Principles of Managerial Finance

Time line for future
value of a single
amount ($800 initial
principal, earning 6%,
at the end of 5 years)

156 PART 2 Important Financial Concepts

PV = $800

012345

FV 5 = $1,070.40

End of Year

second year there would be $116.64 in the account. This amount would represent

the principal at the beginning of year 2 ($108) plus 8% of the $108 ($8.64) in

interest. The future value at the end of the second year is calculated by using

Equation 4.2:

Future value at end of year 2 $108(10.08) (4.2)

$116.64

Substituting the expression between the equals signs in Equation 4.1 for the

$108 figure in Equation 4.2 gives us Equation 4.3:

Future value at end of year 2$100(10.08)(10.08) (4.3)

$100(10.08)^2

$116.64

The equations in the preceding example lead to a more general formula for

calculating future value.

The Equation for Future Value

The basic relationship in Equation 4.3 can be generalized to find the future value

after any number of periods. We use the following notation for the various inputs:

FVnfuture value at the end of period n

PVinitial principal, or present value

iannual rate of interest paid. (Note: On financial calculators, Iis typi-

cally used to represent this rate.)

nnumber of periods (typically years) that the money is left on deposit

The general equation for the future value at the end of period nis

FVnPV(1i)n (4.4)

A simple example will illustrate how to apply Equation 4.4.

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.

FV 5 $800(10.06)^5 $800(1.338)$1,070.40

This analysis can be depicted on a time line as follows: