TIME
VALUE OF MONEY 3-13
Example
For example, let's calculate the future value of a $10,000 investment
for one year at an 8% annual rate compounded continuously. We will
use the values P = $10,000, R = 0.08, and T = 1.
FV
T
= P x e
RT
FV
1
= ($10,000)(2.718282)
(0.08)(1)
FV
1
= ($10,000)(1.083287)
FV
1
= $10,832.87
Discrete vs.
continuous
compounding
A comparison of the investment's future values discretely
compounded for different periods, and continuously compounded,
shows how the value changes -- depending on the frequency of
compounding.
Annually:
$10,800.00
Monthly:
$10,829.95
Weekly:
$10,832.20
Continuously: $10,832.87
You can see that as the compounding period becomes smaller, the
future value of the investment increases. The increase occurs
because we are compounding the interest more frequently.
To further illustrate continuous compounding and compare it to
discrete compounding, refer to the next three graphs (Figures 3.1,
3.2, and 3.3). The first graph shows the growth of $100 of capital
invested at 25% for three years compounded annually. The second
graph shows $100 invested at 25% for three years compounded
semi-annually. The final graph represents the growth of $100
invested at 25% for three years compounded continuously.