Introduction to Finance

Financial Calculator Solution:
Inputs: 7 
–1000 5751
%i 
PMT 
FV
Press: CPT N
Solution: 5.00
Spreadsheet Solution:
Excel’s
 
NPER fi nancial function also can be used to solve for the number of periods in an 
annuity problem, much as we used the function earlier for problems without periodic pay-
ments. The fi nancial function solution would be the following:
= NPER(Rate,Pmt,PV,FV,Type)
= 
NPER(7,–1000,0,5751,0)
= 
5.00
Table-based Solution:
The problem also can be set up by using equation 9.6 and Table 9.3 as follows:
FVA
n
= PMT(FVIFA
7%,
n
)
$5,751 = $1,000(FVIFA
7%,
n
)
FVIFA
7%,
n
= 5.751
Since we know the interest rate is 7 percent, we can turn to Table 9.3 and read down the 
7 percent column until we fi nd FVIFA of 5.751. Notice that this occurs in the year-fi ve row, 
indicating that the time period, 
n
, is fi ve years.

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9.8 Determining Periodic Annuity Payments
239
If we knew the present value of the above ordinary annuity was $4,100, we could also 
work the problem using equation 9.8 and Table 9.4 as follows:
PVA
n
= PMT(PVIFA
7%,
n
)
$4,100 = $1,000(PVIFA
7%,
n
)
PVIFA
7%,
n
= 4.100
Turning to Table 9.4, we read down the 7 percent column until we fi nd PVIFA of 4.100. 
This occurs at the year-fi ve row, indicating that the time period, 
n
, is fi ve years.
9.8
Determining Periodic Annuity Payments
Examples Involving Annual Payments
It is necessary in many instances to determine the periodic equal payment required for an 
ordinary annuity. For example, you may wish to accumulate $10,000 at the end of fi ve years 
from now by making equal annual payments beginning one year from now. If you can invest at 
a compound 6 percent interest rate, what will be the amount of each of your annual payments? 
This is a future value of an ordinary annuity problem. Using a fi nancial calculator, the 
annual payment (PMT) would be found as follows: