Introduction to Finance

Financial Calculator Solution:
Inputs: 3 
8 
–1000
N 
%i 
PMT
Press: CPT FV
Solution: 3246.40
Spreadsheet programs also are available for fi nding future values of annuities. Following 
is a solution using an Excel
 
spreadsheet and future value (FV). The diff erence here is that we 
have a constant periodic payment.
 
Spreadsheet Solution:
We solve for the future value of the annuity as follows:
= FV(Rate,Nper,Pmt,PV,Type)
= 
FV(.08,3,–1000,0,0)
= 
$3,246.40
In addition, tables have been prepared to simplify the calculation eff ort if fi nancial calcu-
lators or computer programs are not available. Equation 9.5 can be rewritten as,
FVA
n
= PMT(FVIFA
r
,
n
) (9.6)
where the [(1 + 
r
)
n
– 1] ÷ 
r
part of equation 9.5 is replaced by a future value interest factor 
of an annuity (FVIFA) corresponding to a specifi c interest rate and a specifi ed time period.

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C H A PT E R 9 Time Value of Money
Table-based Solution:
Table 9.3
shows FVIFA values for a partial range of interest rates and time periods. (Table 3 
in the Appendix is a more comprehensive FVIFA table.) Let’s use Table 9.3 to fi nd the future 
value of an ordinary annuity involving annual payments of $1,000, an 8 percent interest rate, 
and a three-year time period. Notice that at the intersection of the 8 percent column and three 
years we fi nd a FVIFA of 3.246. Putting this information into equation 9.6 gives,
FVA
3 
= $1,000(3.246)
= 
$3,246
TA B L E 9 . 3
Future Value Interest Factor (FVIFA) for a $1 Ordinary Annuity