Introduction to Finance

part of equation 9.3 is replaced by a present value interest factor (PVIF) 
corresponding to a specifi c interest rate and a specifi ed time period.

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C H A PT E R 9 Time Value of Money
Table 9.2
shows PVIF values for a range of interest rates and time periods. (Table 2 in the 
Appendix is a more comprehensive PVIF table.) Let’s use Table 9.2 to fi nd the present 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 a PVIF of 0.463. Putting this 
information in equation 9.4 gives the following.
Table-based Solution:
PV = $1,000(0.463)
= 
$463
Further examination of Table 9.2 shows how a $1 investment decreases with various 
combinations of interest rates and time periods. For example, if another bank off ers to pay 
interest at a 10 percent compound rate, the PVIF at the intersection of 10 percent and ten 
years would be 0.386, resulting in your $1,000 future value being worth an investment of 
$386 ($1,000 × 0.386). The diff erence between required investments at 8 percent and 10 per-
cent interest rates needed to accumulate $1,000 at the end of ten years is $77 ($463 – $386). 
In essence, the present value of a future value decreases as the interest rate increases for a 
specifi ed time period.
The discounting process also can be depicted in graphic form. 
Figure 9.2
shows 
graphic relationships among present values, interest rates, and time periods. For example, 
notice how a $1 future value will decrease diff erently over a ten-year period at 5 percent 
versus 10 percent interest rates. Of course, at a zero interest rate, the present value remains 
at $1 and is not aff ected by time. If no interest is being earned, the $1 future value will have 
a present value of $1 no matter how long the investment is held. At a 5 percent interest 
rate, the present value of $1 declines to $0.61 (rounded) if an investor has to wait ten years 
to receive the $1. This compares with a present value of $1 of only $0.39 (rounded) if the 
interest rate is 10 percent and the investor must wait ten years to receive $1. Notice that the 
present value decreases at an increasing rate as the interest rate is increased and as the time 
period is lengthened.
Equating Present Values and Future Values
Notice that equations 9.1 and 9.3 are two ways of looking at the same process involving 
compound interest rates. That is, if we know the future value of an investment, we can fi nd 
its present value, and vice versa. For example, an initial investment of $1,000 will grow to