CP

Notice that either PV or FVnin Equation 2-2 must be negative to make the equa-

tion true, assuming nonnegative interest rates. Thus, most financial calculators re-

quire that all cash flows be designated as either inflows or outflows, with outflows be-

ing entered as negative numbers. In our illustration, you deposit, or put in, the initial

amount (which is an outflow to you) and you take out, or receive, the ending amount

(which is an inflow to you). Therefore, you enter the PV as 
100. Enter the 
100 by

keying in 100 and then pressing the “change sign” or /
key. (If you entered 100,

then the FV would appear as 
127.63.) Also, on some calculators you are required to

press a “Compute” key before pressing the FV key.

Sometimes the convention of changing signs can be confusing. For example, if you

have $100 in the bank now and want to find out how much you will have after five

years if your account pays 5 percent interest, the calculator will give you a negative an-

swer, in this case 
127.63, because the calculator assumes you are going to withdraw

the funds. This sign convention should cause you no problem if you think about what

you are doing.

We should also note that financial calculators permit you to specify the number of

decimal places that are displayed. Twelve significant digits are actually used in the

calculations, but we generally use two places for answers when working with dollars or

percentages and four places when working with decimals. The nature of the problem

dictates how many decimal places should be displayed.

SPREADSHEET SOLUTION

Spreadsheet programs are ideally suited for solving many financial problems, includ-

ing time value of money problems.^5 With very little effort, the spreadsheet itself be-

comes a time line. Here is how the problem would look in a spreadsheet:

60 CHAPTER 2 Time Value of Money

(^5) In this section, and in other sections and chapters, we discuss spreadsheet solutions to various financial
problems. If a reader is not familiar with spreadsheets and has no interest in them, then these sections can
be omitted. For those who are interested, Ch O2 Tool Kit.xlsis the file on the web site for this chapter that
does the various calculations using Excel. If you have the time, we highly recommendthat you go through the
models. This will give you practice with Excel,which will help tremendously in later courses, in the job mar-
ket, and in the workplace. Also, going through the models will enhance your understanding of financial
concepts.
ABCDEFG
1 Interest rate 0.05
2 Time 01234 5
3 Cash flow
100
4 Future value 105.00 110.25 115.76 121.55 127.63
Cell B1 shows the interest rate, entered as a decimal number, 0.05. Row 2 shows the
periods for the time line. With Microsoft Excel,you could enter 0 in Cell B2, then the
formula B2 1 in Cell C2, and then copy this formula into Cells D2 through G2 to
produce the time periods shown on Row 2. Note that if your time line had many years,
say, 50, you would simply copy the formula across more columns. Other procedures
could also be used to enter the periods.
See Ch 02 Tool Kit.xls.

58 Time Value of Money