Introduction to Finance

237
9.7
Interest Rates and Time Requirements 
for Annuities
How to fi nd, or solve, for interest rates or time periods for problems involving a lump sum present 
value or future value was discussed previously in this chapter. That, originally, involved working 
with four variables: PV = present value, FV = future value, 
r
= interest rate, and 
n
= number of 
periods. A fi fth variable is now added to refl ect payments (PMT) involving ordinary annuities.
Solving for Interest Rates
Assume that the future value of an ordinary annuity is $5,751, the annual payment is $1,000, 
and the time period is fi ve years. What is the interest rate for this problem? 
A fi nancial calculator could be used to solve this problem if either the FV or PV of the 
ordinary annuity is known. If you have a fi nancial calculator and you know the future value, 
enter FV = 5751, PMT = –1000 (for both TI and HP calculators), and N = 5. Press the CPT 
key followed by the %i key to fi nd an 
r
of 7 percent. (Note: Some fi nancial calculators will 
give an error message if the 1000 PMT is entered as a positive number. If the present value of 
the ordinary annuity is known instead of the future value, the preceding procedure would be 
followed except that PV = 4100 would be entered instead of the future value amount.)
Financial Calculator Solution:
Inputs: 5 
–1000 5751
N 
PMT 
FV
Press: CPT %i
Solution: 7.00
Spreadsheet Solution:
Excel’s
 
RATE fi nancial function also can be used to solve this interest rate of an ordinary 
annuity problem, much as the function was used elsewhere in this chapter for problems 
without periodic payments. The fi nancial function solution would be the following:
= RATE(Nper,Pmt,PV,FV,Type)
= 
RATE(5,–1000,0,5751,0)
= 
7.00%