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An Introduction to Financial Calculators

Financial calculators are designed with present value and future value formulas already programmed. Therefore, you can readily solve many problems simply by entering the inputs for the problem and punching a key for the solution.

The basic financial calculator uses five keys that correspond to the inputs for common problems involving the time value of money.

Each key represents the following input:

І n is the number of periods. (We have been using t to denote the length of time or number of periods. Most calculators use n for the same concept.)

І i is the interest rate per period, expressed as a percentage (not a decimal). For example, if the interest rate is 8 percent, you would enter 8, not .08. On some calculators this key is written I/Y or I/YR. (We have been using r to denote the interest rate or discount rate.)

І PV is the present value.

І FV is the future value.

І PMT is the amount of any recurring payment (called an annuity). In single cash-flow problems such as those we have considered so far, PMT is zero.

Given any four of these inputs, the calculator will solve for the fifth. We will illustrate with several examples.

Future Values

Recall Example 3.1, where we calculated the future value of Peter Minuit`s $24 investment. Enter 24 into the PV register. (You enter the value by typing 24 and then pushing the PV key.) We assumed an interest rate of 8 percent, so enter 8 into the i register. Because the $24 had 374 years to compound, enter 374 into the n register. Enter 0 into the PMT register because there is no recurring payment involved in the calculation. Now ask the calculator to compute FV. On some calculators you simply press the FV key. On others you need to first press the ¬compute ­ key (which may be labeled COMP or CPT), and then press FV. The exact sequence of keystrokes for three popular financial calculators are as follows:1

You should find after hitting the FV key that your calculator shows a value of Ј75.979 trillion, which, except for the minus sign, is the future value of the $24.

Why does the minus sign appear? Most calculators treat cash flows as either inflows (shown as positive numbers) or outflows (negative numbers). For example,

if you borrow $100 today at an interest rate of 12 percent, you receive money now (a positive cash flow), but you will have to pay back $112 in a year, a negative cash flow at that time. Therefore, the calculator displays FV as a negative number. The following time line of cash flows shows the reasoning employed. The final negative cash flow of $112 has the same present value as the

$100 borrowed today.

If, instead of borrowing, you were to invest $100 today to reap a future benefit, you would enter PV as a negative number (first press 100, then press the +/ Ј key to make the value negative, and finally press PV to enter the value into the PV register). In this case, FV would appear as a positive number, indicating that you will reap a cash inflow when your investment comes to fruition.

Present Values

Suppose your savings goal is to accumulate $10,000 by the end of 30 years. If the interest rate is 8 percent, how much would you need to invest today to achieve your goal? Again, there is no recurring payment involved, so PMT is zero. We therefore enter the following: n = 30; I = 8; FV = 1,000; PMT = 0. Now compute PV, and you should get an answer of Ј993.77. The answer is displayed as a negative number because you need to make a cash outflow (an investment) of $993.77 now in order to enjoy a cash inflow of $10,000 in 30 years.

Finding the Interest Rate

The 25-year Coca-Cola Enterprises IOU in Example 3.3 sold at $129 and promised a final payment of $1,000. We may obtain the market interest rate by entering n = 25, FV = 1,000, PV = Ј129, and PMT = 0. Compute i and you will find that the interest rate is 8.53 percent. This is the value we computed directly (but with more work) in the example.

How Long an Investment?

In Example 3.5, we consider how long it would take for an investment to double in value. This sort of problem is easily solved using a calculator. If the investment is to double, we enter FV = 2 and PV = Ј1. If the interest rate is 9 percent, enter i = 9 and PMT = 0. Compute n and you will find that n = 8.04 years. If the interest rate is 9.05 percent, the doubling period falls to 8 years, as we found in the example.