Environmental Economics - Mathematics and Statistics for the Environment - page 224

10.4 FUTURE VALUE
The future value (or uniform series compound amount factor) of an amount of money is the equiva-
lent of either a single amount today (the present amount) or a series of amounts to be received or
paid annually over a period of years as compounded at an interest rate over a period of years. The
future value can be calculated from either a single present amount ( P ), or an annual amount ( A ). The
future ( F ) value of a series of equal annual amounts can be calculated by using Equation 10.3. The
equation compounds the interest ( i ) at which the annual amounts ( A ) are invested over the term of
the investment in years ( n ).

n

( 1 +− i

i

) 1

FA = (10.3)

■ EXAMPLE 10.3
Problem: A woman deposits $500 in a bank at the end of each year for 5 years. The bank pays 5%
interest, compounded annually. At the end of 5 years, immediately following her fifth deposit, how
much will she have in her account?

Solution: Given that A = $500, i = 0.05, and n = 5,

n

( 1 +− i ) 1

FA =

i

5

( 1005 + . ) − 1

= $ 500

005 .

= $( . 500 5 526 )

= $ 2763

She will have $2763 in her account following the fifth deposit.

Note: The higher the interest rate ( i ) earned by the investment, the higher the future value will be
because the investment compounds at a higher rate. The longer the term of the investment
( n ), the higher the future value will be because there are more annual payments being made
that compound for a longer time.

10.5 ANNUAL PAYMENT (UNIFORM SERIES SINKING FUND)
Annual amounts of money to be received or paid are the equivalent of either a single amount in the
future or a single amount in the present, when the annual amounts are compounded over a period
of years at a given interest rate. The value of the annual amounts can be calculated from a single
present amount ( P ), or a single future amount ( F ). The value of the annual amount can be calculated
from a single present amount ( P ) or a single future amount ( F ). The annual payments into an invest-
ment can be calculated by using Equation 10.4:

i
i

AF = (10.4)

n

( 1 +− ) 1