Introduction to Finance

Small Business Practice

---

230
C H A PT E R 9 Time Value of Money
9.4
Finding Interest Rates 
and Time Requirements
Recall the four variables from the future value (9.1 and 9.2) and present value (9.3 and 9.4) 
equations: PV = present value, FV = future value, 
r
= interest rate, and 
n
= number of periods. 
As long as we know the values for any three of these variables, we can solve for the fourth, or 
unknown, variable. This is accomplished by using a fi nancial calculator, a fi nancial function 
in a spreadsheet program, or tables.
Solving for Interest Rates
Assume that the present value of an investment is $1,000, the future value is $1,403 and the 
time period is fi ve years. What compound interest rate would be earned on this investment? 
This problem can be solved using a fi nancial calculator. If a fi nancial calculator is used, enter 
PV = 1000, FV = 1403, N
 
= 5, and press CPT followed by the %i
 
key to fi nd an 
r
of 7.01, or 7 
percent rounded (some calculators may require either the PV entry or FV entry to be negative).
Financial Calculator Solution:
Inputs: 5 
1000 1403
N 
PV 
FV
Press: CPT %i
Solution: 7.01
A second way of solving for the interest rate is with a spreadsheet program using a fi n-
ancial function. Excel
 
has a fi nancial function called RATE that makes it possible to solve 
quickly for the interest rate. Click on the fi nancial wizard (
fx
), then on Financial, then RATE. 
Entering the requested data and pressing OK gives the following solution.
Spreadsheet Solution:
= RATE(Nper, Pmt, PV, FV, Type)
= 
RATE(5,0,–1000,1403,0)
= 
7.01%
The number of periods (Nper) is 5, there are zero periodic payments (Pmt), the present 
value (PV) is entered as –1000, the future value (FV) is 1403, and the Type is zero, since cash 
fl ows occur at the end of a time period.