TIME
VALUE OF MONEY 3-11
We can arrive at the same result by using the future value formula
with a two year time frame.
FV
2
= ($500) (1 + 0.12)
2
FV
2
= ($500) (1.2544)
FV
2
= $627.20
The interest earned in the second year is $67.20: $60 dollars on the
$500 principal, and $7.20 on the $60 of interest earned during the
first year. Compounded interest is interest earned on interest.
Discrete Compounding for Nonannual Periods
Adjust for
number of
periods
Many investments are compounded for periods other than annually.
Some bonds are compounded semiannually or quarterly; many savings
accounts are compounded monthly, weekly, or even daily.
We use the future value equation to calculate discrete compounding
for nonannual periods with two slight modifications. First, we adjust
the interest rate by dividing the annual rate (R) by the number of
compounding periods during the year (M). For semiannual
compounding, M is 2; for monthly compounding, M is 12. We also
adjust the number of compounding periods by multiplying the time in
years (T) by the number of compounding periods during the year (M).
Our new future value formula then becomes:
FV
T
= P (1 + R/M)
T x M
Where:
FV
T
= Future value after T years
P
= Principal
R
= Stated annual interest rate
M
= Number of compounding periods within a
year
T
= Number of years