3-10
TIME VALUE OF MONEY
I
=
P (1 + R)
T
- P
I
=
($400,000) (1 + 0.06)
2
- ($400,000)
I
=
($400,000) (1.1236) - ($400,000)
I
=
($449,440) - ($400,000)
I
=
$49,440
Future value of
principal
By adding the interest and principal, you can see that at the end of the
two year period the investment will be worth $449,440. This is the
future value of the $400,000 investment. Future value is the worth of
an investment at a specified rate of interest at the end of a stated
period of time. We can convert the interest payment formula to a
future value formula.
FV
T
=
P (1 + R)
T
Where:
FV
T
= Future value after T paying periods
P
= Principal
R
= Stated interest rate for each interest paying
period
T
= Number of interest paying periods
Future value
interest factor
The expression (I + R)
T
is referred to as the future value interest
factor. The future value is the principal multiplied by the future value
interest factor.
Example
To illustrate, suppose that we invest $500 in an account earning 12%
annual interest. At the end of one year, the future value of our
investment is:
FV
T
= P (1 + R)
T
FV
1
= ($500) (1 + 0.12)
1
FV
1
= ($500) (1.12)
FV
1
= $560
If we leave the $560 dollars in the account for another year, at the
same rate, the future value is:
FV
1
= ($560) (1 + 0.12)
1
FV
1
= ($560) (1.12)
FV
1
= $627.20