BA II PLUS é
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Table of Contents 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 ...........................
Deleting Cash Flows...................................................................... 43 Inserting Cash Flows ..................................................................... 44 Computing Cash Flows ................................................................. 44 Example: Solving for Unequal Cash Flows .................................. 46 Example: Value of a Lease with Uneven Payments .................... 48 Bond Worksheet ...................................................................
Overview of Calculator Operations This chapter describes the basic operation of your BA II PLUS™ 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 $.
• 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.
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 C to compute a value for the displayed variable. ENTER Press ! to assign the displayed value to the displayed variable.
Setting Calculator Formats You can change these calculator formats: To Select Press Display Defaul t Number of decimal places & | DEC 0–9 (Press 9 for 2 Angle units # floating-decimal) DEG (degrees) DEG 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 & |.
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. 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.
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.
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 P P TVM worksheet variables and reset default values & U & ^ One of the 10 memories (without af
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 Use parentheses: 7 Q (3 + 5) Display 7< 93H5 56.
To Press Find natural logarithm: ln 203.45 203.45 > 5.32 .69315 & i 2.00 Round 2 P 3 to the set decimal format 263N & 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) 48 f -1 Find arctangent:** tan (4) Display -0.50 4.01 11.54 120.00 75.
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.
For example, working in the Bond worksheet, you might want to round a computed selling price to the nearest penny (two decimal places) before continuing your calculation. Note: The calculator stores values to an accuracy of up to 13 digits. The decimal format setting rounds the displayed value but not the unrounded, internally stored value. (See “Choosing the Number of Decimal Places Displayed” on page 4.
Memory Operations You can store values in any of 10 memories using the standard calculator keys. Note: You can also use the Memory worksheet. (See “Memory Worksheet” on page 80.) • You can store in memory any numeric value within the range of the calculator. • To access a memory M0 through M9, press a numeric key (0 through 9). Clearing Memory Clearing memory before you begin a new calculation is a critical step in avoiding errors. • To clear an individual memory, store a zero value in it.
• Memory arithmetic changes only the value in the affected memory and not the displayed value. • Memory arithmetic does not complete any calculation in progress. The table lists the available memory arithmetic functions. In each case, the specified memory stores the result. To Press Add the displayed value to the value stored in memory 9 (M9). DH9 Subtract the displayed value from the value stored in memory 3 (M3). D B3 Multiply the value in memory 0 (M0) by the displayed value.
Keystrokes for Constant Calculations This table shows how to create a constant for various operations.
To Press Display Key in a new calculation 2; 2.00 Recall the last answer & x 4.00 Complete the calculation N 16.00 Using Worksheets: Tools for Financial Solutions Thecalculator contains worksheets with embedded formulas to solve specific problems. You apply settings or assign known values to worksheet variables and then compute the unknown value. Changing the values lets you ask what if questions and compare results.
To select Function Press Statistics worksheet (Chapter 6) Analyzes statistics on one- or two-variable data using four regression analysis options & k Percent Change/ Compound Interest worksheet (Chapter 7) Computes percent change, compound interest, and costsell markup & q Interest Conversion worksheet (Chapter 7) Converts interest rates between nominal rate (or annual percentage rate) and annual effective rate & v Date worksheet (Chapter 7) Computes number of days & u between two dates, or dat
Accessing Prompted-Worksheet Variables After you access a worksheet, press # or " to select variables. For example, press & \ to access the Amortization worksheet, and then press # or " to select the amortization variables (P1, P2, BAL, PRN, INT). (See “TVM and Amortization Worksheet Variables” on page 22.) Indicators prompt you to select settings, enter values, or compute results. For example, the # $ indicators remind you to press # or " to select other variables. ((See “Reading the Display” on page 2.
When you display a compute-only variable, the COMPUTE indicator reminds you to press C to compute its value. After you press C, the 7 indicator confirms that the displayed value has been computed. Automatic-Compute Variables When you press # or " to display an automatic-compute variable (for example, the Amortization worksheet INT variable), the calculator computes and displays the value automatically without you having to press C.
Display Indicators • The 1 indicator confirms that the calculator entered the displayed value in the worksheet. • The 7 indicator confirms that the calculator computed the displayed value. • When a change to the worksheet invalidates either entered or computed values, the 1 and 7 indicators disappear.
20 Overview of Calculator Operations
Time-Value-of-Money and Amortization Worksheets Use the Time-Value-of-Money (TVM) variables to solve problems with equal and regular cash flows that are either all inflows or all outflows (for example, annuities, loans, mortgages, leases, and savings). For cash-flow problems with unequal cash flows, use the Cash Flow worksheet. (See "Cash Flow Worksheet"). After solving a TVM problem, you can use the Amortization worksheet to generate an amortization schedule.
TVM and Amortization Worksheet Variables Variable Key Display Type of Variable Number of periods , N Enter-or-compute Interest rate per year - I/Y Enter-or-compute Present value .
• To generate an amortization schedule, press & \, enter the first and last payment number in the range (P1 and P2), and press " or # to compute values for each variable (BAL, PRN, and INT).
Entering Values for I/Y, P/Y, and C/Y • Enter I/Y as the nominal interest rate. The TVM worksheet automatically converts I/Y to a per period rate based on the values of P/Y and C/Y. • Entering a value for P/Y automatically enters the same value for C/Y. (You can change C/Y.) Specifying Payments Due With Annuities Use END/BGN to specify whether the transaction is an ordinary annuity or an annuity due. • Set END for ordinary annuities, in which payments occur at the end of each payment period.
• In worksheet modes the calculator displays only the value you enter or recall, although any variable label previously displayed remains displayed. Note: You can tell that the displayed value is not assigned to the displayed variable, because the = indicator is not displayed. To compute a TVM value, press C and a TVM key in standard-calculator mode. Using [xP/Y] to Calculate a Value for N 1. Key in the number of years, and then press & Z to multiply by the stored P/Y value.
6. Press & \. — or — If INT is displayed, press # to display P1 again. 7. To generate the amortization schedule, repeat steps 2 through 5 for each range of payments. Generating an Amortization Schedule Automatically After entering the initial values for P1 and P2, you can compute an amortization schedule automatically. 1. Press & \. — or — If INT is displayed, press # to display the current P1 value. 2. Press C. Both P1 and P2 update automatically to represent the next range of payments.
To Press Enter loan amount. 75000 . Display PV= 75,000.00Ä € Enter payment amount. 425.84 S / PMT= Compute interest rate. C - I/Y= -425.841 5.50* Answer: The interest rate is 5.5% per year. Examples: Computing Basic Loan Payments These examples show you how to compute basic loan payments on a $75,000 mortgage at 5.5% for 30 years. Note: After you complete the first example, you should not have to reenter the values for loan amount and interest rate.
To Press Display Enter number of payments using payment multiplier. 30 & Z , N= Compute payment. C / PMT= 120.001 -1,279.827 Answer: The quarterly payments are $1,279.82. Examples: Computing Value in Savings These examples show you how to compute the future and present values of a savings account paying 0.5% compounded at the end of each year with a 20-year time frame.
Example: Computing Present Value in Annuities The Furros Company purchased equipment providing an annual savings of $20,000 over 10 years. Assuming an annual discount rate of 10%, what is the present value of the savings using an ordinary annuity and an annuity due? Cost Savings for a Present-Value Ordinary Annuity Cost Savings for a Present-Value Annuity Due in a Leasing Agreement To Press Set all variables to defaults. & } ! RST Enter number of payments. 10 , N= 10.
To Press Display Compute present value (ordinary annuity). C . PV= Set beginning-of-period payments. &] &V BGN Return to calculator mode. & U Compute present value (annuity due). C . 122,891.347 0.00 PV= 135,180.487 Answer: The present value of the savings is $122,891.34 with an ordinary annuity and $135,180.48 with an annuity due. Example: Computing Perpetual Annuities To replace bricks in their highway system, the Land of Oz has issued perpetual bonds paying $110 per $1000 bond.
Because the term (1 + I/Y / 100) -N in the present value annuity equations approaches zero as N increases, you can use these equations to solve for the present value of a perpetual annuity: • Perpetual ordinary annuity PMT PV = -------------------------- I/Y 100 • Perpetual annuity due PMT PV = PMT + --------------------------- I/Y 100 Example: Computing Present Value of Variable Cash Flows The ABC Company purchased a machine that will save these end-of-year amounts: Year 1 2 3 4 Amou
To Press Set all variables to defaults. & } ! RST 0.00 Enter interest rate per cash flow period. 10 - I/Y= 10.001 Enter 1st cash flow. 5000 S 0 FV= -5,000.001 Enter 1st cash flow period. 1, N= Compute present value of 1st cash C . flow. Display PV= Store in M1. D1 Enter 2nd cash flow. 7000 S 0 FV= Enter 2nd cash flow period. 2, N= Compute present value of 2nd cash flow. C . PV= Sum to memory. D H1 Enter 3rd cash flow. 8000 S 0 FV= Enter period number.
Note: Although variable cash flow payments are not equal (unlike annuity payments), you can solve for the present value by treating the cash flows as a series of compound interest payments. The present value of variable cash flows is the value of cash flows occurring at the end of each payment period discounted back to the beginning of the first cash flow period (time zero).
To Press Display Set all variables to defaults. & } ! RST Enter lease payment amount. 1200 S / PMT= Compute present value of lease payments. C . PV= 0.00 -1,200.001 40,573.18 7 Answer: Peach Bright should pay your company $40,573.18 for the machine. Example: Computing Other Monthly Payments If you finance the purchase of a new desk and chair for $525 at 20% APR compounded monthly for two years, how much is the monthly payment? To Press Display Set all variables to defaults.
Example: Saving With Monthly Deposits Note: Accounts with payments made at the beginning of the period are referred to as annuity due accounts. Interest begins accumulating earlier and produces slightly higher yields. You invest $200 at the beginning of each month in a retirement plan. What will the account balance be at the end of 20 years, if the fund earns an annual interest of 7.5 % compounded monthly, assuming beginningof-period payments? To Press Display Set all variables to defaults.
Example: Computing Amount to Borrow and Down Payment You consider buying a car for $15,100. The finance company charges 7.5% APR compounded monthly on a 48-month loan. If you can afford a monthly payment of $325, how much can you borrow? How much do you need for a down payment? To Press Display Set all variables to defaults. & } ! RST Set payments per year to 12. & [ 12 ! P/Y= Return to standard-calculator mode & U Enter number of payments using payment multiplier.
Example: Computing Regular Deposits for a Specified Future Amount You plan to open a savings account and deposit the same amount of money at the beginning of each month. In 10 years, you want to have $25,000 in the account. How much should you deposit if the annual interest rate is 0.5% with quarterly compounding? Note: Because C/Y (compounding periods per year) is automatically set to equal P/Y (payments per year), you must change the C/Y value. To Press Display Set all variables to defaults.
Example: Computing Payments and Generating an Amortization Schedule This example shows you how to use the TVM and Amortization worksheets to calculate the monthly payments on a 30-year loan and generate an amortization schedule for the first three years of the loan. Computing Mortgage Payments Calculate the monthly payment with a loan amount of $120,000 and 6.125% APR. To Press Display Set all variables to defaults. & } ! RST Set payments per year to 12. & [ 12 ! P/Y= 0.00 12.
To Press Display Change beginning period to 10. # 10 ! P1= 10.001 Change ending period to 21. # 21 ! P2= 21.001 Display 2nd year amortization data. # # # BAL= PRN= INT= Move to P1 and press C to enter next range of payments. #C P1= 22.001 Display P2. # P2= 33.001 Display 3rd year amortization data. # # # BAL= PRN= INT= 117,421.60* -1,507.03* -7,242.53* 115,819.62* -1601.98* -7,147.
To Press Display Enter loan amount. 82000 . PV= Compute payment. C / PMT= 82,000.001 -545.55* Generating an Amortization Schedule for Interest and Balloon Payment To Press Select Amortization worksheet. & \ Display P1= 1.00 Enter end period (five years). # 5 & Z ! P2= 60.001 View balance due after five years (balloon payment). # BAL= 77,187.72* View interest paid after five years. ## INT= 27,920.72* If the sellers financed the sale, they would receive: • Monthly payment: $545.
Cash Flow Worksheet Use the Cash Flow worksheet to solve problems with unequal cash flows. To solve problems with equal cash flows, use the TVM worksheet. (See “Time-Value-of-Money and Amortization Worksheets”.) • To access the Cash Flow worksheet and initial cash flow value (CFo), press '. • To access the cash flow amount and frequency variables (Cnn/Fnn), press # or ". • To access the discount rate variable (I), press (. • To compute net present value (NPV), press # or " and C for each variable.
** This guidebook categorizes variables by the method of entry. (See “Types of Worksheet Variables”.) Resetting Variables • To reset CFo, Cnn, and Fnn to default values, press ' and then & z. • To reset NPV to the default value, press ( and then & z. • To reset IRR to the default value, press ) and then & z. • To reset all calculator variables and formats to default values, including all Cash Flow worksheet variables, press & } !. Entering Cash Flows • You must enter an initial cash flow (CFo).
Grouped Cash Flows Cash-flow problems can contain cash flows with unique values as well as consecutive cash flows of equal value. Although you must enter unequal cash flows separately, you can enter groups of consecutive, equal cash flows simultaneously using the Fnn variable. Entering Cash Flows Cash flows consist of an initial cash flow (CFo) and up to 24 additional cash flows (C01-C24), each of which can have a unique value.
The DEL indicator confirms that you can delete a cash flow. 1. Press # or " until the cash flow you want to delete appears. 2. Press & W. The cash flow you specified and its frequency is deleted. Inserting Cash Flows When you insert a cash flow, the calculator increases the number of the following cash flows, up to the maximum of 24. Note: The INS indicator confirms that you can insert a cash flow. 1. Press # or " to select the cash flow where you want to insert the new one.
• Internal rate of return (IRR) is the interest rate at which the net present value of the cash flows is equal to 0. Computing NPV 1. Press ( to display the current discount rate (I). 2. Key in a value and press !. 3. Press # to display the current net present value (NPV). 4. To compute the net present value for the series of cash flows entered, press C. Computing IRR 1. Press ). The IRR variable and current value are displayed (based on the current cash-flow values). 2.
When more than one solution exists, the calculator displays the one closest to zero. Because the displayed solution has no financial meaning, you should use caution in making investment decisions based on an IRR computed for a cash-flow stream with more than one sign change. The time line reflects a sequence of cash flows with three sign changes, indicating that one, two, or three IRR solutions can exist.
Entering Cash-Flow Data To Press Display Select Cash Flow worksheet. ' CFo= Enter initial cash flow. 7000 S ! CFo= -7,000.001 Enter cash flow for first year. # 3000 ! # C01= F01= 3,000.001 1.001 Enter cash flows for years two through five. # 5000 ! #4! C02= F02= 5,000.001 Enter cash flow for sixth year. # 4000 ! # C03= F03= 4,000.001 0.00 4.001 1.
Computing NPV Use an interest rate per period (I) of 20%. To Press Display Access interest rate variable ( I= 0.00 Enter interest rate per period. 20 ! I= 20.001 Compute net present value. NPV= # C 7,266.447 Answers: NPV is $7,266.44. Computing IRR To Press Display Access IRR. ) IRR= 0.00 Compute internal rate of return. # C IRR= 52.717 Answer: IRR is 52.71%.
• What even payment amount at the beginning of each month would result in the same present value? Because the cash flows are uneven, use the Cash Flow worksheet to determine the net present value of the lease. Computing NPV The cash flows for the first four months are stated as a group of four $0 cash flows.
To Press Select NPV. ( I= 0.00 Enter monthly earnings rate. 10 6 12 ! I= 0.831 Compute NPV. #C NPV= 50 Display -138,088.
Cash Flow Worksheet 51
Bond Worksheet The Bond worksheet lets you compute bond price, yield to maturity or call, and accrued interest.You can also use the date functions to price bonds purchased on dates other than the coupon anniversary. • To access the Bond worksheet, press & l. • To access bond variables, press or #. • To change the options for day-count methods (ACT and 360) and coupons per year (2/Y and 1/Y), press V once for each option.
Bond Worksheet Variables Variable Key Display Variable Type Settlement date & l SDT Enter only Annual coupon rate in percent # CPN Enter only Redemption date # RDT Enter only Redemption value (percentage of # par value) RV Enter only Actual/actual day-count method # ACT Setting 30/360 day-count method & V 360 Setting Two coupons per year # 2/Y Setting One coupon per year & V 1/Y Setting Yield to redemption # YLD Enter/compute Dollar price # PRI Enter/compute Accrued
• The calculator assumes that the redemption date (RDT) coincides with a coupon date: • To compute to maturity, enter the maturity date for RDT. • To compute to call, enter the call date for RDT. Entering CPN CPN represents the annual coupon rate as a percentage of the bond par value rather than the dollar amount of the coupon payment. Entering RV The redemption value (RV) is a percentage of the bond par value: • For to maturity analysis, enter 100 for RV.
Bond Worksheet Terminology Term Definition Call Date A callable bond bond can be retired by the issuing agency before the maturity date. The call date for such a bond is printed in the bond contract. Coupon Payment The periodic payment made to the owner of the bond as interest. Coupon Rate The annual interest rate printed on the bond. Dollar Price Price of the security expressed in terms of dollars per $100 of par value. Par (Face) Value The value printed on the bond.
If necessary, change the day-count method (ACT or 360) and couponfrequency (2/Y or 1/Y). The Bond worksheet stores all values and settings until you clear the worksheet or change the values and settings. Entering Known Bond Values 1. Press & l. The current SDT value appears. 2. To clear the worksheet, press & z. 3. If necessary, key in a new SDT value and press !. 4. Repeat step 3 for CPN, RDT, and RV, pressing # once for each variable. Note: To enter dates, use this convention: mm.ddyy (US) or dd.
Example: Computing Bond Price and Accrued Interest You consider buying a semiannual corporate bond maturing on December 31, 2005 and settling on June 12, 2004. The bond is based on the 30/360 day-count method with a coupon rate of 7%, redeemable at 100% of par value. For an 8% yield to maturity, compute the bond’s price and accrued interest. Computing Bond Price and Accrued Interest To Press Display Select Bond worksheet. & l SDT = 12-31-20001 Enter settlement date. 6.
Depreciation Worksheet The Depreciation worksheet lets you generate a depreciation schedule using your choice of depreciation methods. • To access the Depreciation worksheet, press & p. • To change depreciation methods, press & V until the desired method appears. • To access other depreciation variables, press # or ". Note: To easily scroll up or down through a range of variables, press and hold #, or ".
Variable Key Display Variable Type** Year to compute # YR Enter only Depreciation for the year # DEP Auto-compute Remaining book value at the end of the year # RBV Auto-compute Remaining depreciable value # RDV Auto-compute * SLF and DBF are available only if you select the European format for dates or separators in numbers. (See “Setting Calculator Formats ” on page 4.) ** This guidebook categorizes variables by their method of entry. (See “Types of Worksheet Variables” on page 18.
Entering Values for DB and DBX If you choose either the declining balance (DB) or declining balance with crossover to SL (DBX) depreciation method, remember to enter a value representing the percent of declining balance for the DB or DBX variable. Note: The declining balance you enter must be a positive number. Entering Values for LIF • If SL or SLF is selected, the LIF value must be a positive real number. • If SYD, DB, DBX, or DBF is selected, the LIF value must be a positive integer.
Entering Data and Computing Results Because the Depreciation worksheet stores values and settings until you either change them or clear the worksheet, you should not have to perform every step each time you work a problem. Selecting a Depreciation Method 1. To access the Depreciation worksheet, press & p. The current depreciation method is displayed. 2. To clear the worksheet, press & z. 3. Press & V until you display the depreciation method you want (SL, SLF, SYD, DB, DBX, or DBF).
Example: Computing Straight-Line Depreciation In mid-March, a company begins depreciation of a commercial building with a 31½ year life and no salvage value. The building cost $1,000,000. Use the straight-line depreciation method to compute the depreciation expense, remaining book value, and remaining depreciable value for the first two years. To Press Display Access Depreciation worksheet. & p SL Enter life in years. # 31.5 ! LIF = Enter starting month. # 3.5 ! M01 = Enter cost.
62 Depreciation Worksheet
Statistics Worksheet The Statistics worksheet performs analysis on one-and twovariable data with four regression analysis models. • To enter statistical data, press & j. • To choose a statistics calculation method and compute the results, press & k. • To access statistics variables, press # or ".
Variable Key Number of observations # (as Mean (average) of X values needed) Sample standard deviation of X Population standard deviation of X Mean (average) of Y values Sample standard deviation of Y Population standard deviation of Y Linear regression y-intercept Linear regression slope Correlation coefficient Predicted X value Predicted Y value Sum of X values Sum of X squared values Sum of Y values Sum of Y squared values Sum of XY products * Display Variable Type n v Sx sx y** Sy** sy** a** b** r*
• When you enter data for one-variable statistics, Xnn represents the value and Ynn specifies the number of occurrences (frequency). • When you enter a value for Xnn, the value for Ynn defaults to 1. Analyzing One-Variable Statistics To analyze one-variable statistics, select 1-V. Only values for n, v, Sx, sX, GX, and GX2 are computed and displayed for one-variable statistics.
• 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.
Press & k to select the statistical calculation portion of the Statistics worksheet. The last selected statistics calculation method is displayed (LIN, Ln, EXP, PWR, or 1-V). Press & V repeatedly until the statistics calculation method you want is displayed. If you are analyzing one-variable data, select 1-V. 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.
68 Statistics Worksheet
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.
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 OLD 0 NEW 0 NEW 0 To reset default values for all calculator variables and formats, press & } !.
3. 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. 4.
To Press Display Enter stock selling price. # 750 ! NEW= Enter number of years. # # 5 ! #PD= 5.001 Compute annual growth rate. " C 8.457 %CH= 750.001 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= Current value Clear worksheet variables. & z OLD= 0.00 Enter original cost. 100 ! OLD= 100.
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 ".
• 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.
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.
• 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).
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. (See “Percent Change/Compound Interest Worksheet” on page 69.) • To access the Profit Margin worksheet, press & w. • To access profit margin variables, press " or #.
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 C. The calculator displays the computed value. Example: Computing Profit Margin The selling price of an item is $125.
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. (See “Types of Worksheet Variables” on page 18.) Resetting the Breakeven Worksheet Variables • To reset default values for all Breakeven worksheet variables, press & z.
To Press Display Leave profit as is. # PFT= Compute quantity. #C Q= 0.00 600.007 Answer: 600 paddles must be sold to break even. 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 18.) • To access the Memory worksheet, press & {. • To access memory variables, press " or #.
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: • To clear all 10 memories at once, press & z. • 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.
82 Other Worksheets
APPENDIX - Reference Information This appendix includes supplemental information to help you use your BA II PLUSé 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.
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 0 N = L(PV + FV) P PMT where: i =0 –i PV + FV PMT = ----- PV + --------------------------N Gi 1 + i – 1 where: i 0 PMT = L(PV + FV) P N where: i =0 PMT G i
PV = L(FV + PMT Q N) where: i =0 PMT G PMT G N FV = ------------------------i – 1 + i PV + ------------------------i i i where: i 0 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
j ni where:S j = i = 1 0 j1 j = 0 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). 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).
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 is found through an iterative search process using the “Price with more than one coupon period to redemption” formula.
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.
n xy – y x b = -------------------------------------------------------2 n x2 – x y – b x a = --------------------------------n b x r = ------y Interest Rate Conversions EFF = 100 e C Y In x 1 – 1 where: x =.01 Q NOM P C Y NOM = 100 C Y e 1 C Y In x + 1 – 1 where: x =.
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 = 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. Error Messages Note: To clear an error message, press P. Error Possible Causes Error 1 • Overflow A result is outside the calculator range ( 9.9999999999999E99).
Error Possible Causes Error 4 • Out of range Error 5 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.
Error Possible Causes 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.
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.
8. Align the screw holes in the back cover with those in the calculator, then snap the back cover onto the calculator. Replace the screws. Battery Precautions • Do not leave batteries within the reach of children. • Do not mix new and used batteries. Do not mix brands (or types within brands) of batteries. • Do not mix rechargeable and nonrechargeable batteries. • Install batteries according to polarity (+ and –) diagrams. • Do not place nonrechargeable batteries in a battery recharger.
Difficulty Solution The calculator does not display Press & | # # # # to check the correct result in a math or adjust the setting for calculation calculation. method. An error occurs. (See “Error Messages” on page 92.) 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. (See “Resetting the Calculator” on page 6.
Texas Instruments Support and Service For general information Home Page: education.ti.com KnowledgeBase 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 KnowledgeBase and support by e-mail: education.ti.
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.
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 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.
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.
102 APPENDIX - Reference Information
Index – (negative) indicator 3 Symbols ( (mean of X) 63, 65 ( (mean of Y) 63 (x (population standard deviation of X) 63, 65 (X (sum of X) 63, 65 (X2 (sum of X2) 63, 65 (XY (sum of XY products) 63 (y (population standard deviation of Y) 63 (Y (sum of Y) 63 (Y2 (sum of Y2) 63 * (value computed) indicator 3 # $ indicator 3 #PD (number of periods, Percent Change/Compound Interest worksheet) 70 #PD (number of periods) 70, 71, 72 %CH (percent change) 70, 71, 72 = (value assigned) indicator 3 Numerics 1/Y (one c
BGN (beginning-of-period) indicator 3 payments 22, 24 Bond accrued interest (AI) 52 price (PRI) 56 terminology 54 worksheet 51–56 Breakeven worksheet 78–80 C C/Y (compounding periods per year) 22, 24, 74 Calculation method 4, 5 Call date 54 Cash Flow worksheet 41–50 Cash flows computing 44 deleting 42, 43 editing 47 entering 42, 43 formulas 85 grouped 43 inserting 44 uneven 42 CFo (initial cash flow) 41 Chain (Chn) calculation 4, 5, 8 Chn (chain) calculation 4, 5, 8 Clearing calculations 6 calculator 6 cha
Division 8 Dollar price (PRI) 52, 54, 55 DT1 (starting date) 60 DT1, DT2 (date 1 and 2) 57, 76 DUR (modified duration) 52 E EFF (annual effective rate) 74 END (end-of-period) payments 22, 24 Ending payment (P2) 22, 24 End-of-period (END) payments 22, 24 ENTER indicator 3 Error clearing 92 messages 92 Examples accrued interest 56 amortization schedule 38 amount to borrow 36 annuities 30 balloon payment 40 bond price 56 compound interest 71 computing basic loan payments 27 constants 13 converting interest 74
bond yield (more than one coupon period to redemption) 88 bond yield (one coupon period or less to redemption) 87 bonds 86 breakeven 90 cash flow 85 days between dates 91 depreciation 88 depreciation, declining-balance 89 depreciation, straight-line 88 depreciation, sum-of-the-years’digits 88 interest-rate conversions 90 internal rate of return 86 net present value 85 percent change 90 profit margin 90 regressions 89 statistics 89 time-value-of-money 83 French declining balance (DBF) 57, 59, 60 French strai
N n (number of observations) 63, 65 N (number of periods, TVM worksheet) 22 N (number of periods) 24 Negative (–) indicator 3 Net present value (NPV) 41, 44 NEW (new value) 70, 71, 72 New value (NEW) 70, 71, 72 NOM (nominal rate) 74 Nominal rate (NOM) 74 NPV (net present value) 41, 44 Number of observations (n) 63, 65 Number of periods (#PD) 70, 71, 72 Number of periods (#PD), Percent Change/Compound Interest worksheet 70 Number of periods (N) 24 Number of periods (N), TVM worksheet 22 Number separators for
Q bond variables 52 breakeven variables 79 cash flow variables 42 date variables 75 depreciation variables 58 interest conversion variables 73 percent change/compound interest variables 70 statistics variables 64 TVM variables 23 Resetting calculator 6 hard reset 6 pressing keys 6 RI (reinvestment rate) 41 Rounding 10, 94 RV (redemption value) 52, 53, 54, 55 Q (quantity) 79 Quantity (Q) 79 S generating amortization schedules 25, 26 inserting cash flows 44 selecting a depreciation method 60 selecting a s
Statistics worksheet 63–67 Storing to memory 12 Straight line (SL) 57, 59, 60 Subtraction 8 Sum of the years’ digits (SYD) 57, 59, 60 Sum of X ((X) 63, 65 Sum of X2 ((X2) 63, 65 Sum of XY products ((XY) 63 Sum of Y ((Y) 63 Sum of Y2 ((Y2) 63 support and service 98 Sx (sample standard deviation of X) 63, 65 Sy (sample standard deviation of Y) 63 SYD (sum of the years’ digits) 57, 59, 60 T Time-Value-of-Money (TVM) worksheet 15, 16, 18, 21 Time-Value-of-Money and Amortozation worksheets ??–40 Turning calcula
110 Index
