CP

would enter 1 i 1.05 and multiply it by itself four times, or else enter 1.05, then press

the yx(exponential) function key, and then enter 5. In either case, your answer would be

1.2763 (if you set your calculator to display four decimal places), which you would mul-

tiply by $100 to get the final answer, $127.6282, which would be rounded to $127.63.

In certain problems, it is extremely difficult to arrive at a solution using a regular

calculator. We will tell you this when we have such a problem, and in these cases we

will not show a numerical solution. Also, at times we show the numerical solution just

below the time line, as a part of the diagram, rather than in a separate section.

FINANCIAL CALCULATOR SOLUTION

A version of Equation 2-1, along with a number of other equations, has been pro-

grammed directly into financial calculators, and these calculators can be used to find

future values. Note that calculators have five keys that correspond to the five most

commonly used time value of money variables:

Here

N the number of periods. Some calculators use n rather than N.

I interest rate per period. Some calculators use i or I/YR rather than I.

PV present value.

PMT payment. This key is used only if the cash flows involve a series of equal,

or constant, payments (an annuity). If there are no periodic payments in

a particular problem, then PMT 0.

FV future value.

On some financial calculators, these keys are actually buttons on the face of the calcu-

lator, while on others they are shown on a screen after going into the time value of

money (TVM) menu.

In this chapter, we deal with equations involving only four of the variables at any

one time—three of the variables are known, and the calculator then solves for the

fourth (unknown) variable. In Chapter 4, when we deal with bonds, we will use all five

variables in the bond valuation equation.^3

To find the future value of $100 after five years at 5 percent, most financial calcu-

lations solve Equation 2-2:

. (2-2)
The equation has four variables, FVn, PV, i, and n. If we know any three, we can solve
for the fourth. In our example, we enter N 5, I 5, PV –100, and PMT 0.
Then, when we press the FV key, we get the answer, FV 127.63 (rounded to two
decimal places).^4

PV(1i)nFVn  0

Future Value 59

(^3) The equation programmed into the calculators actually has five variables, one for each key. In this chapter,
the value of one of the variables is always zero. It is a good idea to get into the habit of inputting a zero for
the unused variable (whose value is automatically set equal to zero when you clear the calculator’s memory);
if you forget to clear your calculator, inputting a zero will help you avoid trouble.
(^4) Here we assume that compounding occurs once each year. Most calculators have a setting that can be used
to designate the number of compounding periods per year. For example, the HP-10B comes preset with
payments at 12 per year. You would need to change it to 1 per year to get FV 127.63. With the HP-10B,
you would do this by typing 1, pressing the gold key, and then pressing the P/YR key.

Time Value of Money 57