Introduction to Finance

Table-based Solution:
The answer can also be found by using equation 9.2 and Table 9.1 as follows:
FV
n
= PV(FVIF
7%,
n
)
$1,403 = $1,000(FVIF
7%,
n
)
FVIF
7%,
n
= 1.403
Since we know the interest rate is 7 percent, we can turn to Table 9.1 and read down the 
7 percent column until we fi nd the FVIF of 1.403. Notice that this occurs in the year-fi ve row, 
indicating that the time period, 
n
, is fi ve years.
We also can work the problem using equation 9.4 and Table 9.2 as follows:
PV = FV
n
(PVIF
7%,
n
)
$1,000 = $1,403(PVIF
7%,
n
)
PVIF
7%,
n
= .713
Turning to Table 9.2, we read down the 7 percent column until we fi nd the PVIF of 0.713. 
This occurs at the year-fi ve row, indicating that the time period, 
n
is, fi ve years.
Rule of 72
Investors often ask, “How long will it take for my money to double in value at a particular 
interest rate?” Table 9.1 illustrates the process for answering this question. We pick a partic-
ular interest rate and read down the table until we fi nd an FVIF of 2.000. For example, at an 
8 percent interest rate, it will take almost exactly nine years (note the FVIF of 1.999) for an 
investment to double in value. At a 9 percent interest rate, the investment will double in about 

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C H A PT E R 9 Time Value of Money
eight years (FVIF of 1.993). An investment will double in a little over seven years (FVIF of 
1.949) if the interest rate is 10 percent.
A shortcut method referred to as the 
Rule of 72
can be used to approximate the time 
required for an investment to double in value: divide the interest rate into the number 72. For 
example, if the interest rate is 8 percent, 72 divided by 8 indicates that the investment will 
double in value in nine years. Notice that this is the same conclusion drawn from Table 9.1. 
Likewise, at an interest rate of 10 percent it will take approximately 7.2 years (72 ÷ 10) for an 
investment to double in value. It is important to be aware that at very low or very high interest 
rates, the Rule of 72 does not approximate the compounding process as well, and thus a larger 
estimation error occurs in the time required for an investment to double in value.