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Time line for future
value of a single
amount ($800 initial
principal, earning 6%,
at the end of 5 years)
A simple example will illustrate how to apply Equation 4.4.
CHAPTER 4 Time Value of Money 137
EXAMPLE Jane Farber places $800 in a savings account paying 6% interest compounded
annually. She wants to know how much money will be in the account at the end
of 5 years. Substituting PV $800, i0.06, and n 5 into Equation 4.4 gives
the amount at the end of year 5.
FV5$800(1 0.06) 5$800(1.338) $1,070.40
This analysis can be depicted on a time line as follows:
future value interest factor
The multiplier used to calculate,
at a specified interest rate, the
future value of a present amount
as of a given time.
PV = $800
FV 5 = $1,070.40
0 1 2 3 4 5
End of Year
Using Computational Tools to Find Future Value
Solving the equation in the preceding example involves raising 1.06 to the fifth
power. Using a future value interest table or a financial calculator or a computer
and spreadsheet greatly simplifies the calculation. A table that provides values for
(1 i) n in Equation 4.4 is included near the back of the book in Appendix Table
A–1. 1 The value in each cell of the table is called the future value interest factor.
This factor is the multiplier used to calculate, at a specified interest rate, the
future value of a present amount as of a given time. The future value interest factor
for an initial principal of $1 compounded at i percent for n periods is referred
to as FVIFi,n. Future value interest factorFVIFi,n (1 i) n (4.5)
By finding the intersection of the annual interest rate, i, and the appropriate
periods, n, you will find the future value interest factor that is relevant to a particular
problem. 2 Using FVIFi,n as the appropriate factor, we can rewrite the general
equation for future value (Equation 4.4) as follows:
FVnPV (FVIFi,n) (4.6)
This expression indicates that to find the future value at the end of period n of an
initial deposit, we have merely to multiply the initial deposit, PV, by the appropriate
future value interest factor. 3
1. This table is commonly referred to as a “compound interest table” or a “table of the future value of one dollar.”
As long as you understand the source of the table values, the various names attached to it should not create confusion,
because you can always make a trial calculation of a value for one factor as a check.
2. Although we commonly deal with years rather than periods, financial tables are frequently presented in terms of
periods to provide maximum flexibility.
3. Occasionally, you may want to estimate roughly how long a given sum must earn at a given annual rate to double
the amount. The Rule of 72 is used to make this estimate; dividing the annual rate of interest into 72 results in the
approximate number of periods it will take to double one’s money at the given rate. For example, to double one’s
money at a 10% annual rate of interest will take about 7.2 years (72 107.2). Looking at Table A–1, we can see
that the future value interest factor for 10% and 7 years is slightly below 2 (1.949); this approximation therefore
appears to be reasonably accurate.