BA-35 Solar Quick Reference Guide
Table of Contents General Information. The Display.. Arithmetic Operations. Correcting Errors.. Display Formats.. Memory Operations. Math Operations.. Percentage Calculations. Percentage Change Calculations. Margin and Markup Calculations. Compound Interest Calculations. Annuity Calculations. Converting to EFF or APR. Balance, Interest, and Principal. Statistics.. Common Keystroke Sequences. Error Conditions.. In Case of Difficulty.. TI Product Service and Warranty Information.. 38
1996 by Texas Instruments Incorporated
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General Information

Turning the Calculator On and Off u (All Clear/On)Turns on the calculator. This key also clears the display, all pending operations, and values in memory or the mode registers. The calculator turns off automatically when the solar cell panel is no longer exposed to light. Modes The calculator can operate in three different modes. Setting the calculator to a particular mode prepares it to perform special functions. The available modes are statistics, financial, and profit margin. Indicators in the display tell you the calculator's current mode. STAT displays for statistics, FIN for financial. No indicator is displayed for profit margin mode. 2Changes the calculator to the next mode in sequence. To set the calculator to a particular mode, press 2 repeatedly until the appropriate indicator is displayed. Changing to a new mode clears the contents of the mode registers. You can do arithmetic, mathematical, and percentage operations in any mode.
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Second Functions 0 (Second Function)Enables you to perform the second functions that are marked over some of the keys. To perform a second function, press 0 and then the appropriate function key. When you press 0, 2nd appears in the display until you press another key. If you press 0 and then a key that does not have a second function, the key performs its normal function. If you accidentally press 0, press it again to cancel its effect. Clearing the Calculator u (All Clear/On)Clears the calculator completely, including the display, all pending operations, and the memory and mode registers. Pressing u also sets the calculator to floating-decimal format and financial mode. - (Clear Entry/Clear)Clears incorrect entries, error conditions, the display, or pending operations. It does not affect the memory, the mode registers, or the display format. 0 b (Clear Mode Registers)Clears any values that have been stored in the mode registers. Note: Changing to a new mode also clears the contents of the mode registers.
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The Display

The display shows a maximum of 10 digits, although the calculator internally retains a maximum of 13 digits.
Display Indicators Indicator 2nd Meaning The calculator will access the second function of the next key pressed (appears when you press 0). The calculator is in the financial mode. The calculator is in the statistics mode. Note: No indicator displays when the calculator is in profit margin mode. The calculator computes annuities as beginning-ofperiod payments rather than end-of-period payments. (Displayed only in the financial mode.) (continued)

FIN STAT

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Indicator InDep

Meaning The displayed result is for the independent variables (x values). (Displayed only in the statistics mode.) The displayed result is for the dependent variables (y values). (Displayed only in the statistics mode.) The value in the display is the summed principal over a range of payments. (Displayed only in the financial mode.) The value in the display is the principal for a single payment. (Displayed only in the financial mode.) The value in the display is the summed interest over a range of payments. (Displayed only in the financial mode.) The value in the display is the interest for a single payment. (Displayed only in the financial mode.)
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Arithmetic Operations

Entering Numbers
6 - ? (Digits)Enter digits into the display. You can enter a maximum of 10 digits and a decimal point.
A (Decimal Point)Enters a decimal point. @ (Change Sign)Changes the sign of the number in the display. To enter a negative number, first enter the number as a positive value and then press @. Arithmetic Keys p, o, n, mPerform the arithmetic operations of addition, subtraction, multiplication, and division. l (Equals)Completes all pending operations and displays the result of a calculation.

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Correcting Errors

Correcting Entry Errors - (Clear Entry/Clear)To clear a numerical entry, press - once; then enter the correct number. To clear all pending operations and begin the calculation again, press - twice. w (x Exchange y)Exchanges the values of x and y. If you enter x and y in the incorrect order, press w to reverse them. Then complete the calculation. v (Backspace)Removes the last digit or decimal point from the displayed number if you have not yet pressed an operation key (p, o, n, m, etc.). This key is useful for correcting entry errors without having to clear the display and start again. Correcting Immediate Functions You can often correct an immediate function by performing the reverse operation. For example, if you press 0 ] by mistake, you can correct the operation by pressing 0 k.
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Display Formats

Floating-Decimal Format The calculator normally displays numbers in standard floating-decimal format, in which numbers are displayed in the range -9,999,999,999 to -0.000000001, 0, or 0.000000001 to 9,999,999,999. If the result of a calculation is too large or too small to be displayed in the normal format, it is displayed in scientific notation. This means the result is expressed as a base value (mantissa) times 10 raised to a power (exponent). For example, 5.means 5.9 x 10 12. The calculator is always in floating-decimal format when you turn it on. By changing the display format, you can convert a number from one format to another. 0 c (Fixed Decimal)Enables you to set the number of decimal places displayed in a result. To set the number of decimal places, press 0 c and then press the appropriate digit key (6-?). To remove the fixed-decimal setting and restore floating-decimal format, press 0 c A.
If a result has more than the selected number of decimal places, the displayed number is rounded. If a result has fewer than the selected number of decimal places, trailing 0s are added.

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Memory Operations

The memory can store any numeric value within the range of the calculator. You can use the calculators memory to store, sum, and recall a numeric value. You can use the memory in any mode. r (Store)Stores the displayed numeric value in the memory, replacing any value previously stored there. When 0 is displayed, you can clear the memory by pressing r, thereby storing a zero in memory. t (Sum)Adds the displayed numeric value to the contents of the memory. To add a series of numbers to the memory, use r to store the first number (thereby replacing any previous value). Then use t with the remaining numbers. Use s 0 P to display the total. To subtract the displayed value from the value in memory, press @ (to change the sign of the displayed value) and then press t. Use s 0 P to display the total. s 0 P (Recall Memory)Displays (recalls) the number stored in memory, without affecting the contents of the memory.
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Math Operations

0 \ (Reciprocal)Calculates the reciprocal of the displayed number, which is the same as one divided by the number. 0 ] (Square)Raises the displayed number to the second power, which is the same as multiplying the number by itself. The number can be any value whose square is in the range of the calculator. 0 k (Square Root)Calculates the square root of the displayed number. The displayed number must be positive or zero; otherwise, an error condition occurs. The result is always positive. 0 H (Universal Power)Raises any positive number to any power within the range of the calculator or calculates any root of any positive number within the range of the calculator. To calculate a power: 1. Enter the number (y) that you want to raise to a power. 2. Press 0 H. 3. Enter the power (x). 4. Press l or any key that completes the operation.
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To calculate a root: 1. Enter the number (y) whose root you want to find. 2. Press 0 H. 3. Enter the root (x). 4. Press 0 \. 5. Press l or any key that completes the operation. 0 G (Natural Logarithm)Calculates the natural logarithm (base e = 2.718281828459) of the displayed number. The number must be positive; otherwise, an error condition occurs. 0 ^ (Natural Antilogarithm) Calculates the natural antilogarithm of the displayed number. This is equivalent to the value of e raised to the power of the number in the display.

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Percentage Calculations E (Percent)Calculate percentages,
add-ons, discounts, and percentage ratios. Operation Percentage Key Sequence nnEl Function Calculates n% of the principal amount. Calculates n% of the principal amount and adds the result to the principal. Calculates n% of the principal amount and subtracts the result from the principal. Divides the principal amount by n%.

Add-On

Discount

Percentage Ratio

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Percentage Change Calculations
(Percent Change)Calculates the percentage change between two values. To calculate the percentage change: 1. Enter the new value. 2. Press 0 4. 3. Enter the old value. 4. Press l. The percentage change is calculated by the formula: New value - Old value x 100 Old value If the result is positive, there is a percentage increase. If the result is negative, there is a percentage decrease.
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Margin and Markup Calculations
To calculate cost, selling price, gross profit margin, or markup, use 2 to set the calculator to the profit-margin mode (no display indicator). R (Cost)Enters the cost. S (Selling Price)Enters the selling price. U (Margin)Enters the gross profit margin, which is the difference between selling price and cost expressed as a percentage of the selling price. 0 Z (Markup)Enters the markup, which is the difference between selling price and cost expressed as a percentage of the cost. If the percentage is positive, the selling price is greater than the cost. If the percentage is negative, the selling price is less than the cost. 1 (Computation Key)Computes the unknown value for gross profit margin problems and markup problems. Recalling Values To recall a value that you have entered or computed, press s and the appropriate key for the value you want to recall. For example, to recall the value for margin, press s U.

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Performing Gross Profit Margin Calculations To calculate cost, selling price, or gross profit margin: 1. Press 0 b to clear the registers and use 2 to enter the profit margin mode (no display indicator). 2. Enter the two known values (CST, SEL, or MAR). 3. Press 1 and the key for the unknown value. Performing Markup Calculations To calculate cost, selling price, or markup: 1. Press 0 b to clear the registers and use 2 to enter the profit margin mode (no display indicator). 2. Enter the two known values (CST, SEL, or MU). 3. Press 1 and the key (or key sequence) for the unknown value.
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Compound Interest Calculations
To calculate compound interest, use 2 to set the calculator to the to the financial mode (FIN appears in the display). In compound interest calculations in which no payment is involved, the payment (PMT) is assumed to be zero. When the payment has a value other than zero, the calculator treats the problem as an annuity (a series of regular, equal payments). Compound Interest Keys In compound interest calculations, the following keys are used to enter or calculate the values listed below. CTotal number of compounding periods. IPercent interest per compounding period. KPresent value of a future amount. With a savings account, for example, PV represents what your money is worth today. LFuture value of a present amount. With a savings account, for example, FV represents what your money will be worth in the future. 1 (Computation Key)Computes the unknown value for compound interest problems.
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Recalling Values To recall a value that you have entered or computed, press s and the appropriate key for the value you want to recall. For example, to recall the present value, press s K. Performing Compound Interest Calculations To perform a compound interest calculation, you must know any three of the four values (N, %i, PV, or FV). Follow these steps to find the unknown value: 1. Press 0 b to clear the registers and use 2 to enter the financial mode (FIN appears in the display). 2. Enter the three known values (N, %i, PV, or FV). 3. Press 1 and the key for the unknown value. For compound interest calculations, the payment (PMT) must be zero. This value is set automatically when you press 2 to enter the financial mode or when you clear the financial registers.

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Annuity Calculations

For annuity calculations, use 2 to set the calculator to financial mode (FIN appears in the display). An annuity is a series of equal payments made at regular time periods with interest calculated at the end of each period. Ordinary annuities have end-of-period payments; annuities due have beginning-of-period payments. 0 a (Beginning-of-Period)Sets the calculator to compute for annuity-due problems (beginning-of-period payments). Pressing 0 a causes Begin to appear in the display. The beginning-of-period function is in effect until you cancel it (by pressing 0 a again) or leave the financial mode. When Begin is in the display, the calculator solves using beginning-of-period payments. When Begin is not in the display, the calculator solves using end-of-period payments.
Note: If an annuity problem does not use beginning-of-period payments, be sure that Begin is not in the display before you compute the answer. Having Begin in the display has no effect on compound interest calculations in which no payment is involved.
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Annuity Keys In annuity calculations, the following keys are used to enter or calculate the values listed below. CTotal number of payment periods. IPercent interest per payment period. KPresent value of a series of payments plus the present value of FV. With a savings account, PV represents an initial deposit (not including the first payment). With a loan, PV represents the loan amount. MAmount of the regular payment. This value may be positive or negative, depending on the type of problem you are solving (as explained on page 20). LFuture value of a series of payments plus the future value of PV. With a savings account, FV represents the final amount withdrawn. With a loan, FV represents any balloon payment that must be made in addition to the last regular payment. 1 (Computation Key)Computes the unknown value for annuity problems. When Begin is not displayed, the 1 key computes the unknown value for ordinary annuities (annuities with end-of-period payments). When Begin is displayed, the 1 key computes the unknown value for annuities due (annuities with beginning-of-period payments). 19

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Annuity Calculations (Continued)
Recalling Values To recall a value that you have entered or computed, press s and the appropriate key for the value you want to recall. For example, to recall the present value, press s K. Positive or Negative Payments In annuity problems, the present value and future value are usually positive numbers. The payment amount may be positive or negative, depending on the type of problem you are solving. If payments are discounted backward, the payment amount is positive. This is the case in mortgage, loan, bond, and lease problems. These problems have a present value, but they may or may not have a future value. (If there is no future value, FV=0.) If payments are compounded forward, the payment amount is negative. This is the case in savings problems. These problems have a future value, but they may or may not have a present value. (If there is no present value, PV=0.)
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Performing Annuity Calculations To perform an annuity calculation, you must know any four of the five values (N, % i, PV, PMT, or FV). Follow these steps to find the unknown value: 1. Press 0 b to clear the registers, and use 2 to enter the financial mode (FIN appears in the display). 2. Ensure that the calculator is set correctly for the type of annuity calculation desired. For ordinary annuities, Begin should not be displayed. For annuities due, Begin should be displayed.
Press 0 a to turn Begin on or off. 3. Enter the four known values (N, % i, PV, PMT, or FV). 4. Press 1 and the key for the unknown value. Note: Generally, solving for the interest rate requires more time than other calculations. If you use unrealistic values, the calculator may take several minutes before indicating an error condition. If this occurs, press u to clear the calculation.
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Special Functions for Monthly Compounding or Payment Periods 0 h (Monthly Interest)Divides the number in the display by 12 and displays the result. This number can then be stored as the monthly interest rate (%i). To use the 0 h key sequence: 1. Enter the annual interest rate for a compound interest or annuity problem. 2. Press 0 h. Then press I to store the result. The two steps above have the same effect as entering the number of years and then pressing m 12 l. 0 i (Number of Monthly Payments) Multiplies the number in the display by 12 and displays the result. This number can then be stored as the number of compounding periods or payment periods (N). To use the 0 i key sequence: 1. Enter the number of years for a compound interest or annuity problem with monthly compounding or payment periods. 2. Press 0 i. Then press C to store the result. The two steps above have the same effect as entering the number of years and then pressing n 12 l. 22

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Balance, Interest, and Principal (Cont.)
Calculating a Range of Payments To find the summed interest and principal over a range of payments: 1. If necessary, press 0 a to change the calculator to solve for end-of-period payments or beginning-of-period payments. 2. Enter the appropriate values with the C, I, K, L, and M keys. 3. Enter the first payment number (P1) and press X. 4. Enter the second payment number. 5. Press V to calculate the interest. (The Gint indicator is displayed with the result.) 6. Press w to display the principal. (The Gprn indicator is displayed with the result.) If you want to display the interest portion again, press w. Pressing w alternately displays the interest and principal.
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Statistics

To enter a statistics problem, use 2 to set the calculator to the statistics mode (STAT appears in the display). 0 b (Clear Mode Registers)Clears any previously entered data points. g (Statistics Data Entry)Enters the displayed number as a data value in the statistical registers. Each time you press g, the display shows the number of data values currently stored in the statistical registers.
0 f (Statistics Data Removal) Removes a data value from the statistical registers. Each time you press 0 f, the display shows the number of data values currently stored in the statistical registers.
Entering Two-Variable Data Values Use w in conjunction with g to enter data points with both x and y values as follows: 1. Enter an x value and press w. 2. Enter a y value and press g. Repeat the procedure to enter additional data points. You can also follow this procedure with 0 f to remove data points.
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Statistics (Continued)

Mean 0 z (Data Mean)Calculates the mean (average) of all the data values currently stored in the statistical registers. If you have entered data points with x and y values, press 0 z to display the mean of the y values; then press w to display the mean of the x values. Standard Deviation The 0 y and 0 x key sequences calculate the standard deviation of the data values in the statistical registers. If you entered data points with x and y values, press 0 y or 0 x to display the standard deviation of the y values; then press w to display the standard deviation of the x values.
0 y (Population Deviation) Calculates the n weighted (or population) standard deviation.
0 x (Sample Deviation)Calculates the n - 1 weighted (or sample) standard deviation.
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Linear Regression 0 { (Intercept/Slope)Enables you to display the y-intercept and slope of the representative line. To display the y-intercept (b), press 0 {; to display the slope (a), press w after you display the y-intercept. 0 d (Correlation)Calculates the correlation between the x and y values in a set of data points. 0 T, 0 Q (Predicted Value)After you enter an x value, you can press 0 Q to display the y value that corresponds with that x on the best straight line through the data points entered. Similarly, after you enter a y value, you can press 0 T to display the corresponding x value.
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Common Keystroke Sequences
Monthly Payment for a Home Mortgage Purpose: To find the amount of the monthly payment on a mortgage with end-of-month payments (ordinary annuity). Values You Supply: mortgage amount annual interest rate number of years in mortgage Procedure Clear calculator and mode registers; select two decimal places. Press 2 until FIN is displayed. Press 0 a until Begin is not displayed.* Enter mortgage amount. Calculate interest rate. Enter interest rate. Calculate number of payment periods. Enter number of payment periods. Compute monthly payment. * Key Sequence -0b 0c0a mortgage K rate 0 h I years 0 i C 1M

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Procedure Press 0 a until Begin is not displayed.* Enter monthly interest rate. Calculate and enter number of monthly payments. Calculate and store maximum monthly payment. Calculate and enter maximum allowable loan payment (without taxes or insurance). Compute maximum allowable loan amount. Calculate house price (including down payment). Calculate down payment.
Key Sequence 0a rate 0 h I years 0 i C income n percent limit E lr 1 p percent taxes and insurance E l 0\ns 0PlM 1 PV 1 o percent down El0\ nsKl osKl
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Selling Price of a House if Seller Pays Points and Commission Purpose: To find the selling price of a house, assuming that the seller wants to make a certain profit and that the selling price must include points and commission. Values You Supply: original price (dollar amount) profit (dollar amount) points (percentage points) commission (percentage points) Procedure Clear calculator and mode registers; select two decimal places. Press 2 until no mode indicator is displayed. Add original price and profit to calculate cost before points are added on, and enter. Enter points as a margin. Key Sequence -0b 0c2

Compute selling price.

original price p profit l R points p commission l U 1S
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Error Conditions

When an error condition occurs, the word Error appears in the display. The calculator will not accept a keyboard entry until you press - or u to clear the error condition. (Press - twice to clear the condition and all pending operations; press u to clear the calculator completely.) General Error Conditions The error conditions listed below can occur in any mode. Errors occur when you: Calculate a result that is outside the range -9.999999 x to -1 x 10 -99, zero, or 1 x 10 -99 to 9.999999 x 10 99. Divide a number by zero. Calculate 0 G or 0 \ of zero. Calculate for an old value equal to zero. Calculate 0 k, 0 G, or 0 H of a negative number. Use 0 H to raise zero to the power of zero. Press a key or key sequence that cannot be performed in the current mode.
Financial Error Conditions In the financial mode, errors occur when you: Calculate a financial unknown before you have entered enough known variables or when no solution exists. 35
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Error Conditions (Continued)
Financial Error Conditions (Continued) Use 0 O or 0 N when the number of compounding periods per year is zero or very large, or when %i is small. Compute the balance or interest for a payment number less than zero.
Statistics Error Conditions In the statistics mode, errors occur when you: Use g to enter a data point (x or y) such that |x| > 1 x 10 50. Press 0 f when there are less than two data points in the statistical registers. Calculate 0 x with only one data point. Perform a statistical calculation when there are no data points. Perform a linear regression calculation with less than two data points. Perform a linear regression calculation on a vertical line. Enter a series of data values such that the sum of their squares exceeds the upper or lower limit of the calculator.
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In Case of Difficulty

If you have difficulty operating the calculator, you may be able to correct the problem with the solutions suggested in the table below. Observation Display is blank; digits do not appear. Action The display goes blank during a long calculation. Wait for it to finish. Be sure the solar power cells are exposed to an adequate light source. Be sure the calculator is set for the correct mode profit margin, FIN, or STAT. Be sure the display is set to the correct format floating decimal or fixed decimal. Check the error conditions listed on pages 35-36.
A function does not seem to work. The number of decimal digits that you expect is not displayed. An error occurs.
If you experience difficulties other than those listed above, press u to clear the calculator, and then repeat your calculation. Review the operating instructions to be sure that you are performing the calculation correctly.
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TI Product Service and Warranty Information
TI Product and Services Information For more information about TI products and services, contact TI by e-mail or visit the TI calculator home page on the world-wide web. e-mail address: internet address: ti-cares@ti.com http://www.ti.com/calc

Service and Warranty Information For information about the length and terms of the warranty or about product service, refer to the warranty statement enclosed with this product or contact your local Texas Instruments retailer/distributor.
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REVIEW OF CALCULATOR FUNCTIONS FOR THE TEXAS INSTRUMENTS BA-35@
Samuel Brovennan, University of Toronto This note presents a review of calculator financial functions for the Texas Instruments BA-35 calculator. A number of the examples used as illustrations are from the 3rd edition of the book Mathematics of Investment and Credit, by S. Broverman. A detailed guidebook for the operation of and functions available on the BA-35 can be found at the following internet site: http://education.ti.com/us/global!guides.html#finance. It will be assumed that you have available and have reviewed the appropriate guide book for the calculator that you are using. Financial functions will be reviewed in the order that the related concepts are covered in Chapters 1 to 8 of Mathematics of Investment and Credit. Some numerical values will be rounded off to fewer decimals than are actually displayed in the calculator display. It will be assumed that unless indicated otherwise, each new keystroke sequence starts with clear registers. Calculator registers are cleared with the keystroke IAc/oNI.
ACCUMULA TED AND PRESENT VALUE OF A SINGLE PAYMENT USING A COMPOUND INTEREST RATE
Accumulated values and present values of single payments using annual effective interest rates can be detennined using the calculator functions as described below.
Accumulated Value: We use Example 1.1 to illustrate this function. A deposit of 1000 made at time 0 grows at annual effective interest rate 9%. The accumulated value at the end of 3 years is 1000(1.09)3 = 1,295.03. This can be found using the calculator in two ways:
1. Calculator can be in any MODE. Key in I.0912nd[
Key in 3 [;] GJ, Key in 1000 [;]. The screen should display 1,295.029. In this function, y = 1.09 and x = 3. 2. Calculator in "Fin" MODE. Key in 1000jPV[, Key in 9 BTI, Key in 3lliJ ICPTIIFVI. The screen should display 1,295.029. Present Value: We use Example I.5(a) to illustrate this function. The present value of 1,000,000 due in 25 years at effective annual rate.195 is 1,000,000v25 = 1,000,000(l.195r25 = 11,635.96. This can be found using the calculator in two ways: 1. Calculator can be in any MODE.

Key in 1.19512nd[

Key in 251+/-1 [;] GJ, Key in 1000000. [;].
The screen should display 11,635.96 This keystroke sequence can be replaced by:
Key in 1.195 12nd[ 11Ix[ 12nd[

Key in 25 [;] GJ,

Key in 1000000 [;]. 2. Calculator in "Fin" MODE.

Key in 1000000 FV ,

Key in 19.5 BTI, Key in 25 lliJ ICPTllpvl, The screen should display 11,635.96. As a more general procedure, in the equation (PV)(l+i)N = FV, if any 3 of the 4 variables PV, i , N, FV are entered, then the 4th can be found using the ICPT[ function.
Unknown Interest Rate: As an example of solving for the interest rate, we consider Example 1.5(c).
An initial investment of 25,000 at annual effective rate of interest i grows to 1,000,000 in 25 years. Then 25,000(1 +i)25 = 1,000, 000, from which we get i=(40)1/25-1=.I590(15.90%). This can be found using the calculator power function with the following keystrokes: 40 /2ndl [Z].04 [;] g 1 [;], the screen should display.15899723.
Using financial functions, the keystroke sequence solving for i is Key in 25,000Ipyl, Key in 1,000,000 IFyl,

Key in 25lliJ CPT! [!Jj.

The screen should display 15.90 (this is the % measure to the nearest.01%).
Unknown Time Period: As an example of solving for an unknown time period, suppose that an initial investment of 100 at monthly compound rate of interest i grows to 300 in n months at monthly interest rate i =.75%. Then 100(1.0075t which we get n =

calculator

= 300, from
Inl~~75 = 147.03 months. This can be found using the

IIn x I function.

Using financial functions, the keystroke sequence solving for n is Key in 1001pyl, Key in 300 IFyl, Key in.75[!Jj ICPTllliJ. The screen should display 147.03026. Slightly more than 147 months of compounding will be required. The calculator returns a value of n based on compounding including fractional periods, so that the value of 147.03026 means that 100(1.0075)147.03026300. =

EQUIVALENT INTEREST AND DISCOUNT RATES
The annual effective rate of discount can be found from the annual effective rate of interest and vice-versa in the following way. An annual effective interest rate of i =.10 (10%) is equivalent to an annual effective rate of discount of d =.0909 (9.09%). The simple relationships
d = II i and i = I:! d can be used, or the equivalent rates can be found in the following ways with the calculator in "Fin" MODE.
1. 12ndll~ EFF[, Key in 1012nd[I~APRI, Key in 11+/-1 [;]. The screen should display 9.090909091.
We have converted the annual effective interest rate of 10% (Key in 10) to the equivalent annual effective discount rate of 9.091 %.
12ndll~ APRI , Key in 9.09112ndll~ EFFI, Key in 11+/-1 [;],
The screen should display 10.00011.
We have converted the annual effective discount rate of 9.091% (Key in 9.091) to the equivalent annual effective interest rate of 10% (10.0001 due to rounding in 9.091).
ACCUMULATED AND PRESENT VALUES USING A COMPOUND DISCOUNT RATE
Accumulated values and present values of single payments using an annual effective rate of discount can be made in the following way.
Accumulated Value: A deposit of25 made at time 0 grows at annual effective discount rate 6%. The accumulated value at the end of 5 years is: 25(1-.06fs = 25(.94fs = 34.06.
This can be found using the calculator in two ways:
1. Calculator can be in any MODE. Key in.9412ndllZJ, Key in 5 1+/-1 [;] GJ, Key in 25 [;]. The screen should display 34.06 (nearest.01). 2. Calculator in "Fin" MODE. Key in 25 Ipvl, Key in 61+/-1~, Key in 51+/-1 [H] ICPTIIFVI, The screen should display 34.06. We have used the financial functions to calculate PV. (1+ i)N, where PV = 25, i = -.06 and N = -5 , to get 25(1-.06r5.
We could also find the annual effective interest rate and accumulate. Present Value: The present value of 500 due in 8 years at annual effective discount 8% is 500(1-.08)8 = 500(.92)8 = 256.61. This can be found using the calculator in two ways:

rate of

1. Calculator can be in any MODE. Key in.9212ndllZJ, Key in 8[;] GJ, Key in 500[;]. The screen should display 256.61. 2. Calculator in "Fin" MODE. Key in 500IFV[, Key in 81+/-1 ~, The screen should display 256.61.
Key in 81+/-1 [H] ICPTllpv[.
CONVERSION BETWEEN EQUIVALENT NOMINAL AND ANNUAL EFFECTIVE RATES
Given a nominal annual interest rate compounded m times per year, the annual effective rate of interest can be determined using the calculator as illustrated below. A nominal annual interest rate of.24 (24%) compounded monthly is
equivalent to an annual effective rate of interest of i =.2682 (26.82%).

r be found in the following ways with the calculator in "FIN" MODE.

The relationship i = 1+

-1 can be used, or the equivalent rates can
12ndll~APRI, Key in 2412ndll~ EFFI, Key in 12g. The screen should display 26.82. We have converted the nominal annual interest rate of 24% (Key in 24) compounded monthly (Key in 12) to the equivalent annual effective interest rate of26.82%.
Given an annual effective rate of interest, the nominal annual interest rate compounded m times per year can be determined using the calculator as illustrated below.
12nd[I~EFFj, Key in 26.8212ndll~APRI, Key in 12g. The screen should display 23.9966 (round to 24). We have converted the annual effective interest rate of26.82% to the equivalent nominal annual interest rate compounded monthly (Key in 12) of24%.
CONVERSION BETWEEN NOMINAL DISCOUNT AND EFFECTIVE INTEREST RATES
Given a nominal annual discount rate compounded m times per year, the annual effective rate of interest can be determined using the calculator as illustrated below. A nominal annual discount rate of.09 (9%) compounded quarterly is
equivalent to an annual effective rate of interest of i =.0953 (9.53%). --4

The relationship i = 1 -

-1 can be used, or the equivalent
can be found in the following ways with the calculator in "Fin" MODE.
12ndll~APRI, Key in 912ndll~EFFI, Key in 41+/-1[;]. The screen should display 9.53. We have converted the nominal annual discount rate of 9% compounded quarterly to the equivalent annual effective interest rate of9.53%. Given an annual effective rate of interest, the nominal annual discount rate compounded m times per year can be determined using the calculator as illustrated below. 12ndll~ EFFI, Key in 9.5312ndll~ APRI, Key in 41+/-1 [;]. The screen should display 9.00. We have converted the annual effective interest rate of 9.53% to the equivalent nominal annual discount rate compounded quarterly of 9%.
LEVEL PAYMENT ANNUITY VALVA nON
Annuitv Immediate The accumulated value and present value of a level payment annuityimmediate can be found using calculator functions. Clear calculator registers before starting the keystroke sequence. The calculator should be in "Fin" MODE. Accumulated Value: Suppose that a deposit of 1000 is made at the end of each year for 20 years. The deposits earn interest at an annual effective rate of interest of 4%. The accumulate value of the deposits at the time of (and including)
the 20th deposit is 1000s201.o4
= 1000[(1.~6r-l ] = 29,778. This can be
found using the calculator. Key in 10001+/-I]PMTI, Key in 20lliJ, Key in 4~ ICPTIIFVI. The screen should display 29,778 (rounded to nearest 1). Note that the payment amount is entered as a negative quantity when finding accumulated value of an annuity (FV). Present value: Payments of 50 will be made at the end of each month for 10 years. The monthly compound interest rate is % %. The present value of the annuity

one month before the first payment is made is

50al2ol.o075

I-v120

.OOO~~5

]=3,947
(lOyears, 12 months per year).
Key in 501pMTI, Key in 120lli.], Key in.75 [lliJ ICPTllpvl. The screen should display 3,947 (rounded to nearest 1).
In the general equation PV. aNli if any 3 of the 4 variables PV,
PMT, N, i (in %) are given, then the calculator functions can be used to solve for the 4th variable. The same is true for the equation PMr. SNli = FV (in the FV case, PMT must be entered as negative, and will be returned as negative).
Findin!! the Payment: A loan of 1000 is to be repaid with monthly payments for 3 years at a compound monthly interest rate of ~ %. The monthly payment is K
where 1000 = Ka361oo5'so that K =

361005

= 30.42.
This can be found using the folIowing sequence of keystrokes:
Key in 36lli.], Key in.5 [lliJ, Key in 1000IpvllcPTI!PMTI. The screen should display 30.42.
Findin!! the Unknown Interest Rate: Suppose that the loan payment is 35 and the interest rate is to be found.

Then 1000

= 35l136Ji' There is no algebraic

solution

for i. The following

keystrokes give us i.

Key in 36lli.], Key in 1000Ipvl, Key in 35!PMTllcPTI [lliJ.
The screen should display 1.31 (%). That is the effective rate of interest per month.
Findine the Unknown Number ofPavments: We will use Example 2.13 to illustrate the calculator function for finding the unknown number of payments. In Example 2.13, Smith wishes to accumulate 1000 by means of semiannual deposits earning interest at nominal annual rate P) =.08, with interest credited semiannually. In part (a) of Example 2.13, Smith makes deposits of 50 every six months. We wish to solve for n in the equation 1000 = 50. 8n1.04. The following keystrokes give us n. Key in 10001FVI, Key in 501+/-llpMTI, Key in 4ffiTI, Key in ICPTllliJ. The display should read 14.9866. 14 deposits are not sufficient. The accumulated value 6 months after the 14thdeposit is 50,sm04

=50(1.04).8i=951.18.

The next functions reviewed relate to finding the value of an annuity-due. The BA II PLUS has functions that find annuity values when the interest period and the payment period do not coincide. The BA-35 Solar calculator does not have such functions, so we would always find the equivalent interest rate for the payment period for the BA-35.
Annuity-Due The accumulated value and present value of a level payment annuity-due can be found using calculator functions. The same method applies as for annuities-immediate, with the additional requirement that keystrokes 12ndllBGNI must be entered. (BGN makes the calculator view payments as being made at the beginning of each period.) In the equation PV

we can find the 4th.

= PMT. = PMT.
Ctmi'if any 3 of PV, PMT, N, i are entered,

In the equation FV

S-Nliif any 3 of FV, PMT, N, i are entered,
we can find the 4th (PMT is entered and returned as a negative number).
Findin!! the Amount and Time of a Balloon Payment: We can use the calculator functions to find the balloon payment required to repay a loan which has level payments for as long as necessary with a final balloon payment. In Example 2.15(a) of Chapter 2, a loan of 5000 is being repaid by monthly payments of 100 each, starting one month after the loan is made, for as long as necessary plus an additional tractional
payment. At interest rate
=.09, we are to find the number of full
payments that are required to repay the loan, and the amount of the additional fractional payment required if the additional tractional payment is made at the time of the final regular payment. We find the number of payments needed with the following keystrokes. Key in 50001pvl, Key in 100IPMTI, Key in.751RIJ, Key in ICPTllliJ. The display should read 62.9. This indicates that the 62ndpayment is not quite enough to repay the loan. The additional payment needed, say X, at the time of the 62ndregular payment of 100 is found from the relationship X

= 5000(1.0075)62 -100.

s621.oo75

= 89.55.

The keystrokes that will produce the value of X are
Key in 50001pvl, Key in 1001PMTI, Key in.751RIJ, Key in 62lliJ, Key in ICPTIIFVI. The display should read 89.55.
VALVA TION OF INCREASING AND DECREASING ANNUITIES
The values of (fa), nil (present value) and (Ds), nil (accumulated value) can be found using calculator financial functions. From those values we can then find (Is),nil = (Ia),. (1+it, and (Da),. = (Is),nil.vn. The nil nil
following two examples illustrate the method.

Increasine Annuitv:

Suppose that we wish to find (Ia)2ol08 =
numerator with the following keystrokes.

20 am08- 20v.

. We first find the
Key in 12ndII BGN 1 Key in 20 lliJ , Key in 8 ~I]' ' Key in 1IPMTI, 2ol+/-IIFVI, Key in ICPTllpvl.
The display should read 6.3126, which is Q2ol08- 20v20.
In this sequence of keystrokes, we have created a series of 20 payments received of 1 each at the start of each year (lBGNI), combined with a payment of 20 paid out at the end of 20 years (lFVI). The net present
value is Q2ol.08 20v20 = 6.3126. Then, (Ia)2ol80= 6'~01;6= 78.908. Note that instead of entering 11PMTI we could enter.6s IPMTI,
and instead of entering 20 FV we could enter

Then ICPTllpvl

includes division by.08.
Note that we cannot use these calculator functions to find (Is);;];, but since the numerator of (Is),. is s,. - n, we can find s,. first, then nIl nil nil
subtract n, and then divide by i. Decreasine Annuitv:. 35(1.04)35-s351 04.04.'
Suppose that we wish to find (Ds )35104 =
We first find the numerator with the following keystrokes.
Key in 3SlliJ, Key in 4 ~,

Key in 3slpvl,

1IPMTI, Key in ICPTIIFVI.
The display should read 64.4609, which is 35(1.04)35 - S351.04.
In this sequence of keystrokes we have created an initial payment received
and a series of 35 payments of 1 each paid out at the ' end of each year. The net accumulated value at the end of 35 years is 35(1.04)35 -s35104 = 64.4609 (]FVI). Then, of 35 at time 0

(Ds)351.04

= 64:ci~09 -1,611.52.
LEVEL PAYMENT LOAN AMORTIZATION
For a loan with level payments, or with level payments plus an additional lump sum payment at the time of the last regular payment, there are calculator functions for finding outstanding balances, interest or principal paid in a single payment, and interest or principal paid in a range of payments. We use Example 3.3 to illustrate these functions. A homebuyer borrows $250,000 to be repaid over a 30-year period with level monthly payments beginning one month after the loan is made. The interest rate on the loan is a nominal annual rate of 9% compounded monthly. The loan payment is K= ~50,OOO -2,01l.56.

3601.0075 The outstanding balance at the end of the first year (after the 12thmonthly payment) OB12 = 2, 01l.56Cl348Jo075 =248, 292.01. The principal repaid in the 12th payment is PR12 = Kv360-12+1
= 2,01l.56v349 = 148.25,and the
interest paid in the Ith payment is 112=K(1-v360-12+1)=1,863.30. The principal repaid in the 2ndyear (the 13ththrough 24th payments inclusive) is PR 13 + PR 14 +. + PR 23 + PR 24 = K( V348 +v 347 +. +v

= 1,868.21,

the interest paid in the 2nd year is 113+114 +.+123 +124
+1-v347 +'''+I-v338 +1-v337)

K(1-v348

-(PR13+PRI4 +. +PR23+PR24)

= 22,270.46.

These calculations can be done using the calculator functions in "Fin" MODE.
Key in 250000 PV , Key in 360 lliJ Key in.75 !1ill , ' Key in ICPTllpMTI and -2,011.56 is displayed (we must key in the
PMT key in order to continue with the amortization functions).
To find OBI2 use the following keystrokes: Key in 121BAL I.The display should read 248,292.01. This is OB12' To find 112and PR12 use the following keystrokes:
Key in 121lIP I.The display should read 1,863.3 O. This is 112'
Key in Ix~yl. The display should read 148.25. This is PRI2'
To find 113+114 +"'+123 use the following keystrokes: +124 and PR13 +PRI4 +.+PR23 +PR24
Key in l3Ip/P2I, Key in 241I/PI. The display should read 22,270.46. This is 113+ 114+. + 123+ 124 Key in Ix~yl. The display should read 1,868.21. This is PR13+ PRI4 +. + PR23 + PR24
Note that PR13 +PRI4 +.+PR23 from OB12 and OB24 and the relationship

113 +114 +.+123 +124

OB12 -OB24 could be found
113+ 114+. + 123+ h4 can be derived from
= 12K-(PR13+.+PR24) = 12K-(OB12-0B24)
BOND VALVA TION AND AMORTIZATION
It is possible to calculate the price or yield to maturity of a bond using the calculator. We use Example 4.1(a) to illustrate the functions. Findine: Bond Price on a Coupon Date: A 10% bond with semiannual coupons has a face amount (par value) of 100 and is issued on June 18, 1990. The bond has a maturity date of June 18, 2010. We wish to find the price of the bond on its issue date using a nominal annual yield rate of 5% convertible semi-annually.
The bond price is 100v6~5 + 100(.05). G;wJ.025= 162.76 (nearest.01). If
the bond has maturity value 110. then the price is
II OV6~5 + 110(.05). G;wJ.025= 166.48.
These prices can be found using the calculator in the following way:
There are 40 coupons to maturity, and the yield rate is 2.5% per coupon period. Key in 1001FVI, Key in SIPMT\, Key in 2.5 ~, Key in 40lli] ICPTllpvl.

The display should read 162.76. Note that the coupon payment (PMT) is 5. Key in 1101FVI, Key in SIPMTI, Key in 2.5 ~, Key in 40lli] ICPTllpvl.
The display should read 166.48. Note that the coupon payment is 5, and maturity (FV) is 110. Findine: Bond Yield on a Coupon Date: We can use the worksheet to find the yield rate from the price. Suppose that the bond above with face amount 100 has a price of ISO. There is no algebraic solution for the yield-to-maturity P) = 2), where), the 6-
month yield rate is the solution of the equation ISO = 100vJo + SG;wJj'
The yield-to-maturity can be found using the following sequence of keystrokes.
Key in 100 IFVI, Key in 51PMTI ,
Key in 150]pvl, Key in 40lliJ ICPTI~.
The display should read 2.88 (YTM is 2.88% per coupon period). This would be expressed as a nominal annual interest rate of S.76% compound semi-annually.
Bond Amortization: The bond amortization components can be found using the calculator in much the same way they are found for loan amortization. A bond has face amount 1000, coupon rate 5% per coupon period, maturity value 1000, 20 coupon periods until maturity and yield-to-maturity 6% (per coupon period). The bond's amortized value just after the 5thcoupon is BVs

I 000V~6 + 1000(.05).

= 902.88.
This can be found using the following keystrokes:

Key in 1000 FV ,

Key in SOIPMTI,
Key in 6~, Key in 20lliJ ICPTllpvl. Key in SIBALI. The display should read 902.88. As an alternative, the following keystrokes will also give BVs' Key in 1000lFVI, Key in 50IPMTI, Key in 6~, Key in ISlliJ ICPTllpvl. The display should read 902.88. The display should read 885.30. Then
We have found the price of the bond with 15 coupons remaining to maturity, using the original coupon rate and yield to maturity. The BA II PLUS calculator has a function than can find the price of a bond on any date. The BA-35 does not have this function. Also, the BA II PLUS has NPV and IRR functions that are not available on the BA-35.