3-12
TIME VALUE OF MONEY
Example
To illustrate the use of this formula, suppose that you invest $10,000
in an account that earns 8% annual interest compounded quarterly for
five years. Assuming no other transactions, how much will be in your
account at the end of five years? Using the future value formula, P =
$10,000, R = 0.08, M = 4, and T = 5:
FV
T
= P (1 + R/M)
T x M
FV
5
= ($10,000)(1 + 0.08/4)
5 x 4
FV
5
= ($10,000)(1.485947)
FV
5
= $14,859.47
One more example: What is the future value of the $10,000 if it is
invested for one year and compounded monthly at an annual rate of
8%?
FV
T
= P (1 + R/M)
T x M
FV
1
= ($10,000)(1 + 0.08/12)
1 x 12
FV
1
= ($10,000)(1.082995)
FV
1
= $10,829.95
Continuous Compounding
Infinite number
of periods
Continuous compounding is a special case of nonannual
compounding. It extends the notion of compounding periods to a
point where the number of periods becomes infinitely large and the
length of each period is correspondingly small. In other words,
interest is always being calculated and compounded. The future value
interest factor for continuous compounding is represented by the
term e
RT
. For continuous compounding, the future value formula is:
FV
T
=
P x e
RT
Where:
FV
T
= Future value after T periods
P
= Principal
e
= Base of the natural logarithm (2.718282)
R
= Stated (nominal) annual interest rate for
each period
T
= Number of periods