “.”, 2 for “,” ff is “00” to “11” or “13” and indicates the FIX setting (13 is for FIX=-1). m is “1” for “mm.ddyyyy” mode, “2” for “dd.mmyyyy” mode. O r is “1” for Chain mode, “2” for Algebraic mode, and “3” for RPN mode. defines the regression line type. “1” for a*x+b, “2” for a*ln(x)+b, “3” for b*e(ax), “4” for b*xa, “5” for b*ax, “6” for a/x+b and “7” for ax2+bx+c. t is “1” if thousands separators are not visible, “2” if they are visible. v is “1” for 2 variable statistics, “2” for 1 variable, and “3” for 1 variable frequency. :$:u, any illegal value is ignored and this setting will not When using change. For example: 314:$:u will switch to RPN mode. No other setting will change. 86 Programming Solve The solve key is not programmable, but it is a powerful addition to the calculator functionality. The solve function utilizes HP Solve, a feature unique to HP calculators, which allows you to find a number for a variable that will cause a program to return a 0. This can be used to solve complex equations. For example, if you want to solve xx-y=0. 1. :E<<I (select and edit program 2) 2. L1:hL1-L2= (HOLD) (enter program var1var1 -var2=) O to exit. Store 3 into variable 2 by pressing 3:$1. Press :E and note that Prgrm 2 is selected, as the calculator displays the program 3. Press that was last edited. For verification, this program has 11 bytes, and the checksum, 199. : 2 4. Press (HOLD) to solve for variable 2. The calculator will attempt to find what value in variable 2 would cause the program to result in 0. In this case, the result is 27. 10:$2 5. Now store 10 into variable 2: . Since Prgrm 2 was the last program selected in the program menu, you can use the SOLVE feature directly. Press :(HOLD) 1 to solve for variable 1, such that the result of the program is 0. The result this time is 2.506184..., since you stored 10 into variable 2. 6. You can verify this is correct by pressing see that 10 is returned. L1:hL1= and Programming 87 88 Programming 14 Error Messages Error Messages and Calculator Status Table 14-1 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: Square root of a negative number. /(x<0) 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. 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. Error Messages 89 Table 14-1 Error Messages Error Message Status 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. 90 Error Messages 15 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. Warranty, Regulatory, and Contact Information 91 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 the following: a. b. c. d. e. improper or inadequate maintenance or calibration software, interfacing, parts or supplies not supplied by HP unauthorized modification or misuse operation outside of the published environmental specifications for the product 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. Regulatory Information Federal Communications Commission Notice This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC Rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference to radio communications. However, there is no guarantee that interference will not occur in a particular installation. If this equipment 92 Warranty, Regulatory, and Contact Information does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, the user is encouraged to try to correct the interference by one or more of the following measures: • Reorient or relocate the receiving antenna. • Increase the separation between the equipment and the receiver. • Connect the equipment into an outlet on a circuit different from that to which the receiver is connected. • Consult the dealer or an experienced radio or television technician for help. Modifications The FCC requires the user to be notified that any changes or modifications made to this device that are not expressly approved by Hewlett-Packard Company may void the user's authority to operate the equipment. Declaration of Conformity for Products Marked with FCC Logo, United States Only This device complies with Part 15 of the FCC Rules. Operation is subject to the following two conditions: 1. This device may not cause harmful interference 2. This device must accept any interference received, including interference that may cause undesired operation. If you have questions about the product that are not related to this declaration, write to Hewlett-Packard Company P. O. Box 692000, Mail Stop 530113 Houston, TX 77269-2000 For questions regarding this FCC declaration, write to Hewlett-Packard Company P. O. Box 692000, Mail Stop 510101 Houston, TX 77269-2000 or call HP at 281-514-3333 To identify your product, refer to the part, series, or model number located on the product. Canadian Notice This Class B digital apparatus meets all requirements of the Canadian Interference-Causing Equipment Regulations. Avis Canadien Cet appareil numérique de la classe B respecte toutes les exigences du Règlement sur le matériel brouilleur du Canada. European Union Regulatory Notice This product complies with the following EU Directives: Warranty, Regulatory, and Contact Information 93 • • 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. This compliance is indicated by the following conformity marking placed on the product: Hewlett-Packard GmbH, HQ-TRE, Herrenberger Strasse 140, 71034 Boeblingen, Germany The official EU CE declaration of conformity for this device may be found at http:// www.hp.com/go/certificates. Japanese Notice Korean Notice Disposal of Waste Equipment by Users in Private Household in the European Union This symbol on the product or on its packaging indicates that this product must not be disposed of with your other household waste. Instead, it is your responsibility to dispose of your waste equipment by handing it over to a designated collection point for the recycling of waste electrical and electronic equipment. The separate collection and recycling of your waste equipment at the time of disposal will help to conserve natural resources and ensure that it is recycled in a manner that protects human health and the environment. For more 94 Warranty, Regulatory, and Contact Information 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. Perchlorate Material - special handling may apply This calculator's Memory Backup battery may contain perchlorate and may require special handling when recycled or disposed in California. Customer Care In addition to the one year hardware warranty your HP calculator also comes with one year of technical support. If you need assistance, 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. A complete list is available on the web at: www.hp.com/support. Contact Information Table 15-1 Contact Information Country/Region Contact Algeria www.hp.com/support Anguila 1-800-711-2884 Antigua 1-800-711-2884 Argentina 0-800-555-5000 Aruba 800-8000 ; 800-711-2884 Austria Österreich 01 360 277 1203 Bahamas 1-800-711-2884 Barbados 1-800-711-2884 Belgique (Français) 02 620 00 85 Belgium (English) 02 620 00 86 Bermuda 1-800-711-2884 Bolivia 800-100-193 Botswana www.hp.com/support Brazil Brasil 0-800-709-7751 British Virgin Islands 1-800-711-2884 Bulgaria www.hp.com/support Canada 800-HP-INVENT Cayman Island 1-800-711-2884 Chile 800-360-999 Warranty, Regulatory, and Contact Information 95 Table 15-1 Contact Information Country/Region Contact China 800-820-9669 中国 Colombia 01-8000-51-4746-8368 (01-8000-51- HP INVENT) Costa Rica 0-800-011-0524 Croatia www.hp.com/support Curacao 001-800-872-2881 + 800-711-2884 Czech Republic Česká republikaik 296 335 612 Denmark 82 33 28 44 Dominica 1-800-711-2884 Dominican Republic 1-800-711-2884 Egypt www.hp.com/support El Salvador 800-6160 Equador 1-999-119 ; 800-711-2884 (Andinatel) 1-800-225-528; 800-711-2884 (Pacifitel) Estonia www.hp.com/support Finland Suomi 09 8171 0281 France 01 4993 9006 French Antilles 0-800-990-011; 800-711-2884 French Guiana 0-800-990-011; 800-711-2884 Germany Deutschland 069 9530 7103 Ghana www.hp.com/support Greece Ελλάδα 210 969 6421 Grenada 1-800-711-2884 Guadelupe 0-800-990-011; 800-711-2884 Guatemala 1-800-999-5105 Guyana 159 ; 800-711-2884 Haiti 183 ; 800-711-2884 Honduras 800-0-123 ; 800-711-2884 Hong Kong 800-933011 香港特別行政區 Hungary www.hp.com/support India 1-800-114772 Indonesia (21)350-3408 Ireland 01 605 0356 Italy Italia 02 754 19 782 96 Warranty, Regulatory, and Contact Information Table 15-1 Contact Information Country/Region Contact Jamaica 1-800-711-2884 Japan 00531-86-0011 日本 Kazakhstan www.hp.com/support Latvia www.hp.com/support Lebanon www.hp.com/support Lithuania www.hp.com/support Luxembourg 2730 2146 Malaysia 1800-88-8588 Martinica 0-800-990-011; 877-219-8671 Mauritius www.hp.com/support Mexico México 01-800-474-68368 (800 HP INVENT) Montenegro www.hp.com/support Montserrat 1-800-711-2884 Morocco www.hp.com/support Namibia www.hp.com/support Netherlands 020 654 5301 Netherland Antilles 001-800-872-2881 ; 800-711-2884 New Zealand 0800-551-664 Nicaragua 1-800-0164; 800-711-2884 Norway Norwegen 23500027 Panama Panamá 001-800-711-2884 Paraguay (009) 800-541-0006 Peru Perú 0-800-10111 Philippines (2)-867-3351 Poland Polska www.hp.com/support Portugal 021 318 0093 Puerto Rico 1-877 232 0589 Romania www.hp.com/support Russia Россия 495-228-3050 Saudi Arabia www.hp.com/support Warranty, Regulatory, and Contact Information 97 Table 15-1 Contact Information Country/Region Contact Serbia www.hp.com/support Singapore 6272-5300 Slovakia www.hp.com/support South Africa 0800980410 South Korea 00798-862-0305 한국 Spain España 913753382 St Kitts & Nevis 1-800-711-2884 St Lucia 1-800-478-4602 St Marteen 1-800-711-2884 St Vincent 01-800-711-2884 Suriname 156 ; 800-711-2884 Swaziland www.hp.com/support Sweden Sverige 08 5199 2065 Switzerland 022 827 8780 Switzerland (Suisse Français) 022 827 8780 Switzerland (Schweiz Deutsch) 01 439 5358 Switzerland (Svizzeera Italiano) 022 567 5308 Taiwan 00801-86-1047 臺灣 Thailand (2)-353-9000 ไทย Trinidad & Tobago 1-800-711-2884 Tunisia www.hp.com/support Turkey Türkiye www.hp.com/support Turks & Caicos 01-800-711-2884 UAE www.hp.com/support United Kingdom 0207 458 0161 Uruguay 0004-054-177 US Virgin Islands 1-800-711-2884 United States 800-HP INVENT Venezuela 0-800-474-68368 (0-800 HP INVENT) 98 Warranty, Regulatory, and Contact Information Table 15-1 Contact Information Country/Region Contact Vietnam Viêt Nam +65-6272-5300 Zambia www.hp.com/support Warranty, Regulatory, and Contact Information 99 100 Warranty, Regulatory, and Contact Information Symbols A Algebraic mode 12 Amortization 29 Amortization menu 29 creating a schedule 31 menu and menu items 30 resetting menu to defaults 32 Angular mode degrees or radians 3 Annunciators 6 B Battery low battery symbol 1 replacing the batteries 91 Black-Scholes Black-Scholes menu 52 call price 53 dividend 53 example 54 put price 53 resetting menu items to defaults 56 risk-free interest rate 53 signature return 53 Stock price 53 strike price 53 time to maturity 53 Bond accrued interest 48 Bond menu 48 calendars 48 call 48 coupon rate 48 example 49 maturity date 48 price 48 resetting menu to defaults 50 settlement date 48 yield 48 Bond annual, semiannual 48 Bond type Annual, Semiannual 4 Break-even Break-even menu 59 example 59 resetting menu items to defaults 60 Business problems see Percent Calculation menu 61 C Calculation mode Chain, Algebraic, RPN, setting preferences 3 changing the 4 1 Calendar setting, Actual or Cal. 360 4 cash 38 Cash flow analyzing with IRR and NPV 41 diagram, description of 27 editing 41 erasing lists and resetting to defaults 38 example 38 IRR and NPV menu items 41 keys used 38 lists 37 sample cash flow diagrams 46 Chain mode 12 checksum 78 Combinations 21 D Date calculation example 57 Date Calculation menu 57 resetting menu items to defaults 58 setting format for 3 debugging 85 Decimal comma or point, setting preferences 3 Default settings see Mode menu 2 Depreciation cost 67 Declining balance 66 Declining balance crossover 66 Depreciation menu 66 example 67 factor 67 French amortization 66 French Straight line 66 life 67 methods 66 remaining book value 67 remaining depreciable value 67 resetting items to defaults 68 salvage 67 start 67 Straight line 66 Sum-of-the-years’ digits 66 values required 66 year 67 Discounted payback 41 Display contrast 2 degree or radian 3 precision and number format 3 two line 1 2 E Error messages 89 F FMRR 41 I example 44 Insert and delete keys 38 Interest Conversion Interest Conversion menu 33 resetting the menu to defaults 34 using P/YR and C/YR 33 Internal rate of return 41 Investment Rate 41 K Key ANS, last operation, last number 19 change sign 11 cosine 19 equals 6 factorial 19 input key 6 insert and delete 38 LN, natural log 19 natural exponent 19 On/CE 7 parentheses 12 presses 4 random function 19 recall 24 reciprocal 19 round 19 scientific notation 11 secondary functions 4 shift key 4 sine 19 square 19 square root 19 store 24 tangent 19 up and down scroll keys 2 key instructions 76 key presses 75 Keyboard map and legend v L Language M selecting a 1 Margin See Percent Calculation menu 61 Markup See Percent Calculation menu 61 3 Math Math menu 18 Menu Black-Scholes menu 51 Bond menu 47 Break-even menu 59 Data menu 70 Date Calculation menu 57 Depreciation menu 65 Math menu 19 Mode menu, setting preferences and number format 2 NPV and IRR menus 41 Percent Calculation menu 61 Reset menu 7 Statistics menu 70 Time Value of Money keys 27 messages 84 MIRR 41 example 44 mode settings 86 N Net Future Value 41 Net Present Value 41 Net US 41 Number entry 11 last number function 14 rounding 25 storing and recalling 24 Number format O setting preferences 2 on HP 30b 75 P Parentheses prioritizing operations 12 Payback 41 Percent Calculation compounding periods 63 examples 62 markup and margin 61 Percent Calculation menu 61 percentage of total 61 resetting menu items to defaults 64 sub-menus 61 Percentages 25 Permutations 23 PI location of, entering for calculations. See also, Math menu 21 Probability Sub-menu see also, Math menu 21 program step 0 78 4 Programming 75, 76, 78, 79, 83, 84, 85, 86 Decrement, skip 83 display 83 editing programs 80 erasing 80 example 77 executing 80 Program menu 75 R/S pause and return 83 solve 87 sub-function call 82 test and jump 81 R reassigning menu functions 79 Recall number 24 Reverse Polish Notation see RPN 13 RPN description of 13 example 15 manipulating the stack 15 roll down 17 stack 13 swap 18 S Safe interest rate 41 saving, storing, modifying 86 Scientific notation 11 Statistics a slope for linear model 71 b y-intercept for linear model 71 covariance 71 data entry, sub-menus 70 example 72 maximum and minimum 71 median 71 number of items 70 one-variable 70 population standard deviation for X and Y 71 predictions for X and Y 71 quartile 71 resetting items to defaults 74 sample error for X and Y 71 standard deviation, X and Y 70 Statistics menu 69 two-variable 70 X mean 70 Y mean 70 stop 83 Store numbers 24 5 T Thousands separator 3 Time Value of Money see TVM 27 TVM begin mode 28 Canadian Mortgage example 35 end mode 28 example 28 future value 28 keys 28 nominal interest rate 28 number of payments 28 number of payments per year 28 periodic payment value 28 present value 28 setting for TVM Standard or TVM Canada 4 storing and recalling with TVM keys 24 storing values in TVM variables 28 TVM Canada, Canadian mortgages 35 6

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