Introduction to Finance

Financial Calculator Solution:
Inputs: 3 
8 
1000
N 
%i 
PMT
Press: CPT PV
Solution: 2577.10
Spreadsheet programs also are available for fi nding present values of annuities. Following 
is an Excel
 
spreadsheet solution. 
Spreadsheet Solution:
Use the previously described present value (PV) fi nancial function provided by Excel
 
as 
follows:
= PV(Rate,Nper,Pmt,FV,Type)
= 
PV(.08,3,–1000,0,0)
= 
$2,577.10 
In addition, tables have been prepared to simplify the calculation eff ort if fi nancial calcu-
lators or computer programs are not available. Equation 9.7 can be rewritten as:
PVA
n
= PMT(PVIFA
r
,
n
) (9.8)
The {1 – [1 ÷ (1 + 
r
)
n
]}÷ 
r
part of equation 9.7 is replaced by a present value interest 
factor of an annuity (PVIFA)
 
corresponding to a specifi c interest rate and a specifi ed time 
period.
Table-based Solution:
Table 9.4
shows PVIFA values for a partial range of interest rates and time periods. (Table 4 
in the Appendix is a more comprehensive PVIFA table.) Let’s use Table 9.4 to fi nd the 
present 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 
interest rate column and three years we fi nd a PVIFA of 2.577. Putting this information into 
equation 9.8 gives,
PVA
3
= $1,000(2.577)
= 
$2,577
Further examination of Table 9.4 shows how the present value of a $1 annuity decreases 
with various combinations of interest rates and time periods. For example, if $1,000 is paid 
at the end of each year (beginning with year one) for ten years at an 8 percent interest rate, 
the present value of the annuity would be $6,710 ($1,000 × 6.710). If the interest rate is 
10 percent for ten years, the present value of the annuity would be $6,145 ($1,000 × 
6.145). These results demonstrate the costs of higher interest rates on the present values of 
annuities.

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9.7 Interest Rates and Time Requirements for Annuities