Introduction to Finance

part of equation 5.1 is replaced by a future value interest factor (FVIF) 
corresponding to a specifi c interest rate and a specifi ed time period.
Table 9.1
shows FVIF values carried to three decimal places for a partial range of interest 
rates and time periods. (Table 1 in the Appendix is a more comprehensive FVIF table.) Let’s 
use Table 9.1 to fi nd the future value of $1,000 invested at an 8 percent compound interest 
rate for a ten-year period; notice that at the intersection of the 8 percent column and ten years, 
we fi nd an FVIF of 2.159. Putting this information into equation 9.2 gives the following 
solution.
Table-based Solution:
FV
10
= $1,000(2.159)
= 
$2,159
Further examination of Table 9.1 shows how a $1 investment grows or increases with 
various combinations of interest rates and time periods. For example, if another bank off ers 
to pay you a 10 percent interest rate compounded annually, notice that the FVIF at the 

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C H A PT E R 9 Time Value of Money
intersection of 10 percent and ten years would be 2.594, making your $1,000 investment 
worth $2,594 ($1,000 × 2.594). Now the diff erence between the 8 percent and 10 percent rates 
is much more signifi cant, at $435 ($2,594 – $2,159), than the $200 diff erence that occurred 
with simple compounding over ten years. Thus, we see the advantage of being able to com-
pound at even slightly higher interest rates over a period of years. 
The compounding or growth process also can be depicted in graphic form. 
Figure 9.1
shows graphic relationships among future values, interest rates, and time periods. For 
example, notice how $1 will grow diff erently over a ten-year period at 5 percent versus 
10 percent interest rates. Of course, if no interest is being earned, then the initial $1 
investment will remain at $1 no matter how long the investment is held. At a 10 percent 
interest rate, the initial $1 grows to $2.59 (rounded) after ten years. This compares with 
$1.63 (rounded) after ten years if the interest rate is only 5 percent. Notice that the future 
value grows at an increasing rate as the interest rate is increased and as the time period 
is lengthened.
In recent years, the benefi ts of compounding have been tempered by historically low 
interest rates. Recall that the Fed has employed a policy of monetary easing through its open 
market operations and the nontraditional monetary policy tool of quantitative easing.