- SPEADSHEET SOLUTION
70 CHAPTER 2 Time Value of Money
Most spreadsheets have a built-in function to find the number of periods. In Excel, you
would put the cursor on Cell B5, then click the function wizard, indicate that you want
a Financial function, scroll down to NPER, and click OK. Then, in the dialog box, en-
ter B3 or 5% for Rate, 0 for Pmt because there are no periodic payments, B2 or
78.35 for Pv, G2 or 100 for Fv, and 0 for Type. When you click OK, Excelsolves for
the number of periods, 5.
Assuming that you are given PV, FV, and the time period, n, write out an equa-
tion that can be used to determine the interest rate, i.
Assuming that you are given PV, FV, and the interest rate, i, write out an equa-
tion that can be used to determine the time period, n.
Future Value of an Annuity
An annuityis a series of equal payments made at fixed intervals for a specified number
of periods. For example, $100 at the end of each of the next three years is a three-year
annuity. The payments are given the symbol PMT, and they can occur at either the
beginning or the end of each period. If the payments occur at the endof each period,
as they typically do, the annuity is called an ordinary,or deferred, annuity.Payments
on mortgages, car loans, and student loans are typically set up as ordinary annuities. If
payments are made at the beginningof each period, the annuity is an annuity due.
Rental payments for an apartment, life insurance premiums, and lottery payoffs are
typically set up as annuities due. Since ordinary annuities are more common in fi-
nance, when the term “annuity” is used in this book, you should assume that the pay-
ments occur at the end of each period unless otherwise noted.
Ordinary Annuities
An ordinary, or deferred, annuity consists of a series of equal payments made at the end
of each period. If you deposit $100 at the end of each year for three years in a savings
account that pays 5 percent interest per year, how much will you have at the end of
three years? To answer this question, we must find the future value of the annuity,
FVAn.Each payment is compounded out to the end of Period n, and the sum of the
compounded payments is the future value of the annuity, FVAn.
ABCDEFG
1 Time 0 12 3...?
2 Cash flow 78.35 0 0 0... 100
3 Interest rate 5%
4 Payment 0
5 N 5.00
68 Time Value of Money
