Texas Instruments Calculator Users Manual Ba2plus
BA II PLUS PROFESSIONAL guidebook (English) BAIIPLUSPROGuidebook_EN BA II PLUS™ PROFESSIONAL Guidebook
Calculator to the manual 2a3466f6-c319-4b68-bc05-82502a7f3a4c
2015-02-05
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BA II PLUS™ PROFESSIONAL Calculator Important Information Texas Instruments makes no warranty, either express or implied, including but not limited to any implied warranties of merchantability and fitness for a particular purpose, regarding any programs or book materials and makes such materials available solely on an “as-is” basis. In no event shall Texas Instruments be liable to anyone for special, collateral, incidental, or consequential damages in connection with or arising out of the purchase or use of these materials, and the sole and exclusive liability of Texas Instruments, regardless of the form of action, shall not exceed the purchase price of this product. Moreover, Texas Instruments shall not be liable for any claim of any kind whatsoever against the use of these materials by any other party. USA FCC Information Concerning Radio Frequency Interference This equipment has been tested and found to comply with the limits for a Class B digital device, pursuant to Part 15 of the FCC rules. These limits are designed to provide reasonable protection against harmful interference in a residential installation. This equipment generates, uses, and can radiate radio frequency energy and, if not installed and used in accordance with the instructions, may cause harmful interference to radio communications. However, there is no guarantee that interference will not occur in a particular installation. If this equipment does cause harmful interference to radio or television reception, which can be determined by turning the equipment off and on, you can try to correct the interference by one or more of the following measures: • Reorient or relocate the receiving antenna. • Increase the separation between the equipment and receiver. • Connect the equipment into an outlet on a circuit different from that to which the receiver is connected. • Consult the dealer or an experienced radio/television technician for help. Caution: Any changes or modifications to this equipment not expressly approved by Texas Instruments may void your authority to operate the equipment. © 2004 Texas Instruments Incorporated ii Table of Contents 1 Overview of Calculator Operations..................................1 Turning On the Calculator ............................................................. 1 Turning Off the Calculator............................................................. 1 Selecting 2nd Functions ................................................................. 2 Reading the Display ....................................................................... 2 Setting Calculator Formats ........................................................... 4 Resetting the Calculator ................................................................ 6 Clearing Calculator Entries and Memories ................................... 6 Correcting Entry Errors................................................................... 7 Math Operations ............................................................................ 8 Memory Operations ..................................................................... 12 Calculations Using Constants....................................................... 13 Last Answer Feature..................................................................... 14 Using Worksheets: Tools for Financial Solutions ........................ 15 ....................................................................................................... 19 2 Time-Value-of-Money and Amortization Worksheets...21 TVM and Amortization Worksheet Variables ............................. 22 Entering Cash Inflows and Outflows........................................... 25 Generating an Amortization Schedule ....................................... 25 Example: Computing Basic Loan Interest.................................... 26 Examples: Computing Basic Loan Payments ............................... 27 Examples: Computing Value in Savings ...................................... 28 Example: Computing Present Value in Annuities....................... 29 Example: Computing Perpetual Annuities.................................. 30 Example: Computing Present Value of Variable Cash Flows ..... 31 Example: Computing Present Value of a Lease With Residual Value........................................................................................ 33 Example: Computing Other Monthly Payments......................... 34 Example: Saving With Monthly Deposits .................................... 35 Example: Computing Amount to Borrow and Down Payment . 36 Example: Computing Regular Deposits for a Specified Future Amount ................................................................................... 37 Example: Computing Payments and Generating an Amortization Schedule........................................................... 38 Example: Computing Payment, Interest, and Loan Balance After a Specified Payment ..................................................... 39 3 Cash Flow Worksheet......................................................41 Cash Flow Worksheet Variables................................................... 41 Uneven and Grouped Cash Flows................................................ 43 Entering Cash Flows ..................................................................... 43 Table of Contents iii Deleting Cash Flows...................................................................... 44 Inserting Cash Flows ..................................................................... 44 Computing Cash Flows ................................................................. 45 Example: Solving for Unequal Cash Flows ................................. 47 Example: Value of a Lease with Uneven Payments .................... 49 4 Bond Worksheet ............................................................. 53 Bond Worksheet Variables ........................................................... 54 Bond Worksheet Terminology ..................................................... 56 Entering Bond Data and Computing Results .............................. 56 Example: Computing Bond Price, Accrued Interest, and Modified Duration .................................................................. 58 5 Depreciation Worksheet ................................................ 59 Depreciation Worksheet Variables .............................................. 59 Entering Data and Computing Results ........................................ 61 Example: Computing Straight-Line Depreciation ....................... 62 6 Statistics Worksheet ....................................................... 65 Statistics Worksheet Variables ..................................................... 65 Regression Models ........................................................................ 67 Entering Statistical Data............................................................... 68 Computing Statistical Results....................................................... 69 7 Other Worksheets ........................................................... 71 Percent Change/Compound Interest Worksheet ........................ 71 Interest Conversion Worksheet.................................................... 74 Date Worksheet ............................................................................ 76 Profit Margin Worksheet ............................................................. 78 Breakeven Worksheet .................................................................. 80 Memory Worksheet ...................................................................... 82 ....................................................................................................... 83 A Appendix — Reference Information.............................. 85 Formulas ........................................................................................ 85 Error Messages .............................................................................. 96 Accuracy Information ................................................................... 98 AOS™ (Algebraic Operating System) Calculations ..................... 98 Battery Information...................................................................... 99 In Case of Difficulty .................................................................... 100 Texas Instruments Support and Service ..................................... 101 Texas Instruments (TI) Warranty Information ........................... 102 Index.............................................................................. 105 iv Table of Contents 1 Overview of Calculator Operations This chapter describes the basic operation of your BA II PLUS™ PROFESSIONAL calculator, including how to: • Turn on and turn off the calculator • Select second functions • Read the display and set calculator formats • Clear the calculator and correct entry errors • Perform math and memory operations • Use the Last Answer feature • Use worksheets Turning On the Calculator Press $. • If you turned off the calculator by pressing $, the calculator returns to the standard-calculator mode with a displayed value of zero. All worksheets and formats for numbers, angle units, dates, separators, and calculation method retain previous values and configurations. • If the Automatic Power Down™ (APD™) feature turned off the calculator, the calculator turns on exactly as you left it, saving display settings, stored memory, pending operations, and error conditions. Turning Off the Calculator Press $. • The displayed value and any error condition clear. • Any unfinished standard-calculator operation and worksheet calculation in progress cancel. Overview of Calculator Operations 1 • The Constant Memory™ feature retains all worksheet values and settings, including the contents of the 10 memories and all format settings. Automatic Power Down™ (APD™) Feature To prolong battery life, the Automatic Power Down (APD) feature turns off the calculator automatically after about five minutes of inactivity. The next time you press $, the calculator turns on exactly as you left it, saving display settings and stored memory and any pending operations or error conditions. Selecting 2nd Functions The primary function of a key is printed on the key itself. For example, the primary function of the $ key is to turn on or turn off the calculator. Most keys include a second function printed above the key. To select a second function, press & and the corresponding key. (When you press &, the 2nd indicator appears in the upper left corner of the display.) For example, pressing & U exits the selected worksheet and returns the calculator to the standardcalculator mode. Note: To cancel after pressing &, press & again. Reading the Display The display shows the selected variable labels with values up to 10 digits. (The calculator displays values exceeding 10 digits in scientific notation.) 2 Overview of Calculator Operations The indicators along the top of the display tell you which keys are active and offer information about the status of the calculator. Indicator Meaning 2nd Press a key to select its second function. INV Press a key to select its inverse trigonometric function. HYP Press a key to select its hyperbolic function. COMPUTE Press % to compute a value for the displayed variable. ENTER Press ! to assign the displayed value to the displayed variable. SET Press & V to change the setting of the displayed variable. #$ Press " or # to display the previous or next variable in the worksheet. Note: To easily scroll up or down through a range of variables, press and hold # or ". DEL Press & W to delete a cash flow or statistical data point. INS Press & X to insert a cash flow or statistical data point. BGN TVM calculations use beginning-of-period payments. When BGN is not displayed, TVM calculations use end-of-period payments (END). RAD Angle values appear in radians. When RAD is not displayed, angle values appear and must be entered in degrees. The displayed value is entered in the selected worksheet. The indicator clears following a computation. The displayed value is computed in the selected worksheet. When a value changes and invalidates a computed value, the_indicator clears. = The displayed variable is assigned the displayed value. – The displayed value is negative. Overview of Calculator Operations 3 Setting Calculator Formats You can change these calculator formats: To Select Press Display Number of decimal places & | DEC 0–9 (Press 9 for floating-decimal) 2 Angle units # DEG DEG (degrees) Default RAD (radians) Dates # US (mm-dd-yyyy) US Eur (dd-mm-yyyy) Number separators # Calculation method # US (1,000.00 ) US Eur (1.000,00) Chn (chain) Chn AOSé (algebraic operating system) 1. To access format options, press & |. The DEC indicator appears with the selected number of decimal places. 2. To change the number of decimal places displayed, key in a value and press !. 3. To access another calculator format, press # or " once for each format. For example, to access the angle unit format, press #. To access the number-separator format, press " " "or # # #. 4. To change the selected format, press & V. 5. To change another calculator format, repeat step 3 and step 4. — or — To return to the standard-calculator mode, press & U. — or — To access a worksheet, press a worksheet key or key sequence. Choosing the Number of Decimal Places Displayed The calculator stores numeric values internally to an accuracy of 13 digits, but you can specify the number of decimal places you want to display. The calculator displays up to 10 digits with the floating-decimal option. Results exceeding 10 digits appear in scientific notation. 4 Overview of Calculator Operations Changing the number of decimal places affects the display only. Except for amortization and depreciation results, the calculator does not round internal values. To round the internal value, use the round function. (See “Rounding & o” on page 10.) Note: All examples in this guidebook assume a setting of two decimal places. Other settings might show different results. Choosing the Angle Units The angle unit value affects the display of results in trigonometric calculations. When you select radians, the RAD indicator appears in the upper right corner of the display. No indicator appears when you select the default setting of degrees. Using Dates The calculator uses dates with the Bond and Date worksheets and the French depreciation methods. To enter dates, use this convention: mm.ddyy (US) or dd.mmyy (European). After you key in the date, press !. Choosing Calculation Methods When you choose the chain (Chn) calculation method, the calculator solves problems in the order that you enter them. (Most financial calculators use Chn.) For example, when you enter 3 H 2 < 4 N, the Chn answer is 20 (3 + 2 = 5, 5 * 4 = 20). Using AOSé (algebraic operating system), the calculator solves problems according to the standard rules of algebraic hierarchy, computing multiplication and division operations before addition and subtraction operations. (Most scientific calculators use AOS.) For example, when you enter 3 H 2 < 4 N, the AOS answer is 11 (2 Q 4 = 8; 3 + 8 = 11). Resetting Default Values To reset default values for all of the calculator formats, press & z with one of the formats displayed. Overview of Calculator Operations 5 Resetting the Calculator Resetting the calculator: • Clears the display, all 10 memories, any unfinished calculations, and all worksheet data. • Restores all default settings • Returns operation to the standard-calculator mode Because the calculator includes alternative methods that let you clear data selectively, use reset carefully to avoid losing data needlessly. (See “Clearing Calculator Entries and Memories” on page 6.)For example, you might reset the calculator before using it for the first time, when starting a new calculation, or when having difficulty operating the calculator and other possible solutions do not work. (See “In Case of Difficulty” on page 100.) Pressing & } ! 1. Press & }. The RST ? and ENTER indicators appear. Note: To cancel reset, press & U. 0.00 appears. 2. Press !. RST and 0.00 appear, confirming that the calculator is reset. Note: If an error condition exists, press P to clear the display before attempting to reset. Performing a Hard Reset You can also reset the calculator by gently inserting a pointed object (such as an unfolded paper clip or similar object) in the hole marked RESET in back of the calculator. Clearing Calculator Entries and Memories Note: To clear variables selectively, see the specific worksheet chapters in this guidebook. To clear Press One character at a time, starting with the last digit * keyed in An incorrect entry, error condition, or error message 6 P Overview of Calculator Operations To clear Press The prompted worksheet and reset default values &z Calculator format settings and reset default values &| &z • Out of the prompted worksheet and return to standard-calculator mode • All pending operations in standard-calculator mode • In a prompted worksheet, the variable value keyed in but not entered (the previous value appears) • Any calculation started but not completed &U PP TVM worksheet variables and reset default values &U &^ One of the 10 memories (without affecting the others) Q D and a memory number key (0–9) Correcting Entry Errors You can correct an entry without clearing a calculation, if you make the correction before pressing an operation key (for example, H or 4). • To clear the last digit displayed, press *. • To clear the entire number displayed, press P. Note: Pressing P after you press an operation key clears the calculation in progress. Example: You mean to calculate 3 Q 1234.56 but instead enter 1234.86. To Press Begin the expression. 3< Enter a number. 1234.86 Erase the entry error. ** Key in the correct number. 56 1,234.56 Compute the result. N 3,703.68 Overview of Calculator Operations Display 3.00 1,234.86 1,234. 7 Math Operations When you select the chain (Chn) calculation method, the calculator evaluates mathematical expressions (for example, 3 + 2 Q 4) in the order that you enter them. Examples of Math Operations These operations require you to press N to complete. To Press Add 6 + 4 6H4N 10.00 Subtract 6 N 4 6B4N 2.00 Multiply 6 Q 4 6<4N 24.00 Divide 6 P 4 664N 1.50 3 ; 1.25 N 3.95 Find universal power: 3 1.25 Display Use parentheses: 7 Q (3 + 5) 7 <9 3 H 5 :N 56.00 Find percent: 4% of $453 453 < 4 2 N 18.12 Find percent ratio: 14 to 25 14 6 25 2 N 56.00 Find price with percent add-on: $498 + 7% sales tax 498 H 7 2 Find price with percent discount: $69.99 N 10% 69.99 B 10 2 Find number of combinations where: n = 52, r = 5 52 & s 5 N 34.86 532.86 N 7.00 62.99 N 2,598,960.00 Find number of permutations where: 8 & m 3 N n = 8, r = 3 336.00 These operations do not require you to press N to complete. To Square 6.3 Press 6.3 4 2 Display 39.69 15.5 3 3.94 Find reciprocal: 1/3.2 3.2 5 0.31 Find factorial: 5! 5 &g Find natural logarithm: ln 203.45 203.45 > Find square root: 8 15.5 120.00 5.32 Overview of Calculator Operations To Press Display .69315 & i 2.00 Round 2 P 3 to the set decimal format 2 6 3 N&o 0.67 Generate random number* &a 0.86 Store seed value D&a 0.86 Find sine:** sin(11.54°) 11.54 & d 0.20 Find cosine:** cos(120°) 120 & e Find tangent:** tan(76°) 76 & f Find natural antilogarithm: e .69315 .2 8 d -1 Find arcsine:** sin (.2) .5 S 8 e -1 Find arccosine:** cos (-.5) 4 8f -1 Find arctangent:** tan (4) -0.50 4.01 11.54 120.00 75.96 Find hyperbolic sine: sinh(.5) .5 & c d 0.52 Find hyperbolic cosine: cosh(.5) .5 & c e 1.13 Find hyperbolic tangent: tanh(.5) .5 & c f 0.46 5 &c8d 2.31 5 &c8e 2.29 .5 & c 8 f 0.55 -1 Find hyperbolic arcsine: sinh (5) -1 Find hyperbolic arccosine: cosh (5) -1 Find hyperbolic arctangent: tanh (.5) * The random number you generate might be different. ** Angles can be computed in degrees or radians. Examples show angles in degrees. (See “Choosing the Angle Units” on page 5.) Universal Power ; Press ; to raise the displayed positive number to any power (for example, 2-5 or 2(1/3)). Note: Because the reciprocal of an even number (such as, 1/2, 1/4, 1/6) is a complex number, you can only raise a negative number to an integer power or the reciprocal of an odd number. Overview of Calculator Operations 9 Parentheses 9 : Use parentheses to control the order in which the calculator evaluates a numeric expression in division, multiplication, powers, roots, and logarithm calculations. The calculator includes up to 15 levels of parentheses and up to 8 pending operations. Note: You do not have to press : for expressions ending in a series of closed parentheses. Pressing N closes parentheses automatically, evaluates the expression, and displays the final result. To view intermediate results, press : once for each open parenthesis. Factorial & g The number for which you compute a factorial must be a positive integer less than or equal to 69. Random Numbers & a The calculator generates a random real number between zero and one (0zero EXP Y = a bx All Y values > zero PWR Y = a Xb All X and Y values > zero The calculator interprets the X value as the independent variable and the Y value as the dependent variable. The calculator computes the statistical results using these transformed values: • LIN uses X and Y. Statistics Worksheet 67 • Ln uses ln(X) and Y. • EXP uses X and ln(Y). • PWR uses ln(X) and ln(Y). The calculator determines the values for a and b that create the line or curve that best fits the data. Correlation Coefficient The calculator also determines r, the correlation coefficient, which measures the goodness of fit of the equation with the data. Generally: • The closer r is to 1 or -1, the better the fit. • The closer r is to zero, the worse the fit. Entering Statistical Data Because the Statistics worksheet lets you enter and display up to 50 data points, and then stores the values until you clear the worksheet or change the values, you probably will not have to perform every step for each Statistics calculation. 1. To select the data-entry portion of the Statistics worksheet, press & j. X01 is displayed along with any previous value. 2. To clear the worksheet, press & z. 3. Key in a value for X01 and press !. • For one-variable data, X01 is the first data point. • For two-variable data, X01 is the first X value. 4. To display the Y01 variable, press #. 5. Key in a value for Y01 and press !. • For one-variable data, you can enter the number of times the X value occurs (frequency). The default value is 1. • For two-variable data, enter the first Y value. 6. To display the next X variable, press #. 7. Repeat steps 3 through 5 until you enter all of the data points. Note: To easily scroll up or down through a range of variables, press and hold # or ". 68 Statistics Worksheet Computing Statistical Results Selecting a Statistics Calculation Method 1. Press & k to select the statistical calculation portion of the Statistics worksheet. 2. The last selected statistics calculation method is displayed (LIN, Ln, EXP, PWR, or 1-V). 3. Press & V repeatedly until the statistics calculation method you want is displayed. 4. If you are analyzing one-variable data, select 1-V. 5. Press # to begin computing results. Computing Results To compute results based on the current data set, press # repeatedly after you have selected the statistics calculation method. The calculator computes and displays the results of the statistical calculations (except for X' and Y') automatically when you access them. For one-variable statistics, the calculator computes and displays only the values for n, v, Sx, sX, GX, and GX2. Computing Y' 1. To select the Statistics worksheet, press & k. 2. Press " or # until X' is displayed. 3. Key in a value for X' and press !. 4. Press # to display the Y' variable. 5. Press % to compute a predicted Y' value. Computing X' 1. To select the Statistics worksheet, press & k. 2. Press " or # until Y' is displayed. 3. Key in a value for Y' and press !. 4. Press " to display the X' variable. 5. Press % to compute an X' value. Statistics Worksheet 69 70 Statistics Worksheet 7 Other Worksheets The calculator also includes these worksheets: • Percent Change/Compound Interest worksheet (& q) • Interest Conversion worksheet (& v) • Date worksheet (& u) • Profit Margin worksheet (& w) • Breakeven worksheet (& r) • Memory worksheet (& {) Percent Change/Compound Interest Worksheet Use the Percent Change/Compound Interest worksheet to solve percent change, compound interest, and cost-sellmarkup problems. • To access the Percent Change/Compound Interest worksheet, press & q. • To access the Percent Change/Compound Interest variables, press # or ". Percent Change/Compound Interest Worksheet Variables Variable Key Display Variable Type Old value/Cost &q OLD Enter/compute New value/Selling price # NEW Enter/compute Percent change/Percent markup # %CH Enter/compute Number of periods # #PD Enter/compute Note: This guidebook categorizes variables by their method of entry. (See “Types of Worksheet Variables” on page 17.) Other Worksheets 71 Resetting the Percent Change/Compound Interest Worksheet Variables • • To reset the Percent Change/Compound Interest variables to default values, press & z while in the Percent Change/Compound Interest worksheet. Variable Default Variable Default OLD 0 %CH 0 NEW 0 #PD 1 To reset default values for all calculator variables and formats, press & } !. Entering Values • For percent-change calculations, enter values for any two of the three variables (OLD, NEW, and %CH) and compute a value for the unknown variable (leave #PD=1). A positive percent change represents a percentage increase; a negative percent change represents a percentage decrease. • For compound-interest calculations, enter values for the three known variables and compute a value for the unknown fourth variable. • – OLD= present value – NEW= future value – %CH= interest rate per period – #PD= number of periods For cost-sell-markup calculations, enter values for two of the three variables (OLD, NEW, and %CH) and compute a value for the unknown. – OLD = cost – NEW= selling price – %CH= percent markup – #PD= 1 Computing Values 1. To select the Percent Change/Compound Interest worksheet, press & q. The current value for OLD is displayed. 2. To clear the worksheet, press & z. 72 Other Worksheets 3. 4. To enter values for the known variables, press # or " until the variable you want is displayed, then key in a value, and press !. (Do not enter a value for the variable you wish to solve.) • Percent Change — Enter values for two of these three variables: OLD, NEW, and %CH. Leave #PD set to 1. • Compound Interest — Enter values for three of these four variables: OLD, NEW, %CH, and #PD. • Cost-Sell-Markup — Enter values for two of these three variables: OLD, NEW, and %CH. Leave #PD set to 1. To compute a value for the unknown variable, press # or " until the variable you want is displayed and press %. The calculator displays the value. Example: Computing Percent Change First, determine the percentage change from a forecast amount of $658 to an actual amount of $700. Second, determine what the new amount would be if it were 7% below the original forecast. To Press Display Select Percent Change/Compound Interest worksheet. &q OLD= 0 Enter original forecast amount. 658 ! OLD= 658.00 Enter actual amount. # 700 ! NEW= 700.00 Compute percent change. #% %CH= 6.38 Enter -7 as percent change. 7 S! %CH= -7.00 Compute new actual amount. "% NEW= 611.94 Answer: $700 represents a 6.38% increase over the original forecast of $658. A decrease of 7% would result in a new actual amount of $611.94. Example: Computing Compound Interest You purchased stock in 1995 for $500. Five years later, you sell the stock for $750. What was the annual growth rate? To Press Select Percent Change/Compound & q Interest worksheet. Display OLD= 0 Enter stock purchase price. 500 ! OLD= 500.00 Enter stock selling price. # 750 ! NEW= 750.00 Other Worksheets 73 To Press Display Enter number of years. ## 5 ! #PD= 5.00 Compute annual growth rate. "% %CH= 8.45 Answer: The annual growth rate is 8.45%. Example: Computing Cost-Sell-Markup The original cost of an item is $100; the selling price is $125. Find the markup. To Press Display Select Percent Change/Compound Interest worksheet. &q OLD= 0 Clear worksheet variables. &z OLD= 0.00 Enter original cost. 100 ! OLD= 100.00 Enter selling price. # 125 ! NEW= 125.00 Compute percent markup. #% %CH= 25.00 Answer: The markup is 25%. Interest Conversion Worksheet The Interest Conversion worksheet converts interest rates between nominal rate (or annual percentage rate) and annual effective rate. • To access the Interest Conversion worksheet, press & v. • To select interest conversion variables, press # or ". Variable Key Display Variable Type Nominal rate &v NOM Enter/compute Annual effective rate # EFF Enter/compute Compounding periods per year # C/Y Enter-only Note: The calculator categorizes variables by their method of entry. 74 Other Worksheets Comparing the Nominal Interest Rate of Investments Comparing the nominal interest rate (annual percentage rate) of investments is misleading when the investments have the same nominal rate but different numbers of compounding periods per year. To make a more valid comparison, convert the nominal interest rate (NOM) to the annual effective interest rate (EFF) for each investment. • The nominal interest rate (NOM) is the interest rate per compounding period multiplied by the number of compounding periods per year. • The annual effective interest rate (EFF) is the compound annual interest rate that you actually earn for the period of time stated. Resetting Variables • • To reset all calculator variables and formats to default values, including the Interest Conversion worksheet variables, press & } !. Variable Default NOM 0 EFF 0 C/Y 1 To clear the NOM and EFF variables and reset default values without affecting C/Y, press & z in the Interest Conversion worksheet. Converting Variables You can convert a nominal rate to an annual effective rate or vice versa. Entering Values for Nom and EFF Enter a value for NOM or EFF as an annual rate. Converting Interest Rates 1. To access the Interest Conversion worksheet, press & v. The current NOM value appears. 2. To clear the worksheet, press & z. 3. Enter a value for the known interest rate (either NOM or EFF). 4. To enter a value for a known variable, press # or " until NOM or EFF is displayed, key in a value, and press !. 5. Press # to display C/Y. If necessary, change the value and press !. Other Worksheets 75 6. To compute a value for the unknown variable (interest rate), press # or " until NOM or EFF is displayed, and then press %. The calculator displays the computed value. Example: A bank offers a certificate that pays a nominal interest rate of 15% with quarterly compounding. What is the annual effective interest rate? To Press Display Select Interest Conversion worksheet. &v NOM= 0 Enter nominal interest rate. 15 ! NOM= 15.00 Enter number of compounding periods per year. ##4 ! C/Y= 4.00 Compute annual effective interest rate. "% EFF= 15.87 Answer: A nominal interest rate of 15% compounded quarterly is equivalent to an annual effective interest rate of 15.87%. Date Worksheet Use the Date worksheet to find the number of days between two dates. You can also compute a date and day of the week based on a starting date and a specified number of days. • To access the Date worksheet, press & u. • To access the date variables, press # or ". • To select the day-count method (ACT and 360), press & V once for each option. Date Worksheet Variables Variable Key Display Variable Type Date 1 &u DT1 Enter/compute Date 2 # DT2 Enter/compute Days between dates # DBD Enter/compute Actual/actual day-count method # ACT* Setting # 360* Setting 30/360 day-count method 76 Other Worksheets Note: The calculator categorizes variables by their method of entry. (See “Types of Worksheet Variables” on page 17.) Resetting the Date Worksheet Variables • • To reset default values for all calculator variables and formats, including the Date worksheet variables, press & } !. Variable Default Variable Default DT1 12-31-1990 DBD 0 DT2 12-31-1990 Day-count method ACT To clear Date worksheet variables and reset default values without affecting the day-count method, press & z while in the Date worksheet. Entering Dates • The calculator assumes that DT1 is earlier than DT2. • Enter dates for DT1 and DT2 in the selected US or European date format. • When you compute a date for DT1 or DT2, the calculator displays a three-letter abbreviation for the day of the week (for example, WED). Selecting the Day-Count Method Affects Calculations • When you select ACT as the day-count method, the calculator uses the actual number of days in each month and each year, including adjustments for leap years. • When you select 360 as the day-count method, the calculator assumes 30 days per month (360 days per year). You can compute DBD using this day-count method, but not DT1 or DT2. Computing Dates 1. To select the Date worksheet, press & u. The DT1 value is displayed. 2. To clear the worksheet, press & z. 3. Enter values for two of the three variables: DT1, DT2, and DBD. Note: Do not enter a value for the variable you wish to solve for. 4. To enter a value for a variable, press # or " to display the variable. 5. Key in a value and press !. Other Worksheets 77 6. To change the day-count method setting, press # until ACT or 360 is displayed. 7. To compute a value for the unknown variable, press # or " to display the variable, and then press %. The calculator displays the computed value. Example: Computing Days between Dates A loan made on September 4, 2003 defers the first payment until November 1, 2003. How many days does the loan accrue interest before the first payment? To Press Display Select Date worksheet. &u DT1= 12-31-1990 Enter first date. 9.0403 ! DT1= 9-04-2003 Enter second date. # 11.0103 ! DT2= 11-01-2003 Select actual/actual day-count # # method. ACT Compute days between dates. " % DBD= 58.00 Answer: Because there are 58 days between the two dates, the loan accrues interest for 58 days before the first payment. Profit Margin Worksheet The Profit Margin worksheet computes cost, selling price, and gross profit margin. Note: To perform markup calculations, use the Percent Change/Compound Interest worksheet. • To access the Profit Margin worksheet, press & w. • To access profit margin variables, press " or #. • Enter values for the two known variables, and then compute a value for the unknown variable. Profit Margin Worksheet Variables Variable Key Display Variable Type Cost &w CST Enter/compute Selling price # SEL Enter/compute 78 Other Worksheets Variable Key Profit margin # Display Variable Type MAR Enter/compute Note: This guidebook categorizes calculator variables by their method of entry. Gross Profit Margin and Markup The terms margin and markup often are used interchangeably, but each has a distinct meaning. • Gross profit margin is the difference between selling price and cost, expressed as a percentage of the selling price. • Markup is the difference between selling price and cost, expressed as a percentage of the cost. Clearing Profit Margin Worksheet Variables • To clear the Profit Margin worksheet variables and reset default values, press & z. All Profit Margin worksheet variables default to zero. • To reset default values for all calculator variables and formats, including the Profit Margin worksheet variables, press & } !. Computing Profit Margin 1. To select the Profit Margin worksheet, press & w. The CST value appears. 2. To enter a value for one of the two known variables, press # or " to select a variable, then key in a value and press !. 3. Repeat step 2 for the second known variable. 4. To compute a value for the unknown variable, press # or " to select the variable and press %. The calculator displays the computed value. Example: Computing Profit Margin The selling price of an item is $125. The gross profit margin is 20%. Find the original cost. To Press Display Select Profit Margin worksheet. &w CST= 0.00 Enter selling price. # 125 ! SEL= 125.00 Enter profit margin. # 20 ! MAR= Other Worksheets 20.00 79 To Press Display Compute cost. ""% CST= 100.00 Answer: The original cost is $100. Breakeven Worksheet The Breakeven worksheet computes the breakeven point and sales level needed to earn a given profit by analyzing relationships between fixed costs, variable costs per unit, quantity, price, and profit. You operate at a loss until you reach the breakeven quantity (that is, total costs = total revenues). • To access the Breakeven worksheet, press & r. • To access breakeven variables, press " or #. • Enter known values for the four known variables, then compute a value for the fifth, unknown variable. Note: To solve for quantity (Q), enter a value of zero for profit (PFT). Breakeven Worksheet Variables Variable Key Display Variable Type Fixed cost & r FC Enter/compute Variable cost per unit # VC Enter/compute Unit price # P Enter/compute Profit # PFT Enter/compute Quantity # Q Enter/compute Note: This guidebook categorizes calculator variables by their method of entry. Resetting the Breakeven Worksheet Variables • To reset default values for all Breakeven worksheet variables, press & z. All Breakeven worksheet variables default to zero. • To clear all calculator variables and formats and reset default values, including the Breakeven worksheet variables, press & } !. 80 Other Worksheets Computing Breakeven 1. To access the Breakeven worksheet, press & r. The FC variable appears. 2. Press # or " to select a known variable, key in the value, and press !. 3. Repeat step 3 for each of the remaining known variables. 4. To compute a value for the unknown variable, press # or " until the variable is displayed, and then press %. The calculator displays the computed value. Example: Computing Breakeven Quantity A canoe company sells paddles for $20 each. The unit variable cost is $15, and the fixed costs are $3,000. How many paddles must be sold to break even? To Press Display Access Breakeven worksheet. &r FC= 0 Enter fixed costs. 3000 ! FC= 3,000.00 Enter variable cost per unit. # 15 ! VC= 15.00 Enter price. # 20 ! P= 20.00 Leave profit as is. # PFT= Compute quantity. #% Q= 0.00 600.00 Answer: 600 paddles must be sold to break even. Other Worksheets 81 Memory Worksheet The Memory worksheet lets you compare and recall stored values by accessing the calculator’s 10 memories. All memory variables are enter-only. (See “Types of Worksheet Variables” on page 17.) • To access the Memory worksheet, press & {. • To access memory variables, press " or #. Note: You can access memories individually using D, J, and the digit keys. (See “Memory Operations” on page 12.) Memory Worksheet Variables Variables Key Display Variable Type Memory 0 &{ M0 Enter-only Memory 1 # M1 Enter-only Memory 2 # M2 Enter-only Memory 3 # M3 Enter-only Memory 4 # M4 Enter-only Memory 5 # M5 Enter-only Memory 6 # M6 Enter-only Memory 7 # M7 Enter-only Memory 8 # M8 Enter-only Memory 9 # M9 Enter-only Note: This guidebook categorizes calculator variables by their method of entry. (See “Types of Worksheet Variables” on page 17.) Clearing the Memory Worksheet Variables To clear all 10 memories at once, press & z in the Memory worksheet. Using the Memory Worksheet 1. To select the Memory worksheet, press & {. M0 apears. 2. Perform any of the following operations: • 82 To clear all 10 memories at once, press & z. Other Worksheets • To view the contents of the memories, press # or " once for each memory. • To store a value, select a memory (M0-M9), key in a value, and press !. • Memory arithmetic. (See “Memory Arithmetic” on page 12.) Examples: Using the Memory Worksheet To Press Display Access Memory worksheet &{ M0= 0 Select M4. #### M4= 0 Clear M4. 0! M4= 0.00 Store 95. 95! M4= 95.00 Add 65. H6 5 ! M4= 160.00 Subtract 30. B3 0 ! M4= 130.00 Multiply by 95. <95! M4= 12,350.00 Divide by 65. 66 5 ! M4= 190.00 Raise to 2nd power. ;2 ! M4= 36,100.00 Other Worksheets 83 84 Other Worksheets A Appendix — Reference Information This appendix includes supplemental information to help you use your BA II PLUSé and BA II PLUSé PROFESSIONAL calculator: • Formulas • Error conditions • Accuracy information • IRR (internal-rate-of-return) calculations • Algebraic operating system (AOS™) • Battery information • In case of difficulty • TI product service and warranty information Formulas This section lists formulas used internally by the calculator. Time Value of Money i = [e ( y × ln ( x + 1 ) ) ]–1 where: PMT ƒÄ0 y =C/Y P P/Y x =(.01 Q I/Y) P C/Y C/Y =compounding periods per year P/Y =payment periods per year I/Y =interest rate per year (1 ÷ N) i = ( – FV ÷ PV ) –1 where: PMT =0 The iteration used to compute i: –N 1 – (1 + i) –N 0 = PV + PMT × G i ------------------------------ + FV × ( 1 + i ) i Appendix — Reference Information 85 I/Y = 100 × C ⁄ Y × [ e ( y × ln ( x + 1 ) ) – 1] where: x = i y =P/Y P C/Y Gi = 1 + i Q k where: k =0 for end-of-period payments k =1 for beginning-of-period payments PMT × G i – FV × i ln --------------------------------------------- PMT × G i + PV × i N = ---------------------------------------------------------ln ( 1 + i ) where: i ƒ0 N = L(PV + FV) P PMT where: i =0 –i PV + FV PMT = ----- × PV + --------------------------N Gi (1 + i) – 1 where: i ƒ0 PMT = L(PV + FV) P N where: i =0 PMT × G PMT × G 1 PV = ------------------------i – FV × ------------------- – ------------------------i N i i (1 + i) where: i ƒ0 PV = L(FV + PMT Q N) where: i =0 86 Appendix — Reference Information PMT × G PMT × G N FV = ------------------------i – ( 1 + i ) × PV + ------------------------i i i where: i ƒ0 FV = L(PV + PMT Q N) where: i =0 Amortization If computing bal(), pmt2 = npmt Let bal(0) = RND(PV) Iterate from m = 1 to pmt2 I m = RND [ RND12 ( – i × bal ( m – 1 ) ) ] bal ( m ) = bal ( m – 1 ) – I m + RND ( PMT ) then: bal( ) =bal(pmt2) GPrn( ) =bal(pmt2) N bal(pmt1) GInt( ) =(pmt2 N pmt1 +1) Q RND(PMT) N GPrn( ) where: RND =round the display to the number of decimal places selected RND12 =round to 12 decimal places Balance, principal, and interest are dependent on the values of PMT, PV, I/Y, and pmt1 and pmt2. Cash Flow N NPV = CF 0 + ∑ CFj ( 1 + i ) -S – 1 (1 j j=1 j ni where: S j = ∑ i = 1 0 -n – (1 + i) j) ---------------------------------i j≥1 j = 0 Appendix — Reference Information 87 Net present value depends on the values of the initial cash flow (CF0), subsequent cash flows (CFj), frequency of each cash flow (nj), and the specified interest rate (i). p NFV = ( 1 + i ) × NPV where: i is the periodic interest rate used in the calculation of NPV. N p = ∑ nk k=1 where: n k is the frequency of the kth cash flow. IRR = 100 × i, where i satisfies npv() = 0 Internal rate of return depends on the values of the initial cash flow (CF0) and the subsequent cash flows (CFj). i = I/Y ÷ 100 The calculator uses this formula to compute the modified internal rate of return: – NPV (positive, rrate MOD = ----------------------------------------------------NPV (negative, frate) 1⁄N × ( 1 + rrate ) – 1 where: positive = positive values in the cash flows negative = negative values in the cash flows N = number of cash flows rrate = reinvestment rate frate = finance rate NPV (values, rate) = Net present value of the values in the rate described 88 Appendix — Reference Information Bonds1 Price (given yield) with one coupon period or less to redemption: 100 × R RV + -----------------M A 100 × R PRI = --------------------------------------- – --- × -----------------E M Y DSR 1 + ----------- × ----- E M where: PRI =dollar price per $100 par value RV =redemption value of the security per $100 par value (RV = 100 except in those cases where call or put features must be considered) R =annual interest rate (as a decimal; CPN _ 100) M =number of coupon periods per year standard for the particular security involved (set to 1 or 2 in Bond worksheet) DSR =number of days from settlement date to redemption date (maturity date, call date, put date, etc.) E =number of days in coupon period in which the settlement date falls Y =annual yield (as a decimal) on investment with security held to redemption (YLD P 100) A =number of days from beginning of coupon period to settlement date (accrued days) Note: The first term computes present value of the redemption amount, including interest, based on the yield for the invested period. The second term computes the accrued interest agreed to be paid to the seller. Yield (given price) with one coupon period or less to redemption: R RV R PRI A -------- + ----- – ---------- + --- × ----- 100 M 100 E M M×E Y = --------------------------------------------------------------------------- × -------------DSR R PRI A ---------- + --- × ----- 100 E M 1. Source for bond formulas (except duration): Lynch, John J., Jr., and Jan H. Mayle. Standard Securities Calculation Methods. New York: Securities Industry Association, 1986. Appendix — Reference Information 89 Price (given yield) with more than one coupon period to redemption: RV ------------------------------------------DSCY N – 1 + ----------E PRI = 1 + ----- + M R A – 100 × ----- × --M E N ∑ R 100 × ----M -----------------------------------------Y- 1 + --- M K = 1 K – 1 + DSC -----------E where: N =number of coupons payable between settlement date and redemption date (maturity date, call date, put date, etc.). (If this number contains a fraction, raise it to the next whole number; for example, 2.4 = 3) DSC =number of days from settlement date to next coupon date K =summation counter Note: The first term computes present value of the redemption amount, not including interest. The second term computes the present values for all future coupon payments. The third term computes the accrued interest agreed to be paid to the seller. Yield (given price) with more than one coupon period to redemption: Yield is found through an iterative search process using the “Price with more than one coupon period to redemption” formula. Accrued interest for securities with standard coupons or interest at maturity: R A AI = PAR × ----- × --M E where: AI =accrued interest PAR =par value (principal amount to be paid at maturity) Modified duration:2 Duration Modified Duration = -----------------------Y 1 + ----M 2. Source for duration: Strong, Robert A., Portfolio Construction, Management, and Protection, South-Western College Publishing, Cincinnati, Ohio, 2000. 90 Appendix — Reference Information where Duration is calculated using one of the following formulas used to calculate Macaulay duration: • For a bond price with one coupon period or less to redemption: Y- Dur = 1 + --- M • 100 × R Rv + -----------------M Dsr × -----------------------------------------2Dsr ×Y 1 + ------------------- E×M ⋅ ---------------------------------------------------------------E × M × Pri For a bond price with more than one coupon period to redemption: Depreciation RDV = CST N SAL N accumulated depreciation Values for DEP, RDV, CST, and SAL are rounded to the number of decimals you choose to be displayed. In the following formulas, FSTYR = (13 N MO1) P 12. Straight-line depreciation CST – SAL --------------------------LIF CST – SAL LIF First year: --------------------------- × FSTYR Last year or more: DEP = RDV Appendix — Reference Information 91 Sum-of-the-years’-digits depreciation LIF + 2 – YR – FSTYR ) × ( CST – SAL ) -----------------------------------------------------------------------------------------------------( ( LIF × ( LIF + 1 ) ) ÷ 2 ) LIF × ( CST – SAL ) ( ( LIF × ( LIF + 1 ) ) ÷ 2 ) First year: ------------------------------------------------------------ × FSTYR Last year or more: DEP = RDV Declining-balance depreciation RBV × DB% ------------------------------LIF × 100 where: RBV is for YR - 1 CST × DB% LIF × 100 First year: ------------------------------- × FSTYR CST × DB% LIF × 100 Unless ------------------------------- > RDV ; then use RDV Q FSTYR If DEP > RDV, use DEP = RDV If computing last year, DEP = RDV Statistics Note: Formulas apply to both x and y. Standard deviation with n weighting (s x): ∑ 2 x 2 x – -------------------n ----------------------------------------n ∑ 92 1⁄2 Appendix — Reference Information Standard deviation with n-1 weighting (s x): ∑ 2 x x 2 – -------------------n ----------------------------------------n–1 ∑ 1⁄2 (∑ x ) Mean: x = --------------- n Regressions Formulas apply to all regression models using transformed data. n ( ∑ xy ) – ( ∑ y ) ( ∑ x ) b = --------------------------------------------------------2 n ( ∑ x2 ) – ( ∑ x ) (∑ y – b∑ x) a = --------------------------------n bδ r = --------x δy Interest Rate Conversions EFF = 100 × ( e C ⁄ Y × In ( x ÷ 1 ) – 1 ) where: x =.01 Q NOM P CˆY NOM = 100 × C ⁄ Y × ( e 1 ÷ C ⁄ Y × In ( x + 1 ) – 1 ) where: x =.01 Q EFF Percent Change %CH NEW = OLD 1 + -------------- 100 #PD Appendix — Reference Information 93 where: OLD =old value NEW =new value %CH =percent change #PD =number of periods Profit Margin Selling Price – Cost Gross Profit Margin = ----------------------------------------------- × 100 Selling Price Breakeven PFT = P Q N (FC + VC Q) where: PFT =profit P =price FC =fixed cost VC =variable cost Q =quantity Days between Dates With the Date worksheet, you can enter or compute a date within the range January 1, 1950, through December 31, 2049. Actual/actual day-count method Note: The method assumes the actual number of days per month and per year. DBD (days between dates) = number of days II - number of days I Number of Days I= (Y1 - YB) Q 365 + (number of days MB to M1) + DT1 ( Y1 – YB ) 4 + ------------------------ Number of Days II=(Y2 - YB) Q 365 + (number of days MB to M2) + DT2 ( Y2 – YB ) 4 + ------------------------ 94 Appendix — Reference Information where: M1 =month of first date DT1 =day of first date Y1 =year of first date M2 =month of second date DT2 =day of second date Y2 =year of second date MB =base month (January) DB =base day (1) YB =base year (first year after leap year) 30/360 day-count method3 Note: The method assumes 30 days per month and 360 days per year. DBD = ( Y2 – Y1 ) × 360 + ( M2 + M1 ) × 30 + ( DT2 – DT1 ) where: M1 =month of first date DT1 =day of first date Y1 =year of first date M2 =month of second date DT2 =day of second date Y2 =year of second date Note: If DT1 is 31, change DT1 to 30. If DT2 is 31 and DT1 is 30 or 31, change DT2 to 30; otherwise, leave it at 31. 3. Source for 30/360 day-count method formula: Lynch, John J., Jr., and Jan H. Mayle. Standard Securities Calculation Methods. New York: Securities Industry Association, 1986 Appendix — Reference Information 95 Error Messages Note: To clear an error message, press P. Error Possible Causes Error 1 • A result is outside the calculator range (± 9.9999999999999E99). • Tried to divide by zero (can occur internally). • Tried to compute 1/x when x is zero. • Statistics worksheet: a calculation included X or Y values that are all the same. Error 2 • Tried to compute x! when x is not an integer 0-69. Invalid argument • Tried to compute LN of x when x is not > 0. • Tried to compute y x when y < 0 and x is not an integer or the inverse of an integer. • Tried to compute Overflow • x when x < 0. Amortization worksheet: tried to compute BAL, PRN, and INT when P2 < P1. • Depreciation worksheet: a calculation included SAL > CST. Error 3 • Too many pending operations More than 15 active levels of parentheses were tried in a calculation. • A calculation tried to use more than 8 pending operations. Error 4 • Amortization worksheet: the value entered for P1 or P2 is outside the range 1-9,999. • TVM worksheet: the P/Y or C/Y value 0. • Cash Flow worksheet: the Fnn value is outside the range 0.5-9,999. • Bond worksheet: the RV, CPN, or PRI value _0. • Date worksheet: the computed date is outside the range January 1, 1950 through December 31, 2049. • Depreciation worksheet: the value entered for: declining balance percent 0; LIF 0; YR _ 0; CST < 0; SAL < 0; or M01 1 M01 13. Out of range 96 • Interest Conversion worksheet: the C/Y value 0. • The DEC value is outside the range 0-9. Appendix — Reference Information Error Possible Causes Error 5 • No solution exists TVM worksheet: the calculator computed I/Y when FV, (N Q PMT), and PV all have the same sign. (Make sure cash inflows are positive and outflows are negative.) • TVM, Cash Flow, and Bond worksheets: the LN (logarithm) input is not > 0 during calculations. • Cash Flow worksheet: the calculator computed IRR without at least one sign change in the cash-flow list. • Bond and Date worksheets: a date is invalid (for example, January 32) or in the wrong format (for example, MM.DDYYYY instead of MM.DDYY. • Bond worksheet: the calculator attempted a calculation with a redemption date earlier than or the same as the settlement date. Error 7 • Iteration limit exceeded TVM worksheet: the calculator computed I/Y for a very complex problem involving many iterations. • Cash Flow worksheet: the calculator computed IRR for a complex problem with multiple sign changes or for the BA II PLUS™ PROFESSIONAL calculator PB/DPB with no payback period based on input cash flow values. • Bond worksheet: the calculator computed YLD for a very complex problem. Error 8 • Canceled iterative calculation TVM worksheet: $ was pressed to stop the evaluation of I/Y. • Amortization worksheet: $ was pressed to stop the evaluation of BAL or INT. • Cash Flow worksheet: $ was pressed to stop the evaluation of IRR. • Bond worksheet: $ was pressed to stop the evaluation of YLD. • Depreciation worksheet: $ was pressed to stop the evaluation of DEP or RDV. Error 6 Invalid date Appendix — Reference Information 97 Accuracy Information The calculator stores results internally as 13-digit numbers but displays them rounded to 10 digits or fewer, depending on the decimal format. The internal digits, or guard digits, increase the calculator’s accuracy. Additional calculations use the internal value, not the value displayed. Rounding If a calculation produces a result with 11-digits or more, the calculator uses the internal guard digits to determine how to display the result. If the eleventh digit of the result is 5 or greater, the calculator rounds the result to the next larger value for display. For example, consider this problem. 1P3Q3=? Internally, the calculator solves the problem in two steps, as shown below. 1. 1 P 3 = 0.3333333333333 2. 0.3333333333333 Q 3 = 0.9999999999999 The calculator rounds the result and displays it as 1. This rounding enables the calculator to display the most accurate result. Although most calculations are accurate to within ±1 in the last displayed digit, higher-order mathematical functions use iterative calculations, in which inaccuracies can accumulate in the guard digits. In most cases, the cumulative error from these calculations is maintained beyond the 10digit display so that no inaccuracy is shown. AOS™ (Algebraic Operating System) Calculations When you select the AOS calculation method, the calculator uses the standard rules of algebraic hierarchy to determine the order in which it performs operations. Algebraic Hierarchy The table shows the order in which the calculator performs operations using the AOS calculation method. Priority Operations 1 (highest) x2, x!, 1/x, %, 2 nCr, nPr 3 Yx 98 ‡x, LN, e2, HYP, INV, SIN, COS, TAN Appendix — Reference Information Priority Operations 4 Q, P 5 +, - 6 ) 7 (lowest) = Battery Information Replacing the Battery Replace the battery with a new CR2032 lithium battery. Caution: Risk of explosion if replaced by an incorrect type. Replace only with the same or equivalent type recommended by Texas Instruments. Dispose of used batteries according to local regulations. Note: The calculator cannot retain data when the battery is removed or discharged. Replacing the battery has the same effect as resetting the calculator. 1. Turn off the calculator and turn it over with the back facing you. 2. Slide the battery cover up and remove it from the back case. 3. Remove the battery. 4. Install the new battery with the positive sign (+) sign showing. 5. Replace the battery cover. Caution: Risk of explosion if replaced by an incorrect type. Replace only with the same or equivalent type recommended by Texas Instruments. Dispose of used batteries according to local regulations. Battery Precautions • Do not leave battery within the reach of children. • Do not mix new and used batteries. • Do not mix rechargeable and non-rechargeable batteries. Appendix — Reference Information 99 • Install battery according to polarity (+ and - ) diagrams. • Do not place non-rechargeable batteries in a battery recharger. • Properly dispose of used batteries immediately. • Do not incinerate or dismantle batteries. • Seek Medical Advice immediately if a cell or battery has been swallowed. (In the USA, contact the National Poison Control Center collect at 202-625-3333.) Used only for small button cell batteries. Battery Disposal • Do not mutilate, or dispose of batteries in fire. • The batteries can burst or explode, releasing hazardous chemicals. • Discard used batteries according to local regulations. In Case of Difficulty Use this list of possible solutions to difficulties you might encounter with the calculator to determine if you can correct a problem before having to return it for service. Difficulty Solution The calculator computes wrong answers. Check the settings of the current worksheet to make sure they are correct for the problem you are working; for example, in the TVM worksheet, check END and BGN and be sure the unused variable is set to zero. The display is blank; digits do not appear. Select the worksheet again. Be sure the battery is properly installed and replace, if necessary. The calculator does not display Be sure you have selected the correct the correct worksheet worksheet. variables. The calculator does not display Press & | to check or adjust the the correct number of decimal setting for number of decimal places places. displayed. The calculator does not display Press & | # # to check or adjust the correct date format. the setting for date format. The calculator does not display Press & | # # # to check or the correct separator format. adjust the setting for separator format. 100 Appendix — Reference Information Difficulty Solution The calculator does not display Press & | # # # # to check or the correct result in a math adjust the setting for calculation calculation. method. An error occurs. If you experience difficulties other than those listed above, press & } ! to clear the calculator, and then repeat your calculations. Note: You can also perform a hard reset using the reset hole in back of the calculator. Texas Instruments Support and Service For general information Home Page: education.ti.com Knowledge Base and e-mail inquiries: education.ti.com/support Phone: (800) TI-CARES / (800) 842-2737 For U.S., Canada, Mexico, Puerto Rico, and Virgin Islands only International Information: education.ti.com/support (Click the International Information link.) For technical support Knowledge Base and support by e-mail: education.ti.com/support Phone (not toll-free): (972) 917-8324 For Product (hardware) Service Customers in the U.S., Canada, Mexico, Puerto Rico and Virgin Islands: Always contact Texas Instruments Customer Support before returning a product for service. All other customers: Refer to the leaflet enclosed with this product (hardware) or contact your local Texas Instruments retailer/distributor. Appendix — Reference Information 101 Texas Instruments (TI) Warranty Information Customers in the U.S. and Canada Only One-Year Limited Warranty for Commercial Electronic Product This Texas Instruments ("TI") electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This TI electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This TI electronic product is warranted against defective materials and construction. THIS WARRANTY IS VOID IF THE PRODUCT HAS BEEN DAMAGED BY ACCIDENT OR UNREASONABLE USE, NEGLECT, IMPROPER SERVICE, OR OTHER CAUSES NOT ARISING OUT OF DEFECTS IN MATERIALS OR CONSTRUCTION. Warranty Disclaimers. ANY IMPLIED WARRANTIES ARISING OUT OF THIS SALE, INCLUDING BUT NOT LIMITED TO THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, ARE LIMITED IN DURATION TO THE ABOVE ONE-YEAR PERIOD. TEXAS INSTRUMENTS SHALL NOT BE LIABLE FOR LOSS OF USE OF THE PRODUCT OR OTHER INCIDENTAL OR CONSEQUENTIAL COSTS, EXPENSES, OR DAMAGES INCURRED BY THE CONSUMER OR ANY OTHER USER. Some states/provinces do not allow the exclusion or limitation of implied warranties or consequential damages, so the above limitations or exclusions may not apply to you. Legal Remedies. This warranty gives you specific legal rights, and you may also have other rights that vary from state to state or province to province. Warranty Performance. During the above one (1) year warranty period, your defective product will be either repaired or replaced with a reconditioned model of an equivalent quality (at TI's option) when the product is returned, postage prepaid, to Texas Instruments Service Facility. The warranty of the repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other than the postage requirement, no charge will be made for such repair and/or replacement. TI strongly recommends that you insure the product for value prior to mailing. Software. Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements. All software is provided "AS IS." Copyright. The software and any documentation supplied with this product are protected by copyright. Australia & New Zealand Customers only One-Year Limited Warranty for Commercial Electronic Product 102 Appendix — Reference Information This Texas Instruments electronic product warranty extends only to the original purchaser and user of the product. Warranty Duration. This Texas Instruments electronic product is warranted to the original purchaser for a period of one (1) year from the original purchase date. Warranty Coverage. This Texas Instruments electronic product is warranted against defective materials and construction. This warranty is void if the product has been damaged by accident or unreasonable use, neglect, improper service, or other causes not arising out of defects in materials or construction. Warranty Disclaimers. Any implied warranties arising out of this sale, including but not limited to the implied warranties of merchantability and fitness for a particular purpose, are limited in duration to the above one-year period. Texas Instruments shall not be liable for loss of use of the product or other incidental or consequential costs, expenses, or damages incurred by the consumer or any other user. Except as expressly provided in the One-Year Limited Warranty for this product, Texas Instruments does not promise that facilities for the repair of this product or parts for the repair of this product will be available. Some jurisdictions do not allow the exclusion or limitation of implied warranties or consequential damages, so the above limitations or exclusions may not apply to you. Legal Remedies. This warranty gives you specific legal rights, and you may also have other rights that vary from jurisdiction to jurisdiction. Warranty Performance. During the above one (1) year warranty period, your defective product will be either repaired or replaced with a new or reconditioned model of an equivalent quality (at TI's option) when the product is returned to the original point of purchase. The repaired or replacement unit will continue for the warranty of the original unit or six (6) months, whichever is longer. Other than your cost to return the product, no charge will be made for such repair and/or replacement. TI strongly recommends that you insure the product for value if you mail it. Software. Software is licensed, not sold. TI and its licensors do not warrant that the software will be free from errors or meet your specific requirements. All software is provided "AS IS." Copyright. The software and any documentation supplied with this product are protected by copyright. All Other Customers For information about the length and terms of the warranty, refer to your package and/or to the warranty statement enclosed with this product, or contact your local Texas Instruments retailer/distributor. Appendix — Reference Information 103 104 Appendix — Reference Information Index Symbols #PD (number of periods) 72, 73, 74 #PD (number of periods, Percent Change/Compound Interest worksheet) 72 %CH (percent change) 72, 73, 74 (- (negative) indicator 3 (#$ indicator 3 (1 (value entered) indicator 3 (GX (sum of X) 65, 67 (GX² (sum of X²) 65, 67 (GXY (sum of XY products) 65 (GY (sum of Y) 65 (GY² (sum of Y²) 65 (sx (population standard deviation of X) 65, 67 (sy (population standard deviation of Y) 65 (v (mean of X) 65, 67 (w (mean of X) 65 * (value computed) indicator 3 = (value assigned) indicator 3 Numerics 1/Y (one coupon per year) 54, 55, 57 1-V (one-variable statistics ) 65, 67 2/Y (two coupons per year) 54, 55, 57 2nd (second) functions 2 indicator 3 30/360 day-count method (360) 54, 55, 57, 77 360 (30/360 day-count method) 54, 55, 57, 77 A a (y-intercept) 65 Accrued interest (AI) 54, 57, 58 Accuracy 98 ACT (actual/actual day-count method) 54, 55, 57, 77 Actual/actual (ACT) day-count method 77 Index Actual/actual day-count method (ACT) 54, 55, 57 Addition 8 AI (accrued interest) 54, 57, 58 Algebraic Operating System (AOS™) calculations 4, 5, 98 Amortization formulas 87 schedule 21, 25, 26, 38 worksheet 21 Amount of nth cash flow (Cnn) 41 Angle units format 5 Annual coupon rate, percent (CPN) 54, 56, 57 Annual effective rate (EFF) 75, 76 annual interest rate 56, 75, 89 Annuities 21 due 24, 29, 30 ordinary 24, 29, 30 perpetual 30 ANS (Last Answer) feature 14 AOS™ (Algebraic Operating System) calculations 5, 98 APD™ (Automatic Power Down™) feature 1, 2 Arccosine 9 Arcsine 9 Arctangent 9 Automatic Power Down™ (APD™) feature 1, 2 B b (slope) 65 Backspace key 7 BAL (balance) 22, 24 Balance (BAL) 22, 24 Battery 99 precautions 99 replacing 99 Beginning-of-period (BGN) indicator 3 payments 22, 24 BGN (beginning-of-period) indicator 3 105 payments 22, 24 Bond accrued interest (AI) 54 price (PRI) 58 terminology 56 worksheet 53–58 Breakeven worksheet 80–81 Cost-Sell-Markup 73, 74 Coupon payment 56 CPN (annual coupon rate, percent) 54, 55, 56, 57 CST (cost) 59, 62, 79 Curve fitting 67 customer support and service 101 C D C/Y (compounding periods per year) 22, 24, 76 Calculation method 4, 5 Call date 56 Cash Flow worksheet 41–51 Cash flows computing 45 deleting 42, 44 editing 48 entering 42 formulas 87 grouped 43 inserting 44 uneven 43 CFo (initial cash flow) 41 Chain (Chn) calculation 4, 5, 8 Chn (chain) calculation 4, 5, 8 Clearing calculations 6 calculator 6 characters 6 entry errors 6 error messages 6 errors 6 memory 6, 12 worksheets 6 Cnn (amount of nth cash flow) 41 Combinations 8, 10 Compound interest 56, 71, 73, 75 Compounding periods per year (C/Y) 22, 24, 76 COMPUTE indicator 3 Constant Memory™ feature 2 Constants 13 contact information 101 Correcting entry errors 7 Correlation coefficient (r) 65, 68 Cost (CST) 59, 62, 79 Data points 68 Date 1 and 2 (DT1, DT2) 59, 78 Date worksheet 76 Dates 30/360 day-count method (360) 77 actual/actual (ACT) day-count method 77 date 1 and 2 (DT1, DT2) 78 days between dates (DBD) 78 entering 77 Days between dates (DBD) 78 DB (declining balance) 59, 61, 62, 92 DBD (days between dates) 78 DBF (French declining balance) 59, 61, 62 DBX (declining balance with crossover) 59, 61, 62 DEC (decimal format) 4 Decimal format (DEC) 4 Declining balance (DB) 59, 61, 62, 92 Declining balance with crossover (DBX) 59, 61, 62 DEG (degrees) 4, 5 Degree angle units 5 Degrees (DEG) 4, 5 DEL (delete) indicator 3 Delete (DEL) indicator 3 DEP (depreciation) 59, 60, 62 Depreciation (DEP) 59, 60, 62 Depreciation worksheet 59–63 Difficulty 100 Discount bond 56 Discount rate (I) 41 Discounted payback (DPB) 41, 45 Display indicators 3 Division 8 Dollar price (PRI) 54, 56, 57 106 Index DPB (discounted payback) 41, 45 DT1 (starting date) 62 DT1, DT2 (date 1 and 2) 59, 78 DUR (modified duration) 54 E EFF (annual effective rate) 75, 76 END (end-of-period) payments 22, 24 Ending payment (P2) 22, 24 End-of-period (END) payments 22, 24 ENTER indicator 3 Error clearing 96 messages 96 Examples accrued interest 58 amortization schedule 38 amount to borrow 36 annuities 30 balloon payment 40 bond price 58 compound interest 73 computing basic loan payments 27 constants 13 converting interest 76 correcting an entry error 7 cost-sell-markup 74 days between dates 78 discounted payback 49 down payment 36 editing cash flow data 48 entering cash flow data 48 future value (savings) 28 interest received 40 internal rate of return 49 last answer 14 lease with uneven payments 49 memory 12 Memory worksheet 83 modified duration 58 modified internal rate of return 49 monthly payments 40 Index monthly savings deposits 35 mortgage payments 38 net future value 49 net present value 48, 49, 50 other monthly payments 34 payback 49 percent change 73 perpetual annuities 30 present value (annuities) 29 present value (lease with residual value) 33 present value (savings) 28 present value (variable cash flow) 33 profit margin 79 regular deposits for specific goals 37 remaining balance (balloon payment) 40 residual value 33 saving for future 35 straight-line depreciation 62 EXP (exponential regression) 65, 67 Exponential regression (EXP) 65, 67 F Face value 56 Factorial 10 FC (fixed cost) 80, 81 FCC statement ii Fixed cost (FC) 80, 81 Floating-decimal format 4 Fnn (frequency of nth cash flow) 41 Forecasting 67 Formats angle units 4, 5 calculation method 5 decimal places 4 number separators 4 setting 4 Formulas 30/360 day-count method 95 accrued interest 90 actual/actual day-count method 94 amortization 87 107 bond price (more than one coupon period to redemption) 90 bond price (one coupon period or less to redemption) 89 bond yield (more than one coupon period to redemption) 90 bond yield (one coupon period or less to redemption) 89 bonds 89 breakeven 94 cash flow 87 days between dates 94 depreciation 91 depreciation, declining-balance 92 depreciation, straight-line 91 depreciation, sum-of-the-years’digits 92 interest-rate conversions 93 internal rate of return 88 modified duration 90 modified internal rate of return 88, 89 net future value 88 net present value 87 percent change 93 profit margin 94 regressions 93 statistics 92 time-value-of-money 85 French declining balance (DBF) 59, 61, 62 French straight line (SLF) 59, 61, 62 Frequency 44 cash flow 88 coupon 55, 57 one-variable data 68 Y value 65, 67 Frequency of nth cash flow (Fnn) 41 Frequency of X value (Ynn) 67 Future value (FV) 22, 23, 24 FV (future value) 22, 23, 24 G Grouped cash flows 43 108 H Hard reset 6 HYP (hyperbolic) indicator 3 Hyperbolic (HYP) indicator 3 I I (discount rate) 41 I/Y (interest rate per year) 22, 24 Inflows 21, 23, 25 Initial cash flow (CFo) 41 INS (insert) indicator 3 Insert (IND) indicator 3 INT (interest paid) 22, 24 Interest Conversion worksheet 74 Interest paid (INT) 22, 24 Interest rate per year (I/Y) 22, 24 Internal rate of return (IRR) 41, 45 INV (inverse) indicator 3 Inverse (INV) indicator 3 IRR (internal rate of return) 41, 45 L Last Answer (ANS) feature 14 Leases 21 LIF (life of the asset) 59, 61, 62 Life of the asset (LIF) 59, 61, 62 LIN (linear regression) 65, 67 Linear regression (LIN) 65, 67 Ln (logarithmic regression) 65, 67 Loans 21, 24 Logarithmic regression (Ln) 65, 67 M M01 (starting month) 59, 61, 62 M0–M9 (memory) 12, 82 MAR (profit margin) 79 Math operations 8 Mean of X (v) 65, 67 Mean of Y (v) 65 Memory arithmetic 12 clearing 12 examples 12 recalling from 12 storing to 12 Memory worksheet 82–83 Index MOD (modified internal rate of return) 41, 45 Modified duration (DUR) 54 Modified internal rate of return (MOD) 41, 45 Mortgages 21 Multiplication 8 N n (number of observations) 65, 67 N (number of periods) 24 N (number of periods, TVM worksheet) 22 Negative (–) indicator 3 Net future value (NFV) 41, 45 Net present value (NPV) 41, 45 NEW (new value) 72, 73, 74 New value (NEW) 72, 73, 74 NFV (net future value) 41, 45 NOM (nominal rate) 76 Nominal rate (NOM) 75, 76 NPV (net present value) 41, 45 Number of observations (n) 65, 67 Number of periods (#PD) 72, 73, 74 Number of periods (#PD), Percent Change/Compound Interest worksheet 72 Number of periods (N) 24 Number of periods (N), TVM worksheet 22 Number separators format 4 O OLD (old value) 72, 73, 74 Old value (OLD) 72, 73, 74 One coupon per year (1/Y) 54, 55, 57 One-variable statistics (1-V) 65, 67 Outflows 21, 25 Overview of calculator operation 1– 19 P P (unit price) 80, 81 P/Y (payments per year) 22, 24, 25 P1 (starting payment) 22, 24 P2 (ending payment) 22, 24 Index Par value 56 Parentheses 8, 10 Payback (PB) 41, 45 Payment (PMT) 22, 23, 24 Payments per year (P/Y) 22, 24, 25 PB (payback) 41, 45 Percent 8 Percent add-on 8 Percent change (%CH) 72, 73, 74 Percent Change/Compound Interest worksheet 71 Percent discount 8 Percent ratio 8 Permutations 8, 10 PFT (profit) 80, 81 PMT (payment) 22, 23, 24 Population standard deviation of X ((x) 65, 67 Population standard deviation of Y ((y) 65 Power regression (PWR) 65, 67 Predicted X value (X') 65, 67, 69 Predicted Y value (Y') 65, 67, 69 Premium bond 56 Present value (PV) 22, 23, 24 PRI (bond price) 58 PRI (dollar price) 54, 56, 57 Principal paid (PRN) 22, 24 PRN (principal paid) 22, 24 Procedures computing accrued interest 57 computing basic loan interest 26 computing bond price 57 computing bond yield 57 computing breakeven 81 computing breakeven quantity 81 computing compound interest 72 computing cost-sell-markup 72 computing dates 77 computing discounted payback 45 computing internal rate of return 46 computing modified duration 58 computing modified internal rate of return 46 109 computing net future value 45 computing net present value 45 computing payback 45 computing percent change 72 computing profit margin 79 computing statistical results 69 computing X’ 69 computing Y’ 69 constants for various operations 13 converting interest 75 deleting cash flows 44 entering bond data 57 entering data points 68 entering depreciation data 62 generating a depreciation schedule 62 generating amortization schedules 25, 26 inserting cash flows 44 selecting a depreciation method 62 selecting a statistics calculation method 69 selecting bond settings 57 using the memory worksheet 82 Profit (PFT) 80, 81 Profit margin (MAR) 79 Profit Margin worksheet 78–80 PV (present value) 22, 23, 24 PWR (power regression) 65, 67 Q Q (quantity) 80, 81 Quantity (Q) 80, 81 R r (correlation coefficient) 65, 68 RAD (radians) 5 RAD (radians) indicator 3 Radians (RAD) 5 Radians (RAD) indicator 3 Random numbers 10 RBV (remaining book value) 59, 60, 62 RDT (redemption date) 54, 55, 56, 57 110 RDV (remaining depreciable value) 59, 60, 62 Reading the display 2 Recalling from memory 12 Redemption date (RDT) 54, 55, 56, 57 Redemption value (RV) 54, 55, 56 Regression models exponential 67 linear 67 logarithmic 67 power 67 Reinvestment rate (RI) 41 Remaining book value (RBV) 59, 60, 62 Remaining depreciable value (RDV) 59, 60, 62 Resetting amortization variables 23 bond variables 54 breakeven variables 80 cash flow variables 42 date variables 77 depreciation variables 60 interest conversion variables 75 percent change/compound interest variables 72 statistics variables 66 TVM variables 23 Resetting calculator 6 hard reset 6 pressing keys 6 RI (reinvestment rate) 41 Rounding 10, 98 RV (redemption value) 54, 55, 56, 57 S SAL (salvage value) 59, 62 Salvage value (SAL) 59, 62 Sample standard deviation of X (Sx) 65, 67 Sample standard deviation of Y (Sy) 65 Savings 21 Scientific notation 11 SDT (settlement date) 54, 56, 57 Second (2nd) functions 2 Index indicator 3 Quit 2 SEL (selling price) 79 Selling price (SEL) 79 service and support 101 SET (setting) indicator 3 Setting (SET) indicator 3 Settlement date (SDT) 54, 56, 57 SL (straight line) 59, 61, 62 SLF (French straight line) 59, 61, 62 Slope (b) 65 Square 8 Square root 8 Starting date (DT1) 62 Starting month (M01) 59, 61, 62 Starting payment (P1) 22, 24 Statistical data 68 Statistics worksheet 65–69 Storing to memory 12 Straight line (SL) 59, 61, 62 Subtraction 8 Sum of the years’ digits (SYD) 59, 61, 62 Sum of X (GX) 65, 67 Sum of X² (GX²) 65, 67 Sum of XY products (GXY) 65 Sum of Y (GY) 65 Sum of Y² (GY²) 65 support and service 101 Sx (sample standard deviation of X) 65, 67 Sy (sample standard deviation of Y) 65 SYD (sum of the years’ digits) 59, 61, 62 T Time-Value-of-Money (TVM) worksheet 15, 16, 18, 21 Time-Value-of-Money and Amortization worksheets ??–40 Turning calculator off 1 Turning calculator on 1 TVM (Time-Value-of-Money) worksheet 15, 16, 18, 21 Two coupons per year (2/Y) 54, 55, 57 Two-variable statistics 67, 69 Index U Uneven cash flows 43 Unit price (P) 80, 81 Universal power 8 V Value assigned (=) indicator 3 Value computed (*) indicator 3 Value entered (1) indicator 3 Variable cost per unit (VC) 80, 81 VC (variable cost per unit) 80, 81 W warranty 102 What-if calculations 15 Worksheets Amortization 21 Bond 53 Breakeven 80 Cash Flow 41 Date 76 Depreciation 59 display indicators 19 Interest Conversion 74 Memory 82 Percent Change/Compound Interest 71 Profit Margin 78 prompted 18 TVM (Time-Value-of-Money) 15, 16, 18, 21 variables 15, 16, 17, 18 X X value (Xnn) 65, 67 X' (predicted X value) 65, 67, 69 Xnn (X value) 65, 67 xP/Y key (multiply payments per year) 25 Y Y' (predicted Y value) 65, 67 Year to compute (YR) 59, 61, 62 Yield to maturity 56 Yield to redemption (YLD) 54, 57 111 Y-intercept (a) 65 YLD (yield to redemption) 54, 57 112 Ynn (frequency of X value) 65, 67 YR (year to compute) 59, 61, 62 Index
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