Introduction to Finance

Table-based Solution:
The interest rate answer also can be found by setting up the problem using equation 9.2 and 
Table 9.1 as follows:
FV
5
= PV(FVIF
r
,5
)
$1,403 = $1,000(FVIF
r
,5
)
FVIF
r
,5
= 1.403
Since we know that the number of time periods is fi ve, we can turn to Table 9.1 and read 
across the year-fi ve row until we fi nd FVIF of 1.403. Notice that this occurs under the 7 percent 
column, indicating that the interest rate, 
r
, is 7 percent.
We also can work the problem using equation 9.4 and Table 9.2 as follows:
PV = FV
5
(PVIF
r
,5
)
$1,000 = $1,403(PVIF
r
,5
)
PVIF
r
,5
= 0.713

---

9.4 Finding Interest Rates and Time Requirements
231
Turning to Table 9.2, we read across the year-fi ve row until we fi nd the PVIF of 0.713. 
This occurs under the 7 percent column, indicating that the interest rate, 
r
, is 7 percent.
Solving for Time Periods
Now let’s assume an investment has a present value of $1,000, a future value of $1,403, and an 
interest rate of 7 percent. What length of time does this investment involve? 
This problem can be solved using a fi nancial calculator and entering PV = 1000 (or 
–1000), FV = 1403, and %i = 7 and then pressing the CPT key followed by the N key to fi nd 
an 
n
of 5.01, or 5 years rounded.
Financial Calculator Solution:
Inputs:
7 
1000 1403
%i 
PV 
FV
Press: CPT N 
Solution: 5.01
Spreadsheet Solution:
The number of time periods can also be determined by using the Excel
 
fi nancial function 
called NPER. Following the sequence described and, clicking on the NPER fi nancial function, 
we have the following: 
= NPER(Rate,Pmt,PV,FV,Type)
= 
NPER(.07,0,–1000,1403,0)
= 
5.00
The interest rate is 7 percent, there are no payments, the present value is –1000, the future 
value is 1403, and type is zero.