Introduction to Finance

Financial Calculator Solution:
Inputs: 
6 5 10000
%i 
N 
FV
Press: CPT PMT
Solution: 1773.96
Spreadsheet Solution:
Excel’s
 
PMT fi nancial function also can be used to solve for the annual payment amount. The 
fi nancial function solution would be,
= PMT(Rate,Nper,PV,FV,Type)
= 
PMT(.06,5,0,–10000,0)
= 
$1,773.96
Table-based Solution:
Equation 9.6 and Table 9.3 also can be used, as follows:
FVA
n
= PMT(FVIFA
r
,
n
)
$10,000 = PMT(FVIFA
6%,5
)
$10,000 
= 
PMT(5.637)
PMT 
= 
$1,773.99
= $1,774 (rounded)
The FVIFA factor of 5.637 is taken from Table 9.3 at the intersection of the 6 percent column 
and the year-fi ve row.
As another example, we might want to fi nd the equal payment necessary to pay off , 
or 
amortize
, a loan. An 
amortized loan
is repaid in equal payments over a specifi ed time 
period. Let’s assume that a lender off ers you a $20,000, 10 percent interest rate, three-year 
loan that is to be fully amortized with three annual payments. The fi rst payment will be due 
one year from the loan date, making the loan an ordinary annuity. How much will you have 
to pay each year?
This is a present value problem because the $20,000 is the value, or amount, of the loan 
now. The annual payment can be found with a fi nancial calculator, a fi nancial function in 
amortized loan 
a loan repaid in 
equal payments over a specifi ed 
time period

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240
C H A PT E R 9 Time Value of Money
a spreadsheet program, or via a table-based approach using equation 9.8 and Table 9.4 as 
follows:
PVA
n
= PMT(PVIFA
10%,3
)
$20,000 = PMT(2.487)
PMT 
= 
$8,041.82
= $8,042 (rounded)
The PVIFA factor of 2.487 is taken from Table 9.4 at the intersection of the 10 percent 
column and the year-three row.