HP 17bII+ Financial Calculator Owner’s Manual Edition 1 Part Number F2234-90020 File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11
Notice For warranty and regulatory information for this calculator, see the owner’s manual. This manual and any examples contained herein are provided “as is” and are subject to change without notice. Hewlett-Packard Company makes no warranty of any kind with regard to this manual, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose. Hewlett-Packard Co.
Welcome to the HP 17bII+ The HP 17bII+ is part of Hewlett-Packard’s new generation of calculators: ! The two-line display has space for messages, prompts, and labels. ! Menus and messages show you options and guide you through problems. ! Built-in applications solve these business and financial tasks: ! Time Value of Money. For loans, savings, leasing, and amortization. ! Interest Conversions. Between nominal and effective rates. ! Cash Flows.
Contents 1 13 16 List of Examples Important Information 17 17 17 18 18 19 19 21 22 22 23 25 27 28 28 29 30 Getting Started Power On and Off; Continuous Memory Adjusting the Display Contrast Setting the Language What You See in the Display The Shift Key (@) Backspacing and Clearing Doing Arithmetic Keying in Negative Numbers (&) Using the Menu Keys The MAIN Menu Choosing Menus and Reading Menu Maps Calculations Using Menus Exiting Menus (e) Clearing Values in Menus Solving Your Own Equations (SOLVE) Typ
36 36 37 Error Messages Modes Calculator Memory (@M) 2 38 38 38 40 40 40 41 42 43 43 44 45 46 47 48 Arithmetic The Calculator Line Doing Calculations Using Parentheses in Calculations The Percent Key The Mathematical Functions The Power Function (Exponentiation) The MATH Menu Saving and Reusing Numbers The History Stack of Numbers Reusing the Last Result (@L) Storing and Recalling Numbers Doing Arithmetic Inside Registers and Variables Scientific Notation Range of Numbers 3 49 50 50 50 51 52 52 53 Pe
59 59 60 Converting between Two Currencies Storing and Recalling Sets of Currencies Clearing the Currency Variables 5 61 61 64 66 67 71 74 77 78 81 Time Value of Money The TVM Menu Cash Flow Diagrams and Signs of Numbers Using the TVM Menu Loan Calculations Savings Calculations Leasing Calculations Amortization (AMRT) Displaying an Amortization Schedule Printing an Amortization Table 6 84 85 85 87 Interest Rate Conversions The ICNV Menu Converting Interest Rates Compounding Periods Different from Pay
8 108 108 110 Bonds The BOND Menu Doing Bond Calculations 9 114 114 116 116 118 119 Depreciation The DEPRC Menu Doing Depreciation Calculations DB, SOYD, and SL Methods The ACRS Method Partial-Year Depreciation 10 121 122 123 123 124 126 126 127 127 127 128 130 133 138 139 140 Running Total and Statistics The SUM Menu Creating a SUM List Entering Numbers and Viewing the TOTAL Viewing and Correcting the List Copying a Number from a List to the Calculator Line Naming and Renaming a SUM List Starting o
12 142 143 144 144 145 145 147 148 148 149 150 150 151 The Time Menu Setting the Time and Date (SET) Changing the Time and Date Formats (SET) Adjusting the Clock Setting (ADJST) Appointments (APPT) Viewing or Setting an Appointment (APT1-APT10) Acknowledging an Appointment Unacknowledged Appointments Clearing Appointments Date Arithmetic (CALC) Determining the Day of the Week for Any Date Calculating the Number of Days between Dates Calculating Past or Future Dates 153 153 156 157 158 161 161 162 162 162
179 180 181 How the Solver Works Halting and Restarting the Numerical Search Entering Guesses 13 184 185 185 185 186 186 188 188 189 Printing The Printer’s Power Source Double-Space Printing Printing the Display(P) Printing Other Information (@p) Printing Variables, Lists, and Appointments (LIST) Printing Descriptive Messages (MSG) Trace Printing (TRACE) How to Interrupt the Printer 14 190 190 190 191 193 195 197 199 200 200 202 206 208 209 213 215 216 217 217 219 Additional Examples Loans Simple Ann
A 222 222 222 224 224 225 227 228 230 231 231 231 232 233 235 236 237 Assistance, Batteries, Memory, and Service Obtaining Help in Operating the Calculator Answers to Common Questions Power and Batteries Low-Power Indications Installing Batteries Managing Calculator Memory Resetting the Calculator Erasing Continuous Memory Clock Accuracy Environmental Limits Determining If the Calculator Requires Service Confirming Calculator Operation: Self-Test Warranty Service Regulatory information Noise Declaration
248 215 250 251 251 252 252 253 253 253 Cash-Flow Calculations Bond Calculations Depreciation Calculations Sum and Statistics Forecasting Equations Used in (Chapter 14) Canadian Mortgages Odd-Period Calculations Advance Payments Modified Internal Rate of Return C 254 Menu Maps D 261 261 261 262 263 264 264 264 266 266 RPN: Summary About RPN About RPN on the HP 17bII+ Setting RPN Mode Where the RPN Functions Are Doing Calculations in RPN Arithmetic Topics Affected by RPN Mode Simple Arithmetic Calcula
F 12 273 274 275 Reusing Numbers Chain Calculations Exercises 276 RPN: Selected Examples 283 Error Messages 289 Index Contents File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11
List of Examples The following list groups the examples by category.
72 74 75 80 82 172 191 193 194 196 197 198 200 200 202 207 208 214 86 89 97 102 104 105 210 14 An Individual Retirement Account Calculating a Lease Payment Present Value of a Lease with Advanced Payments and Option to Buy Displaying an Amortization Schedule for a Home Mortgage Printing an Amortization Schedule Calculations for a Loan with an Odd First Period Discounted Mortgage APR for a Loan with Fees (RPN example on page 276) Loan from the Lender’s Point of View (RPN example on page 277) Loan with an
111 112 113 215 217 Bonds and Notes Price and Yield of a Bond A Bond with a Call Feature A Zero-Coupon Bond Yield to Maturity and Yield to Call Price and Yield of a Discounted Note 117 118 120 Depreciation Declining-Balance Depreciation ACRS Deductions Partial-Year Depreciation 125 128 134 138 218 220 Running Total and Statistical Calculations Updating a Checkbook Mean, Median, and Standard Deviation Curve Fitting Weighted Mean A Moving Average in Manufacturing 2 Expected Throws of a Die ( χ ) 144 148
Important Information ! Take the time to read chapter 1. It gives you an overview of how the calculator works, and introduces terms and concepts that are used throughout the manual. After reading chapter 1, you’ll be ready to start using all of the calculator’s features. ! You can choose either ALG (Algebraic) or RPN (Reverse Polish Notation) mode for your calculations. Throughout the manual, the “v “in the margin indicates that the examples or keystrokes must be performed differently in RPN.
1 Getting Started v Watch for this symbol in the margin. It identifies examples or keystrokes that are shown in ALG mode and must be performed differently in RPN mode. Appendixes D, E, and F explain how to use your calculator in RPN mode. The mode affects only arithmetic calculations ― all other operations, including the Solver, work the same in RPN and ALG modes. Power On and Off; Continuous Memory To turn on the calculator, press C (clear) (note ON printed below the key).
Setting the Language The calculator can display information in six different languages. The language initially used by the calculator was preset at the factory. To change the language: 1. Press the @ >. 2. Press ! to display the INTL menu, which stands for "international". 3. Press the appropriate menu key to change the language. Table 1-1. Keys for language Key Description "# German $# English %# Spanish &# French '! Italian (# Portuguese What You See in the Display Menu Labels.
Shift (@ ) is active. (page 19) Sending information Alarm going off (or past due). to the printer. (page 147) (page 184) Batteries low. (page 224) Annunciators Calculator line Cursor Menu labels for the MAIN menu. To display the MAIN menu, press @A (that is, first @ , then e). The Shift Key (@) Some keys have a second, shifted function printed in color above the key. The colored shift key accesses these operations. For example, pressing and releasing @ , then pressing C turns the calculator off.
Table 1-2. Keys for Clearing Key Description < C Backspace; erases the character before the cursor. @c This clears all information in the current work area (menu). For example, it will erase all the numbers in a list if you are currently viewing a list (SUM or CFLO). In other menus (like TVM), @c clears all of the values that have been stored. In SOLVE, it can delete all equations. Clear; clears the calculator line.
Doing Arithmetic v The “ ” in the margin is a reminder that the example keystrokes are for ALG mode. This is a brief introduction to doing arithmetic. More information on arithmetic is in chapter 2. Remember that you can erase errors by pressing < or C. To calculate 21.1 ＋ 23.8: Keys: Display: Description: 21.1 + 23.8 $#&#()" $#&#()$%&*" = ++&,(" = completes calculation. Once a calculation has been completed, pressing another digit key starts a new calculation.
65 +( 12 / " 3.5 )= '*&+%" Use parentheses to impose an order of calculation. Keying in Negative Numbers (&) The & key changes the sign of a number. ! To key in a negative number, type that number, then press &. ! To change the sign of an already displayed number (it must be the rightmost number), press &. v Keys: Display: Description: 75 & * 7.1 = /-." Changes the sign of 75. /.%$&.(" Multiplies －75 by 7.1.
(( )) Menu Labels Menu Keys The top row of keys is related to the labels along the bottom of the display. The labels tell you what the keys do. The six keys are called menu keys; the labels are called menu labels. The MAIN Menu The MAIN menu is a set of primary choices leading to other menu options. No matter which menu you currently see, pressing @A redisplays the MAIN menu. The menu structure is hierarchical.
Table 1-3. The MAIN Menu Menu Label Operations Done in This Category " # TVM: Time value of money: (Finance) ## (Business Percentages) $! (Statistics) %# (Time Manager) &! (Equation Solver) '! (Currency Exchange) 24 Covered in: Chapter 5 loans, savings, leasing, amortization. ICNV: Interest conversions. Chapter 6 CFLO: Lists of cash flows for internal rate of return and net present value. Chapter 7 BOND: Yields and prices for bonds.
Choosing Menus and Reading Menu Maps Below is a menu map illustrating one possible path through three levels of menus: from the MAIN menu to the BUS menu to the MU%C (markup as a percent of cost) menu. There are no menus that branch from the MU%C menu because the MU%C menu is a final destination―you use it to do calculations, rather than to choose another menu.
index and examine the menu maps in appendix C. Displaying the MU%C menu: Step 2. To display the MAIN menu, press @A. This step lets you start from a known location on the menu map. Step 3. Press # to display the BUS menu. Step 4. Press ( to display the MU%C menu. Using the MU%C menu: Step 5. Key in the cost and press ) to store 4.10 as the COST. Step 6. Key in the price and press * to store 4.60 as the PRICE. Step 7. Press + to calculate the markup as a percent of cost.
Calculations Using Menus Using menus to do calculations is easy. You don’t have to remember in what order to enter numbers and in what order results come back. Instead, the menus guide you, as in the previous example. All the keys you need are together in the top row. The menu keys both store numbers for the calculations and start the calculations. The MU%C menu can calculate M%C, the percent markup on cost, given COST and PRICE. Keys: Display: Keys: Display: 4.60 4.10 Store 4.60 Store 4.
Many menus in this calculator work like the example above. The rules for using variables are: ! To store a value, key in the number and press the menu key.∗† Arithmetic calculations, as well as single values, can be stored. ! To calculate a value, press the menu key without first keying in a number. The calculator displays 7197491:;<=> when a value is being calculated. ! To verify a stored value, press R (recall) followed by the menu key. For example, R ) displays the value stored in COST.
! If the current menu has a list (SUM, CFLO, or Solver), pressing @c clears the values in the list. To see what value is currently stored in a variable, press R menu label. Solving Your Own Equations (SOLVE) This chapter has introduced some of the built-in menus the calculator offers. But if the solution to a problem is not built into HP 17bII+, you can turn to the most versatile feature of all: the Equation Solver. Here you define your own solution in terms of an equation.
Typing Words and Characters: the ALPHAbetic Menu The ALPHAbetic menu is automatically displayed when you need it to type letters and characters. The ALPHA menu also includes characters not found on the keyboard: ! Uppercase letters. ! Space. ! Punctuation and special characters. ! Non-English letters. ABCDE FGHI F G H : < > # & I JKLM NOPQ space OTHER $ , ! @ .
Keys Characters @A " &/ " 01 5" 2.34 5?" 25,6 5?@A" *78* 2 9 /9= 5?@AB9B" 5?@AB9BCD,8" ,:0; 5?@AB9BCD,87E" <=<> 5?@AB9BCD,87EF:" I 5?@AB9BCD,87EF:" Note that the ? is just a character, part of the variable’s name. It is not an operator, which ÷ is. Editing ALPHAbetic Text The companion to the ALPHA menu is the ALPHA-Edit menu. To display the ALPHA-Edit menu, press * in the SOLVE menu (or press e in the ALPHA menu).
Table 1-4. Alphabetic Editing Operation Label or Key to Press ALPHA-Edit Menu Inserts character before the cursor. Any character. Deletes character at the cursor. ?! Moves the cursor far left, one display-width. @ Moves the cursor left. A Moves the cursor right. B Moves the cursor far right, one display-width. C Displays the ALPHA menu again. D Keyboard Backspaces and erases the character before the cursor. < Clears the calculator line.
Calculate the cost of carpet needed to cover a 9’ by 12’ room. The carpet costs $22.50 per square yard. Starting from the MAIN menu (press @A): Keys: Display: Description: & 5?@AB9BCD,87EF:" Displays the SOLVE menu and the current equation.* " E Displays the customized menu for carpeting. 22.5 " 5?@A 5?@A8$$&.(" Stores the price per square yard in P/YD. 12 8 98#$&((" Stores the length in L. 99 C8,&((" Stores the width in W. ) 7EF:8$-(&((" Calculates the cost to cover a 9’ x 12’ room.
Controlling the Display Format The DSP menu (press D) gives you options for formatting numbers. You can pick the number of decimal places to be displayed, and whether to use a comma or a period to “punctuate” your numbers. Decimal Places To change the number of displayed decimal places, first press the D key. Then either: ! Press + , type the number of decimal places you want (from 0 to 11), and press I; or ! Press , to see a number as precisely as possible at any time (12 digits maximum).
Rounding a Number The @r function rounds the number in the calculator line to the number of displayed decimal places. Subsequent calculations use the rounded value. Starting with two displayed decimal places: Keys: Display: Description: 5.787 .&-*-!" D+ 4I D, " Four decimal places are .&-*-(" displayed. .&-*-" All significant digits; trailing zeros dropped. D+ 2I @S " Two decimal places are .&-," displayed. G499 52H7;F;E< ;FI"Temporarily shows full .&-*-" (hold) @r @S (hold) precision.
Error Messages Sometimes the calculator cannot do what you “ask”, such as when you press the wrong key or forget a number for a calculation. To help you correct the situation, the calculator beeps and displays a message. ! Press C or < to clear the error message. ! Press any other key to clear the message and perform that key’s function. For more explanations, refer to the list of error messages just before the subject index. Modes Beeper.
Language. Press @> ! to change the language. Calculator Memory (@M) The calculator stores many different types of information in its memory. Each piece of information requires a certain amount of storage space.* You can monitor the amount of available memory by pressing @M. Number of bytes of memory still free Percentage of total memory still free The amount of memory available for storing information and working problems is about 30,740 bytes. (Units of memory space are called bytes.
2 Arithmetic If you prefer RPN to algebraic logic, please read appendix D before you read this chapter. The “ v “ in the margin is a reminder that the example keystrokes are for ALG mode. The Calculator Line v The calculator line is the part of the display where numbers appear and calculations take place. Sometimes this line includes labels for results, such as :E:198#$+&'(. Even in this case you can use the number for a calculation. For example, pressing + 2 = would calculate 124.
In the second case, the / key acts like the = key by displaying the result of 750 x 12. Here’s a longer chain calculation. 456 - 75 68 × 18.5 1.9 This calculation can be written as: 456 − 75 ÷ 18.5 x 68 ÷ 1.9. Watch what happens in the display as you key it in: Keys: Display: 456 - 75 / 18.5 * %*#&((D" 68 / 1.9 = #K+((&+%D" $(&.,B" -%-&(-" vUsing Parentheses in Calculations Use parentheses when you want to postpone calculating an intermediate result until you’ve entered more numbers.
Note that you must include a * for multiplication; parentheses do not imply multiplication. v The Percent Key The% key has two functions: Finding a Percentage. In most cases, % divides a number by 100. The one exception is when a plus or minus sign precedes the number. (See “Adding or Subtracting a Percentage,” below.) For instance, 25 % results in (&$.. To find 25% of 200, press: 200 * 25 % =. (Result is .(&((.) Adding or Subtracting a Percentage.
Table 2-1. Shifted Math Functions Key Description @t reciprocal @v square root @w square Keys: Display: Description: 4 @t 20 @v (&$." Reciprocal of 4. +&+-" Calculates .#&'-B" Calculates 4.47 + 47.20. .#&'-B#&$#" Calculates 1.12. '$&.$" Completes calculation of + 47.2 * v1.1 v @w v= 20 . (4.47 + 47.2) x1.12. vThe Power Function (Exponentiation) The power function, u, raises the preceding number to the power of the following number. Keys: Display: 125 @u 3 = #K,.%K#$.
The MATH Menu To display the MATH menu, press @m (the shifted % key). Like the other mathematics functions, these functions operate on only the last number in the display. Table 2-2. The MATH Menu Labels Menu Label Description Common (base 10) logarithm of a positive number. H! Common (base 10) antilogarithm; calculates 10x. 2# 3 Natural (base e) logarithm of a positive number. Natural antilogarithm; calculates ex. I! 4 Factorial. 5 Inserts the value for π into the display.
Saving and Reusing Numbers Sometimes you might want to include the result of a previous calculation in a new calculation. There are several ways to reuse numbers. The History Stack of Numbers When you start a new operation, the previous result moves out of the display but is still accessible. Up to four lines of numbers are saved: one in the display and three hidden. These lines make up the history stack. "Invisible" numbers remaining from previous results.
Pressing @c clears the history stack. Be careful if a menu is active, because then c also erases the data associated with that menu. vKeys: Display: Description: 75.55 - 32.63 " +$&,$" = 150 / 7 = 42.92 moves out of $#&+%" display. Now, suppose you want to multiply 42.92 x 11. Using the history stack saves you time. +$&,$" ] Moves 42.92 back to calculator line.
An equivalent keystroke sequence for this problem would be: 39 + 8 / (123 + 17 ) @v = Storing and Recalling Numbers The s key copies a number from the calculator line into a designated storage area, called a storage register. There are ten storage registers in calculator memory, numbered 0 through 9. The R key recalls stored numbers back to the calculator line. lf there is more than one number on the calculator line, s stores only vthe last number in the display. To store or recall a number: 1.
v The s and R keys can also be used with variables. For example, s + (in the MU%C menu) stores the rightmost number from the display into the variable M%C. R + copies the contents of M%C into the calculator line. If there is an expression in the display (such as $)+!), then the recalled number replaces only the last number. You do not need to clear storage registers before using them. By storing a number into a register, you overwrite whatever existed there before.
You can also do arithmetic with the values stored in variables. For example, 2 s* + (in the MU%C menu) multiplies the current contents of M%C by 2 and stores the product in M%C. Scientific Notation Scientific notation is useful when working with very large or very small numbers. Scientific notation shows a small number (less than 10) times 10 raised to a power. For example, the 1984 Gross National Product of the United States was $3,662,800,000,000. In scientific notation, this is 3.6628 x1012.
Range of Numbers The largest positive and negative numbers available on the calculator are ±9.99999999999 x 10 499; the smallest positive and negative numbers available are ±1 x 10 –499.
3 Percentage Calculations in Business The business percentages (BUS) menu is used to solve four types of problems. Each type of problem has its own menu. FIN BUS %CHG %TOTL SUM MU%C TIME SOLVE CURRX MU%P Table 3-1. The Business Percentages (BUS) Menus Menu Description Percent change (J) The difference between two numbers (OLD and NEW), expressed as a percentage (%CH) of OLD. Percent of total (K) The portion that one number (PART) is of another (TOTAL), expressed as a percentage (%T).
The calculator retains the values of the BUS variables until you clear them by pressing @c. For example, pressing @c while in the %CHG menu clears OLD, NEW, and %CH. To see what value is currently stored in a variable, press R menu label. This shows you the value without recalculating it. Using the BUS Menus Each of the four BUS menus has three variables. You can calculate any one of the three variables if you know the other two. 1.
90000 M E9A8,(K(((&((" Stores 90,000 in OLD. 95000 /
Markup as a Percent of Cost (MU%C) Example. The standard markup on costume jewelry at Balkis’s Boutique is 60%. The boutique just received a shipment of chokers costing $19.00 each. What is the retail price per choker? Keys: Display: Description: #( " Displays MU%C menu. 19 ) 7EF:8#,&((" Stores cost in COST. 60 + 012345678'(&((" Stores 60% in M%C. * 52;7H8%(&+(" Calculates price. Markup as a Percent of Price (MU%P) Example.
Sharing Variables Between Menus If you compare the MU%C menu and the MU%P menus, you’ll see that they have two menu labels in common –– ) and *. %CHG %TOTL MU%C COST PRICE MU%P M%C COST PRICE M%P Shared variables The calculator keeps track of the values you key in according to those labels. For example, if you key in COST and PRICE in the MU%C menu, exit to the BUS menu, and then display the MU%P menu, the calculator retains those values.
4 Currency Exchange Calculations The CURRX menu does currency exchange calculations between two currencies using an exchange rate that you calculate or store. The CURRX Menu FIN BUS SUM TIME SOLVE US$ EUR CURRX RATE C.STO C.RCL SELCT To display the currency exchange menu from the MAIN menu, press '. Currency #1 is US$ (U.
Table 4–1. The CURRX Menu Menu Key Description Curr1 Current currency#1;stores or calculates the number of units of this currency Curr2 Currency currency#2;stores or calculates the number of units of this currency Stores or calculates the exchange rate between the two 7# current currencies. The rate is expressed as the number of units of currency #2 equivalent to 1 unit of currency #1. 8 Stores the current currency #1, currency #2, and RATE.
Table 4–2.
Entering a Rate The following two examples illustrate the two ways to enter an exchange rate. Example: Calculating an Exchange Rate. You have just flown from Canada to United States, and you need to exchange your Canadian Dollars for U.S Dollars. The conversion chart looks this : United States Conversion Chart (in US$) Currency Euro (EUR€) Canadian (CAN$) Hong Kong (HK$) Rate 1.0842 .6584 .1282 The chart states these equivalencies: * 1 EUR€ is equivalent to 1.0842 US$ 1 CAN$ is equivalent to 0.
0.6584 ; 4FN8(&''" Stores equivalent number of US$ 7 21:H8(&''" Calculates the RATE. Part 2: The following keystrokes show that you can reverse the order in which the two currencies are selected. Keys: Display: Description: :; FH9H7: 7422H<7@ $" Select US$ as currency #1 = H<:H2 1 21:H" Select CAN$ as currency #2 1= 71
Converting Between Two Currencies Once the currencies are selected and a RATE has been entered, you can convert any number of units of one currency to the other. Example : Converting between Hong Kong and U.S Dollars. Part 1: Use the exchange rate stored in the previous example to calculate how many U.S dollars you would receive for 3,000 Hong Kong Dollars.
Recalling Sets of Currencies. To recall a stored set of currencies and their exchange rate, press 9 , followed by the appropriate menu key. The HP 17bII+ automatically returns to the CURRX menu. The equivalency message and menu labels show the recalled currencies and RATE. Clearing the Currency Variables Pressing @c while the CURRX menu is displayed sets the RATE to 1.0000. The values of the two current currencies are cleared to 0.
5 Time Value of Money The phrase time value of money describes calculations based on money earning interest over a period of time. The TVM menu performs compound-interest calculations and calculates (and prints) amortization schedules. ! In compound interest calculations, interest is added to the principal at specified compounding periods, thereby also earning interest. Savings accounts, mortgages, and leases are compound-interest calculations.
The time value of money (TVM) menu does many compound-interest calculations. Specifically, you can use the TVM menu for a series of cash flows (money received or money paid) when: ! The dollar amount is the same for each payment.* ! The payments occur at regular intervals. ! The payment periods coincide with the compounding periods. 12 payments (or periods) per year Payment mode: the end of each period To second level of TVM Figure 5-1.
Table 5-1. TVM Menu Labels Menu Label Description First Level Stores (or calculates) the total number of payments or S! compounding periods.*† (For a 30-year loan with @T U V W X monthly payments, N＝12 x 30＝360.) Shortcut for N: Multiplies the number in the display by P/YR, and stores the result in N. (If P/YR were 12, then 30 @ T would set N＝360.) Stores (or calculates) the nominal annual interest rate as a percentage.
Table 5-1. TVM Menu Labels (Continued) Menu Label Description Second Level (Continued) Sets Begin mode: payments occur at the beginning of Z! each period. Typical for savings plans and leasing. (The Begin and End modes do not matter if PMT＝0.) [ Sets End mode: payments occur at the end of each period. Typical for loans and investments. \ Accesses the amortization menu. See page 78. The calculator retains the values of the TVM variables until you clear them by pressing @c.
(receipts) as positive. Perform a calculation from the point of view of either the lender (investor) or the borrower, but not both! (Loan) Money received is a positive number Equal periods 1 2 Money paid out is a negative number 3 4 5 PMT Equal payments (FV is Future Value, if any; e.g. a balloon payment) Figure 5-3. A Cash Flow Diagram for a Loan from Borrower’s Point of View (End Mode) 1 2 3 4 5 Loan Figure 5-4.
Payments occur at either the beginning of each period or the end of each period. End mode is shown in the last two figures; Begin mode is shown in the next figure. Capitalized value of lease 1 2 3 4 5 Figure 5-5. Lease Payments Made at the Beginning of Each Period (Begin Mode) Using the TVM Menu First draw a cash-flow diagram to match your problem. Then: 1. From the MAIN menu, press " ]. 2.
4. Store the values you know. (Enter each number and press its menu key.) 5. To calculate a value, press the appropriate menu key. You must give every variable―except the one you will calculate―a value, even if that value is zero. For example, FV must be set to zero when you are calculating the periodic payment (PMT) required to fully pay back a loan. There are two ways to set values to zero: ! Before storing any TVM values, press @c to clear the previous TVM values.
Keys: Display: Description: "] " Displays TVM menu. @c #$ 5?@2 H
? 0 11.5 30 X 12 12; End mode 1 2 359 360 _630 Keys: Display: " "]! @c Description: Display TVM menu. #$ 5?@2 H
75 ,250 13.8 4 X 12 12; End mode 1 2 47 48 Balloon. The problem is done in two steps: 1. Calculate the monthly payment without the balloon (FV=0). 2. Calculate the balloon payment after 4 years. Keys: Display: Description: "] " Display TVM menu. @c #$ 5?@2 H
Step 2. Calculate the balloon payment after 4 years. 894.33 & " Stores rounded PMT value W 50:8/*,+&%%" for exact payment amount (no fractional cents).* 4@T <8+*&((" Figures and stores number of payments in 4 years. 5O8/-%K+(*&*#" X Calculates balloon payment after four years. This amount plus last monthly payment repays the loan. Savings Calculations Example: A Savings Account. You deposit $2,000 into a savings account that pays 7.2% annual interest, compounded annually.
Keys: Display: Description: "] " Displays TVM menu. @c #$ 5?@2 H
4/15/2003 8.3 2 X 12; End mode 15 X 12X 2 1 2 359 360 4/15/2018 _80 _ 2,000 Keys: Display: Description: "] " Displays TVM menu. It is not necessary to clear data because you do not need to set any of the values to zero. . 24 Y [e " Sets 24 payment periods " per year. End mode. 15 @ T <8%'(&((" $+ 5?@2 H
Leasing Calculations Two common leasing calculations are 1) finding the lease payment necessary to achieve a specified yield, and 2) finding the present value (capitalized value) of a lease. Leasing calculations typically use “advance payments”. For the calculator, this means Begin mode because all payments will be made at the beginning of the period. If there are two payments in advance, then one payment must be combined with the present value.
14 U ;6@28#+&((" Stores annual interest rate. 13500 & " Stores car’s value in PV. V 5O8/#%K.((&((" (Money paid out by lessor.) 7500 X GO8-K.((&((" Stores purchase option value in FV. (Money received by lessor.) 50:8$*,&#," W Calculates monthly payment received. Example: Present Value of a Lease with Advance Payments and Option to Buy. Your company is leasing a machine for 4 years. Monthly payments are $2,400 with two payments in advance.
Keys: Display: Description: "] " Displays TVM menu. @c #$ 5?@2 H
5O8-K%+(&+%" V Calculates present value of the buy option. Step 4: Add the results of step 2 and 3. v+R 0 = ,#K+-'&((" Calculates present, capitalized value of lease. Amortization (AMRT) The AMRT menu (press ] . \ ) displays or prints the following values: ! The loan balance after the payment(s) are made. ! The amount of the payment(s) applied toward interest. ! The amount of the payment(s) applied toward principal.
Table 5-2. AMRT Menu Labels Menu Label Description ^ Stores the number of payments to be amortized, and calculates an amortization schedule for that many payments. Successive schedules start where the last schedule left off. #P can be an integer from 1 through 1,200. Displays the amount of the payments applied toward _! interest. Displays the amount of the payments applied toward `! principal. Displays the balance of the loan. a! Calculates the next amortization schedule, which b! contains #P payments.
2. Store the values for I%YR , PV, and PMT. (Press & to make PMT a negative number.) If you need to calculate one of these values, follow the instructions under “Using the TVM Menu,” on page 66. Then go on to step 3. 3. Press . to display the rest of the TVM menu. 4. If necessary, change the number of payment periods per year stored in Y. 5. If necessary, change the payment mode by pressing JH= or H
Next successive set of payments authorized b. c. To calculate a subsequent schedule with a different number of payments, key in that number and press ^. To start over from payment #1 (using the same loan information), press @c and proceed from step 7. Example: Displaying an Amortization Schedule. To purchase your new home, you have taken out a 30-year, $65,000 mortgage at 12.5% annual interest. Your monthly payment is $693.72.
payments, but does not display it. _ ;<:H2HF:8/*K##%&#'"Displays interest paid in first year. ` 52;<7;5198/$##&+*" Displays principal paid in first year. a J191<7H8'+K-**&.$" Displays balance at end of first year. b P58#$ 50:FI #%/$+" Calculates amortization schedule for next 12 payments. _ ;<:H2HF:8/*K(*.&#."Displays results for second year. ` 52;<7;5198/$%,&+," a J191<7H8'+K.
6. Press \ Ignore the message 3H@ P50:FQ 52HFF RP5S. 7. Press c. 8. Key in the payment number of the first payment in the schedule and press d. (For instance, for the very first payment, FIRST= 1.) 9. Key in the payment number of the last payment in the schedule and press e. 10.Key in the increment ― the number of payments shown at one time― and press f. (For instance, for one year of monthly payments at a time, INCR=12.) 11.Press g.
(1 year). g " Calculates and prints amortization schedule shown below. ;6@28" 5O8" 50:8" GO8" #$&.(" '.
6 Interest Rate Conversions The interest conversion (ICNV) menu converts between nominal and effective interest rates. To compare investments with different compounding periods, their nominal interest rates are converted to effective interest rates. This allows you, for example, to compare a savings account that pays interest quarterly with a bond that pays interest semiannually. ! The nominal rate is the stated annual interest rate compounded periodically, such as 18% per year compounded monthly.
The ICNV Menu TVM FIN BUS ICNV CFLO PER NOM% EFF% SUM TIME SOLVE CURRX BOND DEPRC CONT P NOM% EFF% The ICNV menu converts between nominal and effective interest rates, using either: ! Periodic compounding; for example, quarterly, monthly, or daily compounding. ! Continuous compounding. Converting Interest Rates To convert between a nominal annual interest rate and an effective annual interest rate that is compounded periodically: 1. Press " h to display the interest conversions menu. 2.
To convert between a nominal annual interest rate and an effective annual interest rate that is compounded continuously: 1. Press " h to get the interest conversions menu. 2. Press l for “continuous”. 3. To convert to the effective rate, key in the nominal rate and press j, then press k. 4. To convert to the nominal rate, key in the effective rate and press k, then press j. Values of EFF% and NOM% are shared between the PER and CONT menus.
41 58+&((" Stores number of compounding periods per year for bank #1. 6.7 j
interest rate in the TVM menu. (You can also use TVM if PMT = 0, regardless of the compounding periods.) 1. Call up the periodic interest-rate conversion menu ( " h i ). 2. Calculate the effective annual interest rate from the nominal annual interest rate given by the bank. a. Store annual interest rate in j. b. Store number of compounding periods per year in 1. c. Press k. 3. Calculate the nominal annual interest rate that corresponds to your payment periods. a.
effective interest rate based on your payment periods. Last, convert the effective rate to the nominal rate based on the bank’s compounding periods. Example: Balance of a Savings Account. Starting today, you make monthly deposits of $25 into an account paying 5% interest compounded daily (365-day basis). At the end of 7 years, how much will you receive from the account? Keys: Display: "h FH9H7: Description: 7E05E4
7@T 25& W " Stores 84 deposit periods, " $25 per deposit, and no 0V 5O8(&((" money before the first regular deposit. X GO8$K.#,&'#" Value of account in 7 years. If the interest rate were the unknown, you would first do the TVM calculation to get I%YR (5.01). Then, in the ICNV PER menu, store 5.01 as NOM% and 12 as P for monthly compounding. Calculate EFF% (5.13). Then change P to 365 for daily compounding and calculate NOM% (5.00). This is the bank’s rate.
7 Cash Flow Calculations The cash flow (CFLO) menu stores and analyzes cash flows (money received or paid out) of unequal (ungrouped) amounts that occur at regular intervals.* Once you’ve entered the cash flows into a list, you can calculate: ! The total amount of the cash flows. ! The internal rate of return (IRR%). ! The net present value (NPV), net uniform series (NUS), and net future value (NFV) for a specified periodic interest rate (I%). You can store many separate lists of cash flows.
Table 7-1. CFLO Menu Labels Menu Label Description E Accesses the CALC menu to calculate TOTAL, IRR%, NPV, NUS, NFV. Allows you to insert cash flows into a list. m! Deletes cash flows from a list. n! Allows you to name a list. o! Allows you to switch from one list to another or p! create a new list. Turns the prompting for #TIMES on and off. q! To see the calculator line when this menu is in the display, press I once. (This does not affect number entry.
Money received is a positive number $300 $200 $100 Time periods 1 $250 $200 2 3 $125 $0 4 5 6 7 $ _ 50 8 Money paid out is a negative number Figure 7-1. Cash Flows (Ungrouped) The horizontal timeline is divided into equal compounding periods. The vertical lines represent the cash flows. For money received, the line points up (positive); for money paid out, the line points down (negative). In this case, the investor has invested $700.
1 2 3 4 5 6 7 8 9 $_100 $_100 $_100 $_100 $_100 $_200 $_200 $_200 Figure 7-2. Grouped Cash Flows After an initial payment of $100, the investor pays $100 at the end of periods 1 through 5, and $200 at the end of periods 6 through 8. The investment returns $1,950 at the end of period 9. For every cash flow you enter, the calculator prompts you to indicate how many times (#TIMES) it occurs.
Entering Cash Flows To enter cash flows into a CFLO list: 1. Press " r. You will see either G9ECL(T8U if the current list is empty, or G9ECL# or moreT8U if the list is not empty. This is the bottom of the current list. 2. If the list is not empty, you can do either a or b: a. Clear the list by pressing @c W (see also page 99.) b. Get a new list by pressing p s (The old list must be named first. Press o or see page 97.) 3.
been automatically set to 1, and #&(( is displayed on the calculator line. Do either a or b: a. To retain the value 1 and go on to the next flow, press I (or ]). b. To change #TIMES, key in the number and press I.* Given #TIMES Calculator line 7. Continue entering each cash flow and, for grouped flows, the number of times it occurs. The calculator recognizes the end of the list when a flow is left blank (no value is entered). 8. Press e to end the list and restore the CFLO menu.
The #TIMES prompting is usually on, because it is automatically turned on whenever you clear or get a cash-flow list. Example: Entering Cash Flows. Enter the following ungrouped cash flows in a list and find the percentage internal rate of return (IRR). 0: 1: $－500 125 2: 3: $ 275 200 Keys: Display: Description: "r " @c 79H12 :MH 9;F:U" Asks for confirmation. W G9ECL(T8U" Clears data from list and prompts for initial flow.
The [ and ] keys move up and down one number at a time. @[ and @] display the beginning and end of the list. Changing or Clearing a Number. To change a number after it’s been entered: display the number, key in the new value, and press I. Use this same method to clear a number to zero. (Do not press C or <, which clear the calculator line, not the cash-flow entry.) Inserting Cash Flows into a List. Insertion occurs before (above) the current flow.
The name can be up to 22 characters long and include any character except:＋ － x ÷ ( ) < > : = space * But only the first three to five characters (depending on letter widths) of the name are used for a menu label. Avoid names with the same first characters, since their menu labels will look alike. Viewing the Name of the Current List. Press o, then e. Starting or GETting Another List When you press r, the cash-flow list that appears is the same as the last one used.
To remove just one value at a time from a list, use n. Cash-Flow Calculations: IRR, NPV, NUS, NFV Once you have entered a list of cash flows, you can calculate the following values in the CALC menu. ! Sum (TOTAL). ! Internal rate of return (IRR%). This is a periodic rate of return. To calculate an annual nominal rate when the period is not a year, multiply the IRR% by the number of periods per year.
Table 7-2. The CALC Menu for CFLO Lists Menu Label O Description Calculates the sum of the cash flows. Calculates the internal rate of return―the interest t* ! (discount) rate at which the net present value of the cash flows equals zero. u! Stores the periodic interest rate, expressed as a percentage (sometimes called cost of capital, discount rate, or required rate of return). Given I%, calculates the net present value―the v! present value of a series of cash flows.
Example: Calculating IRR and NPV of an Investment. An investor makes an initial investment of $80,000, and expects returns over the next five years as illustrated below. 115,000 5,500 5,000 1 4,500 2 4,000 3 4 5 $ _ 80,000 (Initial flow) Calculate the total of the cash flows and the internal rate of return of the investment. In addition, calculate the net present value and net future value, assuming an annual interest rate of 10.5%. Start the problem with an empty cash-flow list.
assumed to occur just once. 80000 & G9ECL#T8U" Prompts for next cash I /*(K(((&((" flow. Calculator line shows last number entered. 5000 I G9ECL$T8U" Stores $5,000 for FLOW(1), prompts for next flow. G9ECL%T8U" Stores FLOW(2). G9ECL+T8U" Stores FLOW(3). 4000 I G9ECL.T8U" 115000 I G9ECL'T8U" Stores FLOW(4). 4500 I 5500 I Stores final cash flow and shows end of list. eE " Calculates sum of the cash O :E:198.+K(((&((" flows. t ;2268##&,%" Calculates internal rate of return. 10.
<5O8$K-'$&+%" eE Calculates new NPV. v Example: An Investment with Grouped Cash Flows. You are considering an investment that requires a cash outlay of $9,000, with the promise of monthly cash flows as shown. Calculate IRR%. Also find NPV and NFV at an annual interest rate of 9%. 1,500 1,500 1,500 1,000 1,000 1,000 1,000 500 500 500 0 $ _ 9,000 Since some of these cash flows are grouped (consecutive and equal), the #TIMES prompting must be on so you can specify a number other than 1.
9000 & I G9ECL#T8U" Stores the initial cash flow. P:;0HFL#T8#" 500 I Stores FLOW(1) and prompts for #TIMES(1). G9ECL$T8U" 3I FLOW(1) occurs 3 times; prompts for next cash flow. 1000 I 4 " Stores FLOW(2) four I 0I I G9ECL%T8U" times. " Stores FLOW(3) one time G9ECL+T8U" (the 1 is automatically entered). 1500 I 3 " Stores FLOW(4) three I eE G9ECL.T8U" times. " Displays the CALC menu. t ;2268#&.%" Calculates monthly IRR%. " Stores the periodic, ;68(&-." monthly interest rate.
3,000 3,000 3,000 3,000 2,000 2,000 2,000 2,000 1,000 1,000 1,000 1,000 500 500 500 500 Calculate the annual rate of return for this investment. (The prompting for #TIMES should be on.) Keys: Display: Description: "r " Current cash-flow list. @c " Clears the current list or W " gets a new one. This sets or " the #TIMES prompting on. ps G9ECL(T8U" 20000 & " Stores the initial cash I 500 I G9ECL#T8U" flow.
G9ECL.T8U" I eE " Calculates quarterly rate t ;2268$&+%" of return. ,&-$" Calculates nominal annual v* 4 = rate of return from quarterly rate. Doing Other Calculations with CFLO Data If you would like to do other calculations with cash flows besides those in the CALC menu, you can do so by writing your own Solver equations. There are Solver functions that can access data stored in CFLO lists, and there is a summation function that can combine all or part of the values stored in specific lists.
8 Bonds The BOND menu calculates the yield to maturity or price of a bond. It also calculates yield to call on a coupon date and accrued interest. You can specify the: ! Calendar basis: 30/360 or actual/actual (days per month/days per year). Municipal, state, and corporate bonds issued in the United States are typically 30/360. U.S. Treasury bonds are actual/actual. ! Coupon payments: semi-annual or annual. Most U.S. bonds are semi-annual.
Table 8-1. BOND Menu Labels Menu Label z Description Displays a menu of bond types: 30/360 or actual/actual, semi-annual or annual. Stores the settlement (purchase) date according to the {! current date format (MM.DDYYYY or DD.MMYYYY; see page 143). Stores the maturity date or call date according to the |! current date format. The call date must coincide with a coupon date. Stores the annual coupon rate as a percentage. }! Stores the call price per $100 face value.
Doing Bond Calculations Remember that values in the BOND menu are expressed per $100 face value or as a percentage. A CALL value of 102 means that the bond will be worth $102 for every $100 of face value when called. Some corporate bonds in the United States use the convention that the price of the bond is set to 100 if the coupon rate equals the yield, whether or not the settlement date is a coupon date. The BOND menu does not use this convention. To calculate the price or yield of a bond: 1.
maturity, the CALL value must equal 100. (See step 3.) 8. To calculate a result, first press ) to access the remaining menu labels. Do either a or b: a. Key in the yield and press •. Press * to calculate the price. b. Key in the price and press *. Press • to calculate the yield. To calculate the accrued interest, press €. The total amount owed the seller is PRICE + ACCRU, that is: * + € =. v Calculating Fractional Values.
| 01:8(.?(#?$(#* :4H" 6.75 } 75<68'&-." Stores annual coupon rate. ) /8+8 v3• * " Stores desired yield " (displayed rounded to two @9A68*&%*" decimal places).* 52;7H8*'&%*" Result: price is $86.38 per $100 face value. v+ € *'&%*)#&*." v= **&$%" Adds accrued interest owed the seller. Net price. Suppose that the market quote for the bond is 88¼. What yield does it represent? 88.25 * 52;7H8**&$." Stores quoted price. • @9A68*&#%" Result: yield to maturity.
5.022003 { FH::8" Stores purchase date (.?($?$((% G2;" (MM.DDYYYY format). 3.032022 | 01:8(%?(%?$($$ :M4" Stores maturity date. 75<68'&((" Stores annual coupon ) 5.7 • " rate. Stores yield. * 52;7H8#(%&+%" 6} @9A68.&-(" Calculates price. ) 3.032006 " | 102.75 " Changes maturity date to call date and stores ~ 71998#($&-." a call value. ) • @9A68.&.*" Calculates yield to call. Example: A Zero-Coupon Bond.
9 Depreciation The DEPRC (depreciation) menu calculates depreciation values and remaining depreciable values one year at a time. The methods available are: ! ! ! ! Declining balance. Sum-of-the-years’ digits. Straight line. Accelerated Cost Recovery System. The DEPRC Menu TVM FIN BUS ICNV CFLO SUM TIME SOLVE CURRX BOND DEPRC BASIS SALV LIFE ACRS% ACRS MORE YR# FACT% DB SOYD SL MORE Pressing … displays the DEPRC menu.
Table 9-1. DEPRC Menu Labels Menu Label † Description Stores the depreciable cost basis of the asset at acquisition. Stores the salvage value of the asset at the end of its ‡! useful life. If there is no salvage value, set SALV=0. Stores the expected useful life (in whole years) of the ˆ! asset. Stores the appropriate Accelerated Cost Recovery ‰! System percentage from the published ACRS tables. Calculates the ACRS deduction based on BASIS and Š! ACRS%.
To see the value currently stored in a variable, press R menu label. Doing Depreciation Calculations DB, SOYD, and SL Methods To calculate the depreciation for an asset:* 1. Display the DEPRC menu: press " …. 2. Define the characteristics of the asset: a. Key in the cost basis and press † b. Key in the salvage value and press ‡. If there is no salvage value, enter zero. c. Key in the useful life and press ˆ. 3. Press ) for the rest of the DEPRC menu. 4.
Example: Declining-Balance Depreciation. A metalworking machine, purchased for $10,000, is to be depreciated over 5 years. Its salvage value is estimated at $500. Find the depreciation and remaining depreciable value for each of the first 3 years of the machine’s life using the double-declining-balance method (200% of the straight-line rate). For comparison, find the straight-line depreciation, as well. Keys: Display: Description: " … " Displays DEPRC menu. 10000 † J1F;F8#(K(((&((" Cost basis.
] 2AO8%K*((&((" Remaining depreciable value after third year using SL. The ACRS Method To calculate the amount of tax deduction under the U.S. Accelerated Cost Recovery System: 1. Display the DEPRC menu: press " …. 2. Enter the cost basis of the asset and press † 3. The Internal Revenue Service publishes tables that list the percentage of an asset’s basis that can be deducted each year of its prescribed life. Look up that value, enter it, and press ‰. 4. Press Š to calculate the value of the deduction.
25 ‰ 172F68$.&((" Tabular value, year 2. Š 172F8'K$.(&((" Deduction in second year. 20 ‰ 172F68$(&((" Tabular value, year 3. Š 172F8.K(((&((" Deduction in third year. Partial-Year Depreciation When the acquisition date of an asset does not coincide with the start of the tax or fiscal year, then the amounts of depreciation in the first and last years are computed as fractions of a full year’s depreciation. Except in SL, the intermediate years are computed as sums of fractions.
Calendar Year Depreciation Value 1 (Oct.-Dec.) ¼ x year 1 2 (¾ x year 1) + (¼ x year 2) 3 (¾ x year 2) + (¼ x year 3) 4 (Jan.-Sept.) ¾ x year 3 Example: Partial-Year Depreciation. A movie camera bought for $12,000 has a useful life of 10 years with a salvage value of $500. Using the sum-of-the-years’-digits method, find the amount of depreciation for the fourth year. Assume the first depreciation year was 11 months long. Keys: Display: Description: "… " Displays DEPRC menu.
10 Running Total and Statistics The SUM menu stores and statistically analyzes sets of numbers. As you enter the numbers, the calculator displays their running total. Once you’ve entered the numbers into a list, you can: ! Calculate the mean, median, standard deviation, and range. ! Display the largest and smallest number in the list. ! Sort the list from smallest number to largest number.
The SUM Menu FIN CALC TOTAL INSR SUM DELET NAME MEAN MEDN STDEV MAX SORT TIME SOLVE GET CURRX TOTAL RANGE MORE FRCST MORE … MIN BUS The SUM menu creates lists of numbers and performs calculations with a SUM list. Table 10-1. SUM Menu Labels Menu Label Description E Accesses the CALC menu to calculate the total, mean, median, standard deviation, range, minimum, maximum, sorting, and linear regression (including weighted mean and summation statistics).
To see the calculator line when this menu is in the display, press I once. (This does not affect number entry.) To see this menu when the calculator line is in the display, press e. Creating a SUM List To keep a running total of a list of numbers or do statistical calculations with sets of data, first create a SUM list of the values. Entering Numbers and Viewing the TOTAL To enter numbers into a SUM list: 1. Press $.
After briefly showing ITEM(1), the display shows " ;:H0L$T8U" :E:19=number TOTAL is the updated, running TOTAL of all the numbers in the list (only one number, so far). 4. To enter ITEM(2), key in the value and press I. The prompt for ITEM(3) and the new, updated total appear. 5. Continue entering values for ITEM(3), ITEM(4), etc. The calculator recognizes the end of the list when an item is left blank (no value is entered). 6. Press e to end the list and restore the SUM menu.
Deleting Numbers from a List. Pressing n deletes the current item. Example: Updating a Checkbook. On May 31, your checking account balance was $267.82. The transactions for the first 10 days in June are: Date Transaction 6/1 6/1 6/1 6/2 Balance Deposit Check Check Amount 267.82 837.42 －368.23 －45.36 Date Transaction Amount 6/3 6/7 6/10 －128.90 － 65.35 55.67 Check Check Deposit Update the checkbook by calculating the running balance. Keys: Display: $* " Description: @cW ;:H0L#T8U" 267.
55.67 I ;:H0L*T8U" :E:198..%&(-" e ;:H0L*T8U" Ends list and displays SUM menu again. Copying a Number from a List to the Calculator Line To copy a number from the list into the calculator line, use ] or [ to display the number, then press R I. Naming and Renaming a SUM List A new list has no name. You may name it before or after filling the list, but you must name it in order to store another list. To name a list: 1. Press o from the SUM menu. 2. Use the ALPHA menu to type in a name.
Starting or GETting Another List When you press $, the SUM list that appears is the last one used. To start a new list or switch to a different one, the current list must be named or cleared. If it is named, then: 1. Press p. The GET menu contains a menu label for each named list plus s. 2. Press the key for the desired list. ( s brings up a new, empty list.) Clearing a SUM List and Its Name To clear a list’s numbers and name: 1. Display the list you want to clear, then press @c W.
Calculations with One Variable The CALC menu calculates the following statistical values using one SUM list. Table 10-2. The CALC Menu for SUM Lists Menu Key Description Calculates the sum of the numbers in the list. O! Calculates the arithmetic mean (average). •! Calculates the median. ‘! Calculates the standard deviation.* ’! Calculates the difference between the largest and “! smallest number. ) Finds the smallest (minimum) number in the list. ”! Finds the largest (maximum) number in the list.
Month Phone Expense Phone Expense 1. May $340 4. August $780 2. June $175 5.September $245 3. July $450 6. October $625 Month Calculate the mean, median, and standard deviation of the monthly phone bills. Then display the smallest value in the list. Keys: Display: Description: $ Displays current SUM list and SUM menu keys. @c " Clears current list or gets a W " new one. or " ps ;:H0L#T8U" 340 I ;:H0L$T8U" Stores May’s phone bill; :E:198%+(&((" shows total.
deviation. ) " Displays rest of CALC menu. ” 0;<8#-.&((" Finds smallest number. Calculations with Two Variables (FRCST) The FRCST menu does the following two-variable calculations using two SUM lists: ! Fits x- and y-data to a linear, logarithmic, exponential, or power curve. ! Forecasts estimated values based on that curve. ! Finds the weighted mean and grouped standard deviation. ! Shows you the summation statistics (Σx, Σx2, Σy, Σy2, Σxy, etc.).
CALC TOTAL MEAN MEDN STDEV MIN MAX SORT RANGE MORE FRCST MORE (select x and y) LIN x-list y-list CORR MODL W.MN G.SD LOG EXP X M B MORE SIZE MORE XY MORE PWR Y X2 Y2 After pressing —, you must specify two previously created lists― one for the x-variable and one for the y-variable. The two lists must have the same number of items.
Table 10-3. FRCST Menu Labels Menu Label Description list name for x-variable list name for y-variable These specify the two lists of data to be compared. Also used for estimations:store x and estimate y, or vice-versa. ˜ is the menu label for an unnamed current list. ™* Calculates the correlation coefficient, a number between －1 and ＋1 that measures how closely the x,y data points match the calculated curve. š* Calculates M. For the linear model, this is the slope. ›* Calculates B.
Curve Fitting and Forecasting Curve fitting is a statistical method for finding a relationship between two variables, x and y. Based on this relationship, you can estimate new values of y based on a given x-value, and vice-versa. Each SUM list holds the numbers (data values) for one variable.
To do curve fitting and forecasting : 1. Enter the data into two SUM lists: one for the x-values and one for the y-values. Make sure each list has the same number of items so that the items are in matched pairs. 2. From the SUM menu, press E ) — to display a menu of SUM-list names. The current list is labeled ˜ unless named otherwise. 3. Press a menu key to select a list of x-values (independent variable). 4. Select a list of y-values (dependent variable). 5. Now you see the FRCST menu.
Number of Minutes of Radio Advertising (x-values, MINUTES) Dollar Sales (y-values, SALES) Week 1 2 $1,400 Week 2 1 $ 920 Week 3 3 $1,100 Week 4 5 $2,265 Week 5 5 $2,890 Week 6 4 $2,200 BJ’s wants to determine whether there is a linear relationship between the amount of radio advertising and the weekly sales. If a strong relationship exists, BJ’s wants to use the relationship to forecast sales. A graph of the data looks like this: y (forecasted) 3,000 2,000 SALES in Dollars M 8 5.
Keys: Display: Description: $ " Displays current SUM list and SUM menu keys. @c " W ;:H0L#T8U" 2I 1I " Stores minutes of " advertising (x-values) into 3I 5I " a SUM list. 5I 4I " Clears current list. " ;:H0L-T8U" :E:198$(&((" eo :@5H"1"<10HIV;<54:W" MINUTES " Names this list. (See page I ;:H0L-T8U" 30 to use the ALPHA menu.) Now enter and name the second list. ps ;:H0L#T8U" Gets a new, empty list.
" 0;<4" " F19HF" FH9H7: @ O12;1J9H" Selects MINUTES as x-list, 9;
Weighted Mean and Grouped Standard Deviation Data in one list (x) can be weighted or grouped (by frequency) by data in another list (y). To find the mean of weighted data and the standard deviation of grouped data: 1. Enter the data values―the x-variable―into a SUM list. 2. Enter the corresponding weights or frequencies―the y-variables―into another list. (To calculate G.SD, the y-values should be integers.) 3. From the SUM menu, press E ) — to display a menu of SUM-list names.
216 I ;:H0L.T8U" :E:198*%#&((" eo RENT I " Names this list RENT. (See ;:H0L.T8U" page 30 to use the ALPHA menu.) ps ;:H0L#T8U" Gets a new, empty list. 54 I 32 I " Stores frequencies into " second list. 88 I 92 I " ;:H0L.T8U" :E:198$''&((" eE " )— FH9H7: X O12;1J9H" SUM lists. " 2H<:" " Displays names of all FH9H7: @ O12;1J9H" Specifies RENT as the x-list. ˜ 9;
statistics for just one list of data, specify the same list for both x and y. 2. To see n, press ) ¡. 3. Press ) again to display the summation menu, and press the menu label for the value you want. Doing Other Calculations with SUM Data If you would like to do other statistical calculations with SUM data besides those in the CALC menu, you can do so by writing your own Solver equation.
11 Time, Appointments, and Date Arithmetic The calculator contains a clock and calendar in the TIME menu. You can select a 12-hour or 24-hour clock, and a month-day-year or daymonth-year calendar. You can: ! Record appointments that set alarms with optional messages. ! Determine the day of the week for a particular date. ! Calculate the number of days between two dates using the 360-day, the 365-day, or the actual calendar. Viewing the Time and Date To view the time and date, press Y in the MAIN menu.
The TIME Menu FIN BUS SUM CALC APT1 TIME APPT APT2 SOLVE ADJST CURRX SET APT10 Table 11-1. The TIME Menu Labels Menu Label Description Displays the CALC menu, for calculating the day of E! the week and other date arithmetic. Displays the APPT menu for setting and viewing §! appointments. Displays the ADJST menu for adjusting the clock ¨! setting. Displays the SET menu for setting the time and date, ©! and for selecting the time and date formats.
Setting the Time and Date (SET) Table 11-2. The SET Menu Labels Menu Label Description Z Sets the date to the displayed number (MM.DDYYYY or DD.MMYYYY). Y Sets the time to the displayed number (HH.MMSS). [ Switches between AM and PM (12-hour clock). \ Switches between month/day/year and day.month.year formats. ] Switches between 12-hour and 24-hour clock formats. ^ Displays the formats for entering the clock’s date and time. To set the time: 1. Press Y © to display the SET menu. 2.
Example: Setting the Date and Time. Set the date and time to April 5, 2003, 4:07 p.m. Keys: Display: Description: © " Displays SET menu. 4.052003 F1: (+?(.?(% time" Sets date. 4.07 Y " Sets time. Press [ if [ F1:" necessary. Z (+?(.?(% (+I(-Ixx5" Changing the Time and Date Formats (SET) Use the SET menu to change the time and date formats. To switch between the 12- and 24-hour clocks, press ]. To switch between the month/day/year and day.month.year calendars, press \.
Appointments (APPT) You can record up to ten appointments, each with an alarm. An appointment can contain a message. You can also create repeating appointments―appointments that recur at regular intervals. APPT APT1 APT2 MORE APT9 APT10 for each appointment DATE TIME A/PM MSG RPT HELP Viewing or Setting an Appointment (APT1-APT10) Table 11-3. Menu Labels for Setting Appointments Menu Label Description Z Sets the appointment date.
To set an appointment or view its current setting: 1. Press Y, then §. The display tells you which appointments (numbered 1-10) are set and which are past due (expired with unacknowledged alarms). Pressing ) displays the status and menu labels for appointments 6 through 10. 2. Press a menu key ― c through d. The display shows the current appointment, if any, and the menu labels for setting appointments. 3. Optional: press @c to remove any old information.
message, press a. Type the message (refer to page 30 for using the ALPHA menu). Messages are limited to a maximum of 22 characters. Press I when done. (Press e to negate any changes and retain the original message.) 7. The repeat interval (optional): To set, view, or change a repeat interval, press b. Key in an integer and press the appropriate key. For example, 2 e causes the appointment to go off at the same time every other day; 90 ” sets the repeat interval to 1½ hours.
Unacknowledged Appointments An appointment not acknowledged during its alarm becomes past due. The alarm annunciator remains on. To acknowledge a past-due appointment: 1. Press Y §. 2. Press the menu key for the past-due appointment. 3. Press e to return to the APPT menu. The acknowledged appointment is no longer listed as past due. A repeating appointment is deactivated while it is past due and will not go off subsequently until the past-due appointment has been acknowledged.
h appointment #4. @c +I ((?((?(( #$I((1"Clears appt. #4. 2.15 Y +I F4<" Stores appt. time and (+?$(?(% $I#.1" supplies current date. +I F4<" Sets appt. time to PM. [ (+?$(?(% $I#.5" 4.22 Z +I :4H" Stores appt. date. (+?$$?(% $I#.5" a " STAFF I +I :4H" Enters message: “staff”. (+?$$?(% $I#.5" b 25:8
Table 11-4. CALC Menu Labels for Date Arithmetic Menu Label Description ª « Stores or calculates a date. Also displays the day of the week. If you omit the year, the calculator uses the current year. ¬ Stores or calculates the number of actual days between DATE1 and DATE2 , recognizing leap years. Calculates the number of days between DATE1 and -! DATE2 using the 360-day calendar (30-day months).
2. Key in the second date and press «. 3. Press ¬, -, or ® to calculate the number of days using that calendar. Example: Calculating the Number of Days between Two Dates. Find the number of days between April 20, 2003 and August 2, 2040, using both the actual calendar and the 365-day calendar. Assume the date format is month/day/year. Keys: Display: Description: YE " Displays CALC menu. 4.202003 " Stores Apr. 20, 2003 ª A1:H#8" as first date and (+?$(?$((% F4<" displays its day of the week.
3. Press «. This calculation always uses the actual calendar. Example: Determining a Future Date. On February 9, 2003, you purchase a 120-day option on a piece of land. Determine the expiration date. Assume the date format is month/day/year. Keys: Display: Description: YE " Displays CALC menu. 2.092003 " Stores Feb. 9, 2003. ª A1:H#8" ($?(,?$((% F4<" 120 ¬ « 17:419 Stores number of days into A1@F8#$(&((" the future. A1:H$8" Calculates expiration date ('?(,?$((% 0E<" (DATE2).
12 The Equation Solver The Equation Solver (the SOLVE menu) stores equations that you enter and creates menus for them. You can then use those menus to do calculations. Enter Solver equations in algebraic form regardless of the calculation mode (ALG or RPN). The Solver can store many equations― the number and length of equations is limited only by the amount of memory available. The equations are stored in a list.
Regardless of how you do this calculation (even if you do it longhand), you are using an equation: Next Forecast = Old Forecast + Change in Old Forecast = Old Forecast + (Projected Percentage Changes xOld Forecast) or: NEXT = OLD + ((A% + B% + C%) ÷ 100 x OLD) Using the SOLVE and ALPHAbetic menus, you can type in this equation as
+( A %+ B %+ C % )/ 100 * " OLD >A)L16)J6)76T" for the display. " " D#((BE9A" I Enters equation into list. " *# " CC# >A)L16)J6)76T" Controls view of full equation. D#((BE9A" e Displays SOLVE menu. " Calculating with the Solver. Suppose last month’s forecast for a product was 2,000 units. In the meantime, three market changes have occurred that affect this forecast.
15 & " 76" 768/#.&((" Stores effect of competitor’s new product on sales. b
Table 12-1. The SOLVE Menu Labels Menu Label Description E Verifies the current equation and creates menu labels for it. This is necessary before doing any calculations. * Accesses the ALPHA-Edit menu (page 31) so you can alter the current equation. The arrow keys move long equations across the display. n Deletes the current equation or just its variables (that is, the space allotted in memory for the variables). / Allows you to enter a new equation.
while the Solver checks that the equation is mathematically valid. (However, the Solver has no way of checking whether the equation is the right one for your problem.) If the equation cannot be solved, the calculator briefly displays: ;
1. Store values in all but one of the variables (for example, 2000 M, etc.). Remember that you can verify stored values by pressing R menu label. 2. To start the calculation, press the menu key for the variable you want to calculate. In most cases, this is all you need to know about how the Solver works. However, certain types of equations are more difficult to solve. If, during the calculation, the display temporarily shows two lines of changing numbers, such as 1I#&.
Keys: Display: Description: @A " Restores MAIN menu. &/ :@5H HY41:;E/AHJ:B6;<:/:1XT" DHY:@" I 2EH8L1FFH:B6H2<" Stores the equation. /AHJ:B>" " E Verifies the equation and displays the menu labels for ROE, ASSET, %ERN, DEBT, %INT, and (press )) TAX and EQTY.
Editing an Equation (EDIT) If you have an ;
Finding an Equation in the Solver List To display an entry in the Solver list, display the SOLVE menu and move through the list using the [ and ] keys. @[ moves to Z: E5 E G 9 ;F :[ and @] moves to Z JE :: E0 E G 9 ;F :[ . Shared Variables If two or more equations contain the same variable, that variable is shared among those equations.
Make sure that the menu for the variables is in the display. (The equation itself should not be in the display. If it is, press E.) Pressing @c now sets NEXT; OLD, A%, B%, and C% to zero. Variables are also cleared when their equation is edited. If the SOLVE menu is displayed (rather than the SOLVE CALC menu), then pressing @c will prompt AH9H:H 199 Note O12;1J9HFU . Press X, otherwise you will lose the variables in all the equations. (See “Deleting All Equations or Variables in the Solver,” page 164.
Deleting One Equation or Its Variables (DELET) To delete an equation or its variables: 1. Display the equation. 2. Press j in the SOLVE menu. 3. To delete the equation, respond W to both questions: A H9 H: H :M H O1 2; 1J 9H FU " A H9 H: H :M H HY 41 :; E< U " (If the entry has no variables allocated, then only the second question appears.) 4. To delete just the variables, respond X to A H9 H: H :M H HY 41 :; E< U . This preserves the equation.
a+b +c d − e ×f Since a Solver equation appears all on one line, you must group the numerator and denominator separately by using parentheses, such as L 1) J) 7T DL A/ HB GT " Order of Calculations. Operations occur from left to right but do: ! Exponentiation first. For example, 1 BJ\ %8 7 is interpreted as A × B3 = C. B is raised to the 3rd power and then multiplied by A. To raise A × B to the 3rd power, write the equation as L 1B JT \% 87 . ! Multiplication and division before addition and subtraction.
A + B × C (D + 5) × E could be entered as 1 )JB 7D LL A) .T BH T& " What Can Appear in an Equation Long Equations. There is no limit on the length of an equation (or the number of variables it has) if there is enough memory to store it. An equation longer than one display line (22 characters) moves to the left and adds an ellipsis (...). To view a long equation, move the cursor using the arrow keys on the ALPHA-Edit menu.
Parentheses. Do not use brackets or braces. Parentheses determine order, but do not imply multiplication. For example, the equation Psn ＝ Ps (1－F) would be typed into the Solver as 5 F< 85 FB L# /G T . The × sign must be inserted between 5 F and the parenthesis. Functions and Conditional Expressions. An equation can contain any of the functions and conditional expressions given in the table on pages 168-171. Some of these functions also have typing aids. Math Operators (“Typing Aids”).
, " : G17" < " > G17:" ( 25 )= G17:L$.T8" , - " This calculates 25! G17:L$.T81" (factorial). 2. Using a Typing Aid Keys: Display: Description: @m " MATH menu labels appear. 4# G17:L" The ALPHA menu automatically returns after one MATH selection. 25 )= G17:L$.T8" , - " This also calculates 25!, G17:L$.T81" and with fewer keystrokes. Solver Functions Here is a complete list of functions that you can include in Solver equations.
Table 12-2. Solver Functions for Equations Function ABS(x) ALOG(x) CDATE CTIME DATE(d1:n) DDAYS(d1:d2:cal) EXP(x) EXPM1(x) FACT(x) FLOW(CFLO-listname:flow#) FP(x) Description Absolute value of x. Common (base 10) antilogarithm; 10x. Current date. Current time. The date n days after (when n is positive) or before (when n is negative) date d1. The format for d1 is set in the TIME/SET menu. Number of days between dates d1 and d2.
Table 12-2. Solver Functions for Equations (Continued) Function HMS(time) HRS(time) IDIV(x:y) IF(cond:expr1:expr2) INT(x) INV(x) IP(x) ITEM(SUM-listname:item#) LN(x) LNP1(x) LOG(x) MAX(x:y) MIN(x:y) MOD(x:y) PI RND(x:y) S(variable name) SGN(x) Description Converts time in decimal hours to HH.MMSS format. Converts time in HH.MMSS format to decimal hours. Integer part of the quotient of x/y. Conditional expression: if cond is true, use expr1; if cond is false, use expr2. See page 174.
Table 12-2. Solver Functions for Equations (Continued) Function Σ(cfr:c1:c2:s:expr) SIZEC(CFLO-listname) SIZES(SUM-listname) SPFV(i%:n) SPPV(i%:n) SQ(x) SQRT(x) #T(CFLO-listname:flow#) TRN(x:y) USFV(i%:n) USPV(i%:n) Description Summation of the algebraic expression expr for values of the counter ctr, stepping from c1 to c2 at increments of s. See page 176. The number of the last flow in specified CFLO list. The number of items in specified SUM list. Future value of a single $1.
Example Using a Solver Function (USPV): Calculations for a Loan with an Odd First Period. Suppose an auto purchase is financed with a $6,000 loan at 13.5% annual interest. There are 36 monthly payments starting in one month and five days. What is the payment amount? Use the following formula when the time until the first payment is more than one month but less than two months.
Keys: Display: Description: & @] ZJE::E0 EG 9;F:[" Displays SOLVE menu and bottom of Solver list. :@5H HY41:;E
Conditional Expressions with IF Equations can include conditional expressions using the function IF. The syntax of the IF function is: IFLconditional expression I algebraic expression I algebraic expressionT * then or else For example, the solver accepts the equation: J E< 4F 8; GL F1 9H F[ %( (( I& ($ B F 19 HF I& (# B F1 9H FT " According to this equation, if SALES is greater than 3000, then the BONUS equals .02 × SALES; otherwise (“or else”), BONUS equals .01 × SALES. Logical Operators.
Examples of Conditional Equations. ! J = ; G L 1[- 1
Press & /, then enter the equation: < H C8 E 9A " ] " L# ) ;G L2 8 #I & (% I; G L2 8 $I &( ' I& # TT T" To do the calculation: Keys: Display: Description: I " Stores, verifies, and E creates menu labels for the equation. 27500 M E9A8$-K.((&((" Stores old salary. 2R 28$&((" Stores rating. /
calculated and added to the sum. Thus the stored value of X is used to calculate X + 2X2 + 3X3 + 4X4 + 5X5 + 6X6. The following equation uses a variable as the ending value, 0 as the beginning value, and a step size of 2. F H2 ;H F8 ^ L ;I (I 91 F: I$ I; BX \; T " If 8 is stored in LAST, I takes on values of 0, 2, 4, 6, and 8. Then the stored value of X will calculate 2X2 + 4X4 + 6X6 + 8X8.
“Chi-Squared Statistics” in chapter 14 illustrates another use of the Σ function with SUM lists. Creating Menus for Multiple Equations (S Function) The S (solving for) function is used in conjunction with the IF function to group related equations together and to specify the criteria for choosing one of them to solve. S(variable name) The advantage over two separate equations is that the single equation gives you a single menu with all possible variables.
;GLFL3=T E2 FL9JTI3=B$&$#/9JI0B%&$*/G:T" Press I to store it, then E to verify it and create its menu: 1. Convert 225 pounds to kilograms. " " 9J" 3=" Result is 3= 8#( #& *# . Press 225 2. How many feet equal 100 meters? " " 0" G:" Result is G:8%$*&((& Press 100 Note that you do not have to clear variables between steps 1 and 2. The S function considers only those values in the part of the equation that it is solving. How the Solver Works The Solver has two ways of finding an answer.
The process of finding a solution iteratively is very complex. There are four possible outcomes. Refer to “Solver Calculations” in appendix B for additional descriptions of these outcomes. ! Case 1: The calculator displays a result. It is very likely that this is a solution to the equation. To check how good this result is, you can repeat the calculation by pressing the menu key for the variable you solved for.
Entering Guesses Entering your own guesses serves two purposes. First, it can save time by telling the Solver where to start searching. Second, if more than one solution exists, entering guesses may lead the Solver to a solution in a specified range. The closer your guesses are to the desired solution, the better chance the Solver has of finding it. You can enter guesses at these times: ! Before beginning the calculation, after you’ve stored a value for every variable except the unknown variable.
Profit ＝ (Price × Quantity) － (Variable costs × Quantity) － Fixed Costs The C-Sharp Piano Corporation sells pianos for $6,000. Variable costs are $4,100; fixed costs per year are $112,000. How many pianos must C-Sharp sell this year in order to earn a profit of $130,000? (In past years, C-Sharp has had to sell between 100 and 200 pianos to make an acceptable profit. You can use this information as initial guesses.
" Y:@" Y:@I$((&(((((((((/"Solves for QTY iteratively.
13 Printing The calculator can print information using the HP 82240 Infrared Printer, which accepts the infrared signal from the printer port. This chapter describes information you can print. Operation of the printer is covered in the printer owner’s manual.* Port The print annunciator ( )appears in the display whenever the calculator sends information through its printer port.
The Printer’s Power Source The speed of the printer depends on whether it is using its optional ac adapter. To optimize printing performance, set the printing speed mode in the calculator appropriately. To view or change the printing speed mode: 1. Press @>. 2. Press . to change and display the new mode. If necessary, press . again to set the desired mode: ! 5 2; <: H2 I 1 7 1A 15 :H 2 ! 5 2; <: H2 I < E 17 1 A15 :H 2 3. Press e.
Printing Other Information (@p) PRINTER LIST STK REGS TIME MSG TRACE The PRINTER menu provides the ability to print most of the information you’ve stored, including the contents of variables, lists, appointments, the history stack, registers, and the current date and time. You can also transmit descriptive notes to label the output. (To print amortization schedules, see “Printing an Amortization Table,” page 81.) From within any menu you can press @p to bring up the PRINTER menu.
Printing the Values Stored in Variables. You can print a listing giving the values of all variables whose menu labels are displayed.* For example, if the calculator is in the FIN TVM menu, it displays the labels T U V W X .. Pressing @p k now produces a print-out like this: <8" %'(&((" ;6@28" #$&.(" 5O8" '.K(((&((" 50:8" /',%&((" GO8" *&((" 5?@28" #$&((" H
Printing Appointments. To print all stored appointments, display the § menu (press § then press @p k. This produces a listing like this for each appointment: # I CH A ( -? $% ?( % #( I( (1 " A H0 E G E2 F 0; :M " 2 5: 8< E< H" Menus Not Associated with Stored Data. Remember that many menu labels do not represent data, but rather activities, such as " , #, n and ©. They contain no information for printing. The calculator beeps if there is nothing to print when you press @p k.
2. Press n to change the setting. A message informs you that tracing is on or off. If necessary, press n again to display the desired message. 3. Press e. Example: Trace-Printing an Arithmetic Calculation. Produce a record of the keystrokes you use to do the following calculation and store the result in the TVM variable PMT. 1 /12× 4,800 + 125 Press @p n to set 5 2; <: 0 EA HI : 21 7H E < . If you see 5 2; <: 0 EA HI :21 7H EG G , press n again.
14 Additional Examples Loans Simple Annual Interest See appendix F for RPN keystrokes for this example. Example: Simple Interest at an Annual Rate. Your good friend needs a loan to start her latest enterprise and has requested that you lend her $450 for 60 days. You lend her the money at 7% simple annual interest, to be calculated on a 365-day basis.
For instructions on entering Solver equations, see “Solving Your Own Equations,” on page 29. If you know the dates for the course of the loan, rather than the number of days, use this for an actual-calendar basis: AHJ:89E1<)9E1
3. Finally enter current values for N (less number of payment periods already passed, or 5 × 12－42) and PV (proposed purchase price, $79,000); then calculate I%YR for the annual yield. Step 1: Calculate PMT. Make sure FV = 0. Keys: Display: Description: "] . " Selects menu; sets 12 " payments per year and @c e 20 @ T " End mode. #$ 5?@2 H
Step 3: Enter actual, current values for N and PV; then find new I%YR for discounted mortgage with balloon. Keys: Display: Description: RT - 42 T " Stores number of <8#*&((" payments remaining in v 5-year loan. 79000 & " Stores proposed, V 5O8/-,K(((" discounted purchase price (new present value). U ;6@28$(&-$" Calculates percent annual yield. Annual Percentage Rate for a Loan with Fees See appendix F for RPN keystrokes for the next two examples.
1. Since the payment amount is not given, calculate it (PMT) first. Use the given mortgage amount (PV = $60,000) and interest rate (I%YR = 111/2%). 2. To find the APR (the new I%YR), use the PMT calculated in step 1 and adjust the mortgage amount to reflect the points paid (PV = $60,000 － 2%). All other values remain the same (term is 30 years; no future value). Keys: Display: Description: " ] . " If necessary, sets 12 " payments per year and " End mode.
calculate the monthly PMT = (loan x 12%) ÷ 12 mos.) When calculating the I%YR, the FV (a balloon payment) is the entire loan amount, or $1,000,000, while the PV is the loan amount minus the points. Keys: Display: Description: "] . " If necessary, sets 12 " payments per year and @c e #$ 5?@2 H
first payment, and a 30-day month is assumed.* A Solver Equation for Odd-Period Calculations: EAAI 5OBL;6D#((BG5LA1@FD%(T)#T8/;GLA1@FZ%(I" L#);6D#((TB50:I50:TB4F5OL;6I
u ;68#&$." interest rate. 46 ¬ A1@F8+'&((" Stores days until first payment. 0X GO8(&((" No balloon payment. W 50:8/#.-&(%" Calculates payment. Example: Loan with an Odd First Period Plus Balloon. A $10,000 loan has 24 monthly payments of $400, plus a balloon payment of $3,000 at the end of the 24th month. If the payments begin in 8 days, what annual interest rate is being charged? Select equation ODD. Keys: Display: Description: " Creates menu. 10000 V 5O8#(K(((&((" Stores known values.
2. Store 0 W, 6 T, and 200 V. 3. Add 200 to the annual interest rate, make the number negative, and store it in X. 4. Press U to calculate the Canadian mortgage factor. 5. Continue the problem by supplying the other mortgage values and solving for the unknown item. Do not change I%YR from step 4. Example: Canadian Mortgage. What is the monthly payment required to fully amortize a 30-year, $30,000 Canadian mortgage if the interest rate is 12%? Keys: Display: " "] .
(For the \ operator press @u.) PV = loan amount, or present value. PMT = monthly payment amount. I%YR = annual (Canadian) interest rate as a percent. N = total number of payment periods for the life of the loan. FV = remaining balance, or future value. For instructions on entering Solver equations, see “Solving Your Own Equations,” on page 29. Advance Payments (Leasing) Occasionally payments are made in advance, such as in leasing.
I%YR = the annual interest rate as a percent. N = the total number of payments. #ADV = the number of advance payments. The following example assumes that you have entered the equation ADV, above, into the Solver. For instructions on entering Solver equations, see “Solving Your Own Equations,” on page 29. Example: Leasing with Advance Payments. Equipment worth $750 is leased to you for 12 months. The equipment is assumed to have no salvage value at the end of the lease.
1. Because the compounding periods and the withdrawal periods are not coincident, you must first convert the nominal interest rate to one in terms of the withdrawal periods. You can do this using the ICNV menu, as explained on page 87, “Compounding Periods Different from Payment Periods.” 2. The rest of the calculation is a straightforward TVM problem. Remember that money deposited is paid out and therefore negative; money withdrawn is received and therefore positive.
< #(&(*" Clears message to show NOM% value still in calculator line. sU ;6@28#(&(*" Stores adjusted nominal interest rate in I%YR. . 4Y Ze " Sets 4 payments " (withdrawals) per year + 5?@2 JH=;< 0EAH" and Begin mode. 750000 & " Stores present (initial) V 5O8/-.(K(((&((" value of fund. 20000 W 50:8$(K(((&((" Stores withdrawal amount. 4T <8+&((" Stores number of withdrawals in 1 year. X GO8-+%K%'+&%#" Value of fund at end of year 1.
Suppose you want to start saving now to accommodate a future series of cash outflows. An example of this is saving money for college. To determine how much you need to save each period, you must know when you’ll need the money, how much you’ll need, and at what interest rate you can invest your deposits. Use a CFLO list to calculate the net uniform series (NUS) of the future withdrawals: 1. Store zero for all cash flows except the withdrawals.
1 2 $0 $0 144 $15,000 0 $0 $15,000 $15,000 $15,000 $0 $0 $0 $0 $0 156 $0 $0 168 180 Figure 14-1. Flow of Withdrawals 9.00 0 1 2 3 178 179 180 Figure 14-2. Flow of Deposits Keys: Display: Description: " r " Displays current cash-flow list and CFLO menu keys. @cW " or " ps G9ECL(T8U" Clears current list or gets a new one.
Step 1: Set up a CFLO list. 0I G9ECL#T8U" Sets initial cash flow, FLOW(0), to zero. 0I P:;0HFL#T8#" Stores zero in FLOW(1) and prompts for the number of times it occurs. 12 12 - 1 * vI " Stores 143 (for 11 years, G9ECL$T8U" 11 months) in #TIMES(1) for FLOW(1). 15000 I P:;0HFL$T8#" Stores amount of first withdrawal, at end of 12th year. I 0I G9ECL%T8U" P:;0HFL%T8#" Stores cash flows of zero... 11 I 15000 I G9ECL+T8U" ...for the next 11 months.
Step 2: Calculate NUS for the monthly deposit. Keys: / 12 v9u Display: Description: " Figures the periodic ;68(&-." (monthly) interest rate and stores it in I%. w <4F8#*$&%(" Amount of monthly deposit needed to meet planned withdrawals. v <5O8#-K,-%&+*" Calculates the net present value of the monthly deposits, which is the same as the NPV of the four future withdrawals. Value of a Tax-Free Account See appendix F for RPN keystrokes for this example.
Example: Tax-Free Account. Consider opening an IRA account with a dividend rate of 8.175%. 1) If you invest $2,000 at the beginning of each year for 35 years, how much will you have at retirement? 2) How much will you have paid into the IRA? 3) How much interest will you have earned? 4) If your post-retirement tax rate is 15%, what is the after-tax future value of the account? Assume only the interest will be taxed. (Assume the principal was taxed before deposit.
v* 15 % = &+R vX = v X +-K'+'&(-" Taxes at 15% of interest. " Subtracts taxes from total %%,K,,+&%," FV to calculate after-tax FV. GO8%%,K,,+&%," Stores after-tax future value in FV. 8U " Calculates present-value 0W " purchasing power of the V 5O8/$$K,,.&%'" above after-tax FV at 8% inflation rate. Value of a Taxable Retirement Account See appendix F for RPN keystrokes for this example.
Keys: Display: Description: "] " Displays TVM menu. Sets 1 payment per year .1Y " # 5?@2 JH=;< 0EAH" and Begin mode. Ze 35 T <8%.&((" Stores years until retirement. 8.175 - 28 % vU v 0V *&#*/$&$," Calculates and stores ;6@28.&*," interest rate diminished by tax rate. Stores no present value. 5O8(&((" 3000 & W 50:8/%K(((&((" Stores annual payment. X GO8%+.K.(.&'#" Calculates future value.
a liquid account. The figure generally used is a short-term security (T-bill) or bank passbook rate. Positive cash flows are reinvested at a reinvestment rate that reflects the return on an investment of comparable risk. An average return rate on recent market investments might be used. 1. In the CFLO menu, calculate the present value of the negative cash flows (NPV) at the safe rate and store the result in register 0. Enter zero for any cash flow that is positive. 2.
or " ps G9ECL(T8U" 180000 & " Stores initial cash flow, I 0I G9ECL#T8U" FLOW(0). P:;0HFL#T8#" Stores FLOW(1) as zero new one. since the flow amount is positive. 5I G9ECL$T8U" Stores 5 for #TIMES(1). 100000 & " Stores FLOW(2). I 5I P:;0HFL$T8#" Stores FLOW(2) 5 times. G9ECL%T8U" You can skip FLOW(3) and FLOW(4) because they are equal to zero for this part. eE <5OK <4FK
5I G9ECL%T8U" 5 times. 0I 9I " Stores zero for FLOW(3), G9ECL+T8U" 9 times. 200000 I " I eE" Stores FLOW(4), 1 time. G9ECL.T8U" <5OK <4FK
Price of an Insurance Policy The price of an insurance policy, other than term life insurance, is rarely apparent at first glance. The price should include not only the premium payments, but also the interest that could have been earned on the cash value or savings portion of the policy. The following equation calculates the price per $1,000 of protection for one policy year and the interest rate earned on the savings portion of the policy.
Example: Insurance Policy. You are evaluating your $50,000 insurance policy. The premium of $1,010 is due at the beginning of the year, and a dividend of $165 is received at the end of the policy year. The cash value of the policy is $3,302 at the beginning of the year; it will grow to $4,104 by the end of the year. You can earn 6% on a savings account. What is the annual price per $1,000 protection? Select the correct equation in the Solver. Keys: Display: Description: E " Creates menu.
Reference: Joseph M. Belth, Life Insurance―A Consumer’s Handbook, Indiana University Press, 1973, p. 234. Bonds Example: Yield to Maturity and Yield to Call. On March 16, 2003 you consider the purchase of a $1,000 bond that was issued on January 1, 2001. It has a 10.5% semiannual coupon using a 30/360 calendar, and matures on January 1, 2031. The bond is callable on January 1, 2006 at 110 (that is, $1,100). The bond is now selling at 115.174 (that is, $1,151.74).
Second, calculate the yield to call: Keys: Display: Description: ) @9A68,&((" Returns to first BOND menu. 1.012006 " | 01:8(#?(#?$((' F4<" to the call date. 110 ~ 71998##(&((" Stores call value. )• @9A68-&'%" Calculates a yield to Changes maturity date call. Discounted Notes A note is a written agreement to pay to the buyer of the note a sum of money plus interest. Notes do not have periodic coupons, since all interest is paid at maturity.
The following example assumes that you have entered the NOTE equations into the Solver. For instructions on entering Solver equations, see “Solving Your Own Equations,” on page 30. Example:Price and Yield of a Discounted Note. What are the price and yield of the following U.S. Treasury Bill: settlement date October 14, 2003; maturity date March 17, 2004; discount rate 8.7%? (Assume month/day/year format.) Select the NOTE:PRICE equation in the Solver. Keys: Display: Description: E " Creates menu. 10.
A Solver Equation for Moving Averages: 01O=8^L;I01XL#I91F:/<)#TI91F:I#I;:H0LnameI;TTD" 0;
4040 I 3200 I " ;:H0L-T8U" :E:198$%K.-(&((" eo VOL I e& (use ] and [ " Names the list VOL. ;:H0L-T8U" " Displays the MAVG equation. Make sure if necessary) name is VOL. E " Displays menu. 3T <8%&((" Stores number of points. 3e " 01O=" 4e " 01O=" 5e " 01O=" 6e " 01O=" " Calculates average for 01O=8+K$$(&((" months 1, 2, and 3. " Calculates average for 01O=8%K,-'&'-" months 2, 3, and 4. " Calculates average for 01O=8%K.%'&'-" months 3, 4, and 5.
In other words, it tests whether discrepancies between the observed frequencies (Oi) and the expected frequencies (Ei) are significant, or whether they might reasonably result from chance. The equation is: n χ2 = ∑ i =1 (Oi − Ei )2 Ei If there is a close agreement between the observed and expected frequencies, χ2 will be small. If the agreement is poor, χ2 will be large.
Number Frequency Observed 1 25 2 17 3 15 4 23 5 24 6 16 Keystroke: Display: Description: $! " Displays SUM menu and current list. @cW " or " ps ;:H0L#T8U" 25 I 17 I " 15 I 23 I " 24 I 16 I " Clears current list or gets a new one. Enters observed values. " " ;:H0L-T8U" :E:198#$(&((" eo OBS I e& (use [ and ] " Names the list OBS. ;:H0L-T8U" " Displays the CHI equation. Make sure if necessary ) name1 is OBS. E " Displays menu. 20 I HX58$(&((" Stores expected value. 7M;8.
A Assistance, Batteries, Memory, and Service Obtaining Help in Operating the Calculator Hewlett-Packard is committed to supporting users of HP calculators. You can obtain answers to your questions about using the calculator from our Calculator Support department. We suggest reading “Answers to Common questions,” below, before contacting us. Past experience has shown that many of our customers have similar questions.
Q: How do I change the number of decimal places the calculator displays? A: The procedure is described in “Decimal Places” on page 34. Q: How do I clear all or portions of memory? A: C clears the calculator line. @c clears the data lists or variables accessible from the current menu. Erasing the entire contents of memory is covered in “Erasing Continuous Memory” on page 230.
A: Refer to “Managing Calculator Memory” on page 227 for instructions on how to reclaim memory for your use. annunciator is Q: The calculator is operating slowly, and the blinking. Why? A: The calculator is trace printing. Press @p n e to turn off tracing. Q: How can I change the sign of a number in a list without keying in the number again? A: Press R I & I . Q: The beeper is not working. A: Check the beeper mode by pressing @> -. See also page 36.
due to a borderline low-battery condition. The calculator can detect that there is insufficient power for printing before the battery annunciator comes on. If you continue to use the calculator after the battery annunciator comes on, power can eventually drop to a level at which the calculator stops powering the display and keyboard. The calculator will require fresh batteries before it can be turned back on.
4. Never remove two old batteries at the same time, in case memory lost. Remove one of the two batteries once. Insert a new battery, making sure that the positive sign (+) is facing outward. Do not mutilate, puncture, or dispose of batteries in fire. The batteries can burst or explode, releasing hazardous chemicals. Warning 5. Remove and insert the other battery as step 4. Make sure that the positive sign (+) on each battery is facing outward. 6. Replace the battery compartment cover. 7. Press on.
Managing Calculator Memory The calculator has approximately 30,740 units (or “bytes”) of user memory available. (This is separate from the system memory that stores all the unerasable information with which the calculator is manufactured.) The calculator displays ;
Resetting the Calculator If the calculator doesn’t respond to keystrokes or is behaving unusually, attempt to reset it. Resetting the calculator halts the current calculation, clears the calculator line, and displays the MAIN menu. Stored data remains intact except setting those conditions: double-space printing off, printer tracing off, printer without the ac adapter, and beeper on. To reset the calculator, hold down C while pressing the third menu key from the left. Repeat if necessary.
For selecting English language: ! ALG mode ! Month/day/year date format, 12-hour clock ! 2 decimal places, period (.) decimal point ! Double-space printing off, printer tracing off, printer without the ac adapter ! Beeper on ! APPT default time 00.00.00 12:00A, default time WED 01.01.03 12:00:00A ! Erased Continuous Memory ! U.S Dollars and EURO Dollars currencies and the rate equals 1.0000.
For selecting the other languages: ! ALG mode ! Day/month/year date format, 24-hour clock ! 2 decimal places, comma (,) decimal point ! Double-space printing off, printer tracing off, printer without the ac adapter ! Beeper on ! APPT default time 00.00.00 00:00, default time WED 01.01.03 00:00:00 ! Erased Continuous Memory ! U.S Dollars and EURO Dollars currencies and the rate equals 1.0000.
! Maintains the selected mode－ALG or RPN. Erasing Continuous Memory does not affect the current time and date, date and the selected language. To erase Continuous Memory, press and hold down C, the leftmost menu key, and the rightmost menu key. (Press three keys simultaneously). When the three keys are released, the calculator displays 0H0E2@ 9EF:. Continuous Memory can inadvertently be erased if the calculator is dropped or if power is interrupted.
! If the calculator won’t turn on: 1. 2. Attempt to reset the calculator (see page 228). If the calculator fails to respond after step 1, replace the batteries (see page 225). If you have just replaced the batteries, see page 227. If these steps do not help, the calculator requires service. ! If the calculator doesn’t respond to keystrokes: 1. 2. Attempt to reset the calculator (see page 228). If the calculator still fails to respond, attempt to erase Continuous Memory (see page 230).
information is printed during the test. 3. If possible, return to the MAIN menu (press @A). 4. To start the self-test, hold down C while you press the fifth menu key from the left. Once the self-test has begun, do not press any keys until you are ready to halt the test. 5. During the test, the calculator beeps periodically and displays various patterns and characters.
3. 4. 5. 6. 7. 8. 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.
the express warranty statements accompanying such products and services . Nothing herein should be construed as constituting an additional warranty.HP shall not be liable for technical or editorial errors or omissions contained herein.
Asia Pacific L.America Other European countries Country : Australia Singapore Country : Argentina Brazil Mexico Venezuela Chile Columbia Peru Central America & Caribbean Guatemala Puerto Rico Costa Rica N.
USA This calculator generates, uses, and can radiate radio frequency energy and may interfere with radio and television reception. The calculator complies 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. However, there is no guarantee that interference will not occur in a particular installation.
B More About Calculations IRR% Calculations The calculator determines IRR% for a set of cash flows using mathematical formulas that “search” for the answer. The process finds a solution by estimating an answer and then using that estimate to do another calculation―in mathematical terms, this is called an iterative process. In most cases, the calculator finds the desired answer, since there is usually only one solution to the calculation.
This is the only answer. ! Case 4: The calculator displays the message: 0 1< @?
may be additional positive or negative answers, or no true solution at all. You can continue searching for other solutions by halting the calculation and entering a different guess. One way to obtain a good guess for IRR% is to calculate NPV for various interest rates (I%). Since IRR% is the interest rate at which NPV equals zero, the best estimate of IRR% is the interest rate that yields the value for NPV closest to zero.
For certain equations, the unknown can be isolated, but an answer cannot be calculated with the values stored. Then the calculator displays: F E9 4: ;E < < E: GE 4
Iterative Solutions If the Solver is not able to isolate the unknown variable, it cannot provide a direct solution. In these cases, the Solver searches iteratively for a solution.* In its iterative search for a solution, the Solver looks for a value that sets the left side of the equation equal to the right side. To do this, the Solver starts with two initial estimates of the answer, which we’ll call estimate #1 and estimate #2.
The iterative search for a solution sometimes takes several minutes. (You can halt the search at any time by pressing any key except @ ) There are four possible outcomes: ! Case 1: The calculator displays an answer. This is very likely the true solution for the unknown variable. There are two situations in which the Solver returns a case 1 answer: ! ! Case la: LEFT－RIGHT is exactly zero. Case lb: LEFT－RIGHT is not zero for either estimate.
restart the search. ! Case 2: The calculator displays the values of LEFT and RIGHT, which are unequal. To see the calculator’s result, press < or C. If LEFT and RIGHT are relatively close to one another in value, the result is probably a true solution. Otherwise, the result is probably not a true solution. If the result seems unreasonable, it could be because the equation has more than one solution. You might want to enter one or two guesses and restart the search.
Case 2a: Case 2b: have opposite signs. The two estimates are "neighbors". have opposite signs. The two estimates are far apart. Case 2c: have the same sign.. ! Case 3: The calculator displays: J 1A = 4H FF HF I " 5 2H FF V79 2W :E O;H C " " The Solver is unable to begin its iterative search for a solution using the current initial estimates (guesses).
entering different estimates. The closer you can estimate the answer, the more likely that the Solver will find a solution. ! Case 4: The calculator displays: FE94:;E<
n i% 1 ＋ － 1 100 USFV (i % : n) ＝ i% 100 Percentage Calculations in Business (BUS) NEW － OLD %CHANGE ＝ OLD PART %TOTAL ＝ × 100 TOTAL PRICE － COST MARKUP %C ＝ COST × 100 × 100 － PRICE COST MARKUP %P ＝ × 100 PRICE Time Value of Money (TVM) S = payment mode factor (0 for End mode; 1 for Begin mode).
INT’ ＝ BAL x i (INT’ is rounded to the current display setting; INT’ ＝ 0 for period 0 in Begin mode) INT ＝ INT’ (with sign of PMT ) PRIN ＝ PMT + INT’ PRIN ＝ PMT + INT’ BALnew ＝ BALold + PRIN ∑INTnew ＝ ∑INT old + INT ∑PRINnew ＝ ∑PRIN old + PRIN Interest Rate Conversions Periodic compounding P NOM% EFF % ＝ 1 + − 1 × 100 100 × P Continuous compounding NOM% EFF % ＝ e 100 − 1 × 100 Cash-Flow Calculations j ＝ the group number of the cash flow.
k NFV ＝ NPV × SPFV (i % : N ) where N ＝ ∑ nj j =1 NUS ＝ NPV USPV (i % : N ) k TOTAL ＝ ∑ (nj × CFj ) j =0 Bond Calculations Reference: Lynch, John J., Jr. and Jan H. Mayle, Standard Securities Calculation Methods, Securities Industry Association, New York, 1986. A＝accrued days, the number of days from beginning of coupon period to settlement date. E＝number of days in coupon period bracketing settlement date. By convention, E is 180 (or 360) if calendar basis is 30/360.
CALL PRICE ＝ N − 1+ Y 1 + M CPN % N M ＋ ∑ K − 1+ K =1 Y 1 + M DSC E DSC E CPN % A − E × M The “end-of-month” convention is used to determine coupon dates in the following exceptional situations. (This affects calculations for YLD%, PRICE, and ACCRU.) ! If the maturity date falls on the last day of the month, then the coupon payments will also fall on the last day of the month.
For the last year of depreciation, DB equals the remaining depreciable value for the prior year. Sum and Statistics n＝number of items in the list. x’＝an element of the sorted list. TOTAL = Σxi MEDIAN = x j′ MEDIAN = for odd n, where (x j′ + x j ′) +1 2 STDEV = W .MN = Σxi n n + 1 j = 2 MEAN = x = Σ (yi - xi ) Σyi for even n, where j = n 2 Σ( xi − x )2 n − 1 G.
Let: ΣX i n SX 2 = Σ ( X i − X )2 X = ΣYi n SX 2 = Σ (Yi − Y )2 Y = SXY = Σ ( X i − X ) (Yi − Y ) SXY M = SX 2 Then: B = b for LIN and LOG models, and B = eb for EXP and PWR models, where b = Y − M X CORR = SXY SX 2 × SY 2 Equations Used in Chapter 14 Canadian Mortgages 1 − (1 + r )−N −N PV = − PMT − FV (1 + r ) r 1 CI %YR 6 r = 1 + − 1 200 where: N CI%YR PV PMT FV = = = = = total number of monthly payments annual interest rate (as a percent) loan amount monthly
Odd-Period Calculations DAYS PV 1 + i × = 30 1 − (1 + i )−N −N − (1 + i × S ) × PMT × − FV (1 + i ) i Where: PV = loan amount i = periodic interest rate as a decimal DAYS = actual number of days until the first payment PMT = periodic payment amount N = total number of payments FV = balloon payment amount S = 1 if DAYS < 30 S = 0 if DAYS ≥ 30 Advance Payments − PV − FV (1 + i )−N 1 − (1 + i )− (N − # ADV ) + # ADV i payment amount loan amount balloon payment amount periodic
C Menu Maps The following maps show how to display each of the menus. There is a map for each menu label in the MAIN menu and for each menu found on the keyboard. The menu labels for variables are enclosed in boxes to illustrate how they are used: Variable used to store and calculate values. Variable used to calculate or display values; cannot be used to store values. Variable used to store values; cannot be used to calculate values.
CURRX CURR1 CURR2 RATE C.STO C.RCL SELCT Currencies Figure C-2.
FIN TVM ICNV NOM% EFF% CALC P INSR CFLO NOM% DELET EFF% NAME ＊NEW TOTAL N I%YR PV IRR% I% PMT P/YR FV BEG #P NPV NUS GET #T? Names of Lists NFV OTHER END INT AMRT PRIN BAL NEXT TABLE FIRST LAST INCR GO Figure C-3.
FIN BOND DEPRC BASIS SALV DB YR# TYPE SETT A/A SEMI SOYD MAT YLD% 360 LIFE ACRS MORE SL MORE MORE PRICE ANN Figure C-3 (continued).
SUM INSR CALC DELET NAME GET TOTAL ALPHA-Edit menu* ALPHA menu* TOTAL RANG MORE MEAN MEDN MIN MAX Names of lists SORT FRCST MORE (Select x and y) x-list y-list CORR MODL W.MN LIN LOG EXP M G.SD B MORE SIZE MORE PWR MORE Figure C-4. SUM Menu * For the complete menu, see pages 30-31.
TIME SET APPT CALC APT1 APT2 ...MORE ... TIME A/PM MSG RPT HELP MIN A/PM M/D 12/24 HELP DATE1 DAYS 360D 365D Figure C-5. TIME Menu * * For the complete menu, see pages 30-31.
SOLVE * EDIT NEW ALPHA-Edit menu* ALPHA menu* CALC Figure C-6. SOLVE Menu DISP FIX . , EXP N! PI RPN INTL ALL MATH LOG LN MODES BEEP PRNT DBL ALG PRINTER LIST STK REGS TIME MSG TRACE Figure C-7. DSP, MATH, MODES, and PRINTER Menus * For the complete menu, see pages 30-31.
D RPN: Summary About RPN The RPN appendixes (D, E, and F) are especially for those of you who want to use or learn RPN―Hewlett-Packard’s original Reverse Polish Notation for operating calculators. This calculator can use either RPN or algebraic logic for calculations―you choose which. HP’s RPN operating logic is based on an unambiguous, parentheses-free mathematical logic known as “Polish Notation,” developed by the Polish logician Jan Łukasiewicz (1878－ 1956).
All other operations－including the Solver－work the same in RPN and ALG modes. (The Solver uses algebraic logic only.) For more information about how RPN works, see appendix E, “RPN: The Stack.” For RPN keystrokes of selected examples from chapter 14, see appendix F, “RPN: Selected Examples.” Continue reading in chapter 2 to learn about the other functionality of your calculator. Watch for this symbol in the margin earlier in the manual.
Where the RPN Functions Are Function Name Definition Key to Use ENTER Enters and separates one number from the next. = LASTX Recalls last number in X-register. @L R↓ Rolls down stack contents. ~ (same as () R↑ Rolls up stack contents. [ (except in lists) X<>Y X-register exchanges with Y-register. x (same as )) CHS Changes sign.
Using INPUT for ENTER and ▼ for R↓. Except in CFLO and SUM lists, the I key also performs the E function and the ] key also performs the ~ function. ! In lists: I stores numbers. Use = to enter numbers into the stack during arithmetic calculations. ! In lists: [ and ] move through lists. Use ~ to roll through stack contents. Doing Calculations in RPN Arithmetic Topics Affected by RPN Mode This discussion of arithmetic using RPN replaces those parts of chapter 2 that are affected by RPN mode.
To select RPN mode, press @>1. To Calculate: Press: Display: 12 + 3 12 E 3 + 12 E 3 - #.&((" 12 E 3 * 12 E 3 / 12 @w %'&((" 12 @v 12 @t %&+'" 12 – 3 12 x 3 12 ÷ 3 12 2 12 1/12 ,&((" +&((" #++&((" (&(*" You do not need to use E before an operator, only between keyed-in numbers. Key in both numbers (separated by E) before pressing the operator key. The Power Function (Exponentiation). The power function uses the @u keys.
27% of 200 200 less 27% RPN Mode ALG Mode 200 E 27 % 200 E 27 %- 200 * 27 %= 200 - 27 %= Calculations with STO and RCL The store (s) and recall (R) operations work identically in ALG and RPN modes (see “Storing and Recalling Numbers” and “Doing Arithmetic Inside Registers and Variables” in chapter 2). The keystrokes are the same for simple storing and recalling and for doing arithmetic inside registers and variables.
The cube root example and the percentage addition example (previous topics) are two simple examples of chain calculations. For another example, calculate 7 x (12 + 3) Start the calculation inside the parentheses by finding 12 + 3. Notice that you don’t need to press E to save this intermediate result (15) before proceeding. Since it is a calculated result, it is saved automatically－without using parentheses. Keys: Display: Description: 12 E 3 + 7* #.&((" Intermediate result. #(.
E RPN: The Stack This appendix explains how calculations take place in the automatic memory stack and how this method minimizes keystrokes in complicated calculations. What the Stack Is Automatic storage of intermediate results is the reason that RPN mode easily processes complicated calculations－without using parentheses. The key to automatic storage is the automatic RPN memory stack. The memory stack consists of up to four storage locations, called registers, which are “stacked” on top of each other.
Reviewing the Stack (Roll Down) The ~ (roll down) function (on the ( key) lets you review the entire contents of the stack by “rolling” the contents downward, one register at a time. While in RPN mode you don’t need to press the shift key for ~. The ] key has the same effect as ~. except in a CFLO or SUM list, when ] affects the list and not the stack. Likewise, the [ key rolls the contents of the stack upward, except in lists. Rolling a Full Stack.
The x function is used primarily to swap the order of numbers in a calculation. For example, an easy way to calculate 9 ÷ (13x8) is to press 13 E 8 * 9 x/. Arithmetic－How the Stack Does It The contents of the stack move up and down automatically as new numbers enter the X-register (lifting the stack), and as operators combine two numbers to produce one new number in the X-register (dropping the stack).
How ENTER Works You know that E separates two numbers keyed in one after the other. In terms of the stack, how does it do this? Suppose the stack is filled with a, b, c, and d. Now enter and add two new numbers: 5＋6： a (lost) b (lost) T a b c c c Z b c d d c Y c d 5 5 d X d 5 5 E Lift 5 Lift 6 6 + No lift 11 Drop E replicates the contents of the X-register into the Y-register.
3. Calculate future sales by pressing * for each of the next 3 years. 2 2 2 2 2 E 2 2 E E 2 84 84 2 2 2 2 2 2 2 2 2 * 168 * 336 * 672 Sales for the next 3 years are projected to be $168,000; $336,000; and $672,000. Clearing Numbers Clearing One Number. Clearing the X-register puts a zero in it. The next number you key in (or recall) writes over this zero. There are two ways to clear the number in the X-register: ! Press <. ! Press C.
T a Z b Y c X d @c 0.00 Because of the automatic movement of the stack, it is not necessary to clear the stack before starting a calculation. Note that if an application menu is currently displayed, pressing @c also clears the application’s variables. The LAST X Register Retrieving Numbers from LAST X The LAST X register is a companion to the stack: It stores the number that had been in the X-register just before the last numeric operation (such as a * operation).
Keys: Display: Description: 96.74 E 52.39 + ,'&-+" #+,&#%" Intermediate result. @L .$&%," Retrieves the number before the + operation, saved in LAST X. / $&*." Final result. Chain Calculations The automatic lifting and dropping of the stack’s contents let you retain intermediate results without storing or reentering them, and without using parentheses. This is an advantage the RPN stack has over algebraic calculator logic.
Exercises Here are some extra problems that you can do to practice using RPN. Calculate: (14 + 12) x (18 – 12) ÷ (9 – 7)＝78.00 A Solution: 14 E 12 + 18 E 12 -* 9 E 7 -/ Calculate: 232 – (13 x 9) + 1/7＝412.14 A Solution: 23 @w 13 E 9 *- 7 @t + Calculate: A Solution: (5.4 × 0.8) ÷ (12.5- 0.73 ) = 0.60 5.4 E .8 * .7 E 3 @u 12.5 x-/@v or 5.4 E .8 * 12.5 E .7 E 3 @u-/@v Calculate: 8.33 × (4 - 5.2) ÷ [ (8.33- 7.46) × 0.32] = 4.57 4.3 × (3.15- 2.75) - (1.71× 2.01) A Solution: 4 E 5.2 - 8.33 *@L 7.46 - .
F RPN: Selected Examples The following examples selected from chapter 14 (“Additional Examples”) have been converted to RPN keystrokes. These examples illustrate how to convert algebraic to RPN keystrokes in less common situations: with %, with R, and in a CFLO list. Example: Simple Interest at an Annual Rate. Your good friend needs a loan to start her latest enterprise and has requested that you lend her $450 for 60 days.
adjust the mortgage amount to reflect the points paid (PV = $60,000 －2%). All other values remain the same (term is 30 years; no future value). Keys: Display: Description: "] . " If necessary, sets 12 " payments per year and @c e " End mode. #$ 5?@2 H
Keys: Display: Description: "] . " If necessary, sets 12 " payments per year and @c e " End mode. #$ 5?@2 H
Keys: Display: Description: "r " Displays current cash-flow list and CFLO menu keys. @c " Clears current list or gets a W " new one. or " ps G9ECL(T8U" Step 1: Set up a CFLO list. Keys: Display: Description: 0I G9ECL#T8U" Sets initial cash flow, FLOW(0), to zero. 0I P:;0HFL#T8#" Stores zero in FLOW(1) and prompts for the number of times it occurs. 12 E 12 * 1 - " G9ECL$T8U" I For E, press =, not I. Stores 143 (for 11 years, 11 months) in #TIMES(1) for FLOW(1).
0 I 11 I G9ECL'T8U" Stores cash flows of zero for the next 11 months. 15000 II G9ECL-T8U" Stores third withdrawal, 0 I 11 I G9ECL*T8U" for junior year. Stores cash flows of zero for the next 11 months. 15000 II G9ECL,T8U" Stores fourth withdrawal, for senior year. eE <5OK <4FK
after-tax future value of the account? Assume only the interest will be taxed (the principal was taxed before deposit). 5) What is the purchasing power of that amount, in today’s dollars, assuming an 8% annual inflation rate? Keys: Display: Description: "] .1Y Ze " Sets 1 payment per year " and Begin mode. # 5?@2 JH=;<" 0EAH" 35 T <8%.&((" Stores number of payment periods until retirement (1 x 35). 8.175 U ;6@28*&#*" Stores dividend rate.
8U0W " Calculates present-value V 5O8/$$K,,.&%'" purchasing power of the above after-tax FV at 8% inflation rate. Example: Taxable Retirement Account. If you invest $3,000 each year for 35 years, with dividends taxed as ordinary income, how much will you have in the account at retirement? Assume an annual dividend rate of 8.175% and a tax rate of 28%, and that payments begin today.
Error Messages The calculator beeps and displays an error message under certain circumstances－for example, when you attempt an operation that is not allowed. The calculator distinguishes between math errors that occur on the calculator line and other types of messages by preceding math-error messages with the word H22E2I. Press C or < to erase the message and restore the previous display. J 1A = 4H FF HF I 5 2H FF V 79 2W :E O;H C The Solver cannot begin a numerical search using the initial estimates.
Attempted to take the base 10 or natural log of a negative number or zero. This can happen during curve-fitting calculations if you attempt to calculate: ! A logarithmic forecasting model with a negative or zero x-value. ! An exponential model with a negative or zero y-value. ! A power model with a negative or zero x- or y-value. H22E2I
The numbers stored into built-in variables caused a division by zero in the calculation. You must change one or more stored values. (Refer to the equations in appendix B to see which variables appear in the divisor.) ;
! The number entered cannot be interpreted as a proper date. Check its format (page 143). ! Attempted to set a date outside the range 1/1/2000 through 12/31/2099, or attempted date arithmetic outside the range 10/15/1582 through 12/31/9999. ;
01<@ E2
No solution was found for a Solver equation using the current values stored in its variables. Refer to page 246 in appendix B. 4
Index #Special Characters -, 47 low-battery annunciator, 17, 184, 224 shift annunciator, 19 ], 143 2, 42 -, 150 ®, 150 ( J menu formula, 247 using, 50 %, 40 %TOTL menu formula, 247 using, 51 ) alarm annunciator, 147 &, 22 ´ or ³, 174 B, C, A, @, 32 Σ, 139, 171, 176–77, 220 @, 19 G, 35 F, 35 ^, 78 q, 92, 95, 96–97 s, 127 J, 49, 50 K, 49, 51 Q, 51 ¢, 132, 139 £, 132, 139 ¤, 132, 139 ¥, 132, 139 ¦, 132, 139 _, 144 `, 144 ] or [, 43, 269 editing a list, 98 in a list, 96, 162 with history stack, 43 <,
0, 36, 262 €, 109 , key, 34 c through d, 145 [, appointment-setting menu, 145 ABS (absolute value) function, 169 Accrued interest, on bond, 109, 111 Accuracy of the clock, 231 Acknowledging appointments, 147 Actual calendar actuarial equations, 246 for arithmetic, 149 for bonds, 110 Addition, 21 ADJST menu, 144 Advance payments, 74–77, 199–200, 253.
equations, 249 fractional values for, 111 price, 111 type, 109, 110 yield, 111 RPN examples, 275 Arithmetic priority, 154 Arrow keys for changing current equation, 156 for editing, 32 for finding an equation, 162 for rolling the history stack, 43 for viewing long equations, 166 B BOND menu, 108–9 Bonds, 215–16 Bottom of the current list, in CFLO, 95 of the Solver list, 162 Braces in equations, 167 Brackets in equations, 167 E, 56 ›, 132 a, 78 Z, 64 †, 115 R, 56 Brightness of the display, 17 Backspace
9, 55 U, 56 V, 56 ) key, 53 =, F, 56 @c, 20, 28–29 C, 17, 20, 32 v, 16, 17, 262 CALC menu in CFLO menu, 101 in SOLVE menu, 158–59 in SUM menu, 128 in TIME menu, 150 Calculations, RPN order of, 274 parenthesis in, 266, 274 Calculator not functioning, 231–32 resetting, 225, 228–30 Support, 222 Calculator line arithmetic in, 38–48 definition, 18 displaying alphabetic information, 31–32 editing, 20 Calendar.
signs of numbers, 92 starting a new list, 99 viewing name of current list, 99 viewing numbers, 97 Chain calculations, 21, 38–39, 38 in RPN, 266, 274 Changing batteries, 225–26 the sign of a number, 22 Characters for CFLO list, 98–99 for equation names, 161 for SUM list, 126 in equations, 166–67 inserting and deleting, 31–32 Chi-squared, 219–20 Clearing, 20 %CHG variables, 50 %T variables, 50 AMRT variables, 80 appointments, 146, 148 BOND variables, 109 BUS variables, 50 calculator memory, 28–29 CFLO lists,
equations, 251 Correlation coefficient, 132 Cost markup on, 49, 52 of capital, 101 Counter variable,in summation function, 176 Coupon basis, 108–9 payments, 108 Creating a CFLO list, 94–96, 99 a new equation, in the Solver, 157–58 a SUM list, 123–24, 127 CTIME, 169 Cube root, 41 in RPN, 265 Currency clearing variables, 60 converting, 59 entering a rate, 57 exchange, 57, 58 selecting, 55 storing and recalling, 59 Currency#1, 55 Currency#2, 55 Current equation, 156 deleting, 162–64 printing, 187 CURRX menu,
144 DDAYS, 169 Decimal places, 34, 47 Decimal point, 35 Declining balance depreciation.
entering, 157 erasing, 163 for built-in menus, 246–53 invalid, 158 length of, 153 long, viewing, 166 naming, 161 verifying, 157–58 writing, 164 Editing alphabetic information, 31–32 equations, 161 keys, 31–32 Effective interest rate, 84–87, 100 End payment mode, 64, 65 Ending value, in summation function, 176 Erasing.
X key, 63 + key, 34 Grouped standard deviation, 138–39 Face value, bond, 110 Guesses entering in the Solver, 181–83 IRR%, entering, 238–40 Solver, 245 FACT, 169 Factorial, 42, 169 FIN menu, 256–57 FLOW, Solver, 169 Forecasting calculations, 130–37 equations, 251 values, 121, 132–34 H ^ in the appointment-setting menu, 145 in the SET menu, 143 Foreign language, 224 Formatting number, 34 FP, 169 I, 56 Fractional part, 169 Halting a numerical search, 180 FRCST menu, 130, 132 Hierarchy of menus, 24
t, 101 u, 101 ', 18 U key, 63 S, G, 56 I, 98 for storing equations, 30 in CFLO menu, 92 in RPN, 264 in the Solver list, 157–58 in SUM list, 123 I%, 101 ICNV equations, 248 menu, 84–85 variables, clearing, 86 on loan, amount of PMT applied toward, 80–81 simple, 61 Interest rate conversions, 84–90, 201, 248 effective and nominal, 84 Intermediate results, RPN, 268, 274 Internal rate of return.
ITEM, 170 LN, 170 Iteration in Solver, 179–83, 240, 242–46 LNP1, 170 L ˆ, 115 •, 132 k, 186 o, 42 3, 42 L, 44 in RPN, 273 Language, setting, 224 Large number available, 47 in a list, 128 Large numbers, keying in and displaying, 47 Last result, copying, 44 LAST X register, RPN, 273 Leasing, 74–77, 199–200 LEFT-RIGHT, interpreting, 242–46 Letter keys, 30 Linear estimation, 121, 132–34 Linear model, 130, 133 Linear regression, 121 List.
) key, 25 146 @A, 22–26 Messages, error, 283 @M, 37 MIN, Solver, 170 MAIN menu, 19 MOD, 170 Manual, organization of, 16 Mode of payments (Begin and End), 64 Markup on cost, 49, 52 on price, 49, 52 Math in equations, 165, 167 MATH menu, 42, 260 MAX, 170 Mean, 251 calculating, 128–30 weighted, 138–39 Median, 251 calculating, 128–30 Memory.
in arithmetic, 21, 38–40 in equations, 165 N O, 56 b, 78 S, 63 o in CFLO list, 98–99 in SUM list, 126 v, 101 w, 101 x, 101 /, 157 @, 56 B, 56 J, 56 4, 42 j, 85–86 @ S, 63 N, non-integer, 63, 72 Names of equations, 161 of lists, clearing, 99 of variables, 166 Negative numbers in arithmetic calculations, 22 in cash-flow calculations, 92–94 in TVM calculations, 64 Neighbors in Solver, 243 Nested IF function, in the Solver, 175 Net future value, 91, 101 Net present value, 91, 101 Net uniform series, 91, 101
O, 17 Odd-period calculations, 172–73, 195, 253 Operators, in equations, 164–67 in RPN, 266, 268, 274 Option to buy, for a lease, 74–75 OR, 174 Order of calculation, in the Solver, 165 OTHER menu, 146–47 Overdue appointments. See Past- due appointment Overview, 3 P H, 56, 63 `, 78 W, 63 Y, 62 ^, 78, 82, 85 *, 52, 109 P, 51 ž, 121, 132 T, 56 5, 42 (, 18 @p, 186 P, 186 Parentheses in arithmetic calculations, 39–40 in equations, 165, 167 in RPN, 266, 268, 274 Partial period.
Periodic rate of return, 100 Principal of loan, amount of PMT applied toward, 80–81 Periods, 35. See also Payment periods in numbers in numbers, 35 Printer power for, 185 using, 184 85–86 Periodic interest rate, 101 PI, 42, 170 PMT. See also Payments in TVM, 63 rounded amortization calculations, 78 Positive numbers in cash flow calculations, 92–94 in TVM, 64 Power.
R “, 128 b, 145 7, 55 K, 56 P, 56 1, 36 m, 186 R, 56 @r, 35 ~, 43, 263 115, 116 Renaming lists. See CFLO list; SUM list; the Solver list Repeating appointments past-due, 148 setting, 147 Replacing batteries, 225–26 Required rate of return, 101 Resetting the calculator, 228 Reusing a number, RPN, 271, 273 calculator memory, 37, 230 Reverse Polish Notation, 261 R, 45–46, 98 in RPN calculations, 266 with variables, 28 Rounding a PMT, 71 R↑, 263 Rounding numbers, 35 Radix (decimal point), 34 RPN.
C, 56 Q, 56 l, 186 ¡, 132 @S, 34 s, 45–46 calculations with, RPN, 266 in equations, 162 in ICNV, 86 Shift, 19 Sign of numbers in cash-flow calculations, 92 in TVM calculations, 64 S (function), 170 Simple interest, 40 with annual rate, 190 with annual rate, RPN, 276 Sample standard deviation, 128 Slope, in curve-fitting, 132, 134 Saving numbers, 43 Small numbers, keying in and displaying, 47 Savings account, 71–72 college, 202–6 college, RPN, 278 regular, 200–202 retirement, 208 retirement, RPN, 282
definition, 153 deleting equations, 157, 162–64 deleting variables from, 162–64 editing an equation, 157 empty, 156 entering equations, 157–58 printing, 187 Solver menu, 156–57 for multiple equations, 178 Solver solutions, types of, 243–46 Solver variables.
correcting, 124 creating, 123–24 definition, 121–22 deleting numbers, 125 editing, 122, 124–25 entering numbers in, 123–24 FRCST menu, 132 GETting a new list, 127 inserting numbers, 124 largest number in, 128 name, deleting, 127 naming, 126 printing, 187 smallest number in, 128 sorting, 121, 128 starting a new list, 127 viewing numbers, 124 viewing the name of the current list, 126 145 in PRINTER menu, 186 in SET menu, 143 c, 78 O, 51 of a SUM list, 122, 128 z, 109 ¯, 150 n, 186 O, sum of cash flows, 101
Turning calculator on and off, 17 TVM calculations, 61–83 equation, 247 instructions, 66–67 menu, 61–64, 66 variables, clearing, 64 Typing aids, 167 Typing alphabetic characters, 30 U ;, 56 >, 56 Unacknowledged appointments, 148 Unit conversions, in the Solver, 178 Unknown variables in Solver, 240, 241 Variable, dependent, 134 independent, 134 Variables statistical, 130–34 Variables, built-in, 27 printing, 187 statistical, 128 Variables, Solver, 154 clearing, 163 deleting, 163 names of, 166 shared, 162 Va
to maturity, bond, 108 Y •, 109 ‹, 115 M, 56 y-intercept, in curve-fitting, 132, 134 y-values, in forecasting, 133–34 u, 41, 265 Yield of lease, 74–75 to call, bonds, 108 Z Zero-coupon bond, 113 Index 309 File name : 17BII-Plus-Manual-E-PRINT-030709 Print data : 2003/7/11
This regulation applies only to The Netherlands Batteries are delivered with this product, when empty do not throw them away but collect as small chemical waste. Bij dit produkt zijn batterijen geleverd. Wanneer deze leeg zijn, moet u ze niet weggooien maar inleveren als KCA.
