Future Value of a Dollar
FUTURE
VALUE ( FV ) OF A DOLLAR
A
future value is a dollar amount that occurs at some point in the future.
It may either be a cash inflow or a cash outflow.
Future values are calculated using compound rates of return (equivalent
to compound interest rate returns). Even if not stated, the Future Value
calculation process implicitly assumes that the compound interest (or compound
return) process has been used to arrive at this future dollar amount.
FUTURE
VALUE OF A SINGLE DOLLAR AMOUNT PROBLEM ( FV $ PROBLEM)
This
is a particular type of future value calculation that assumes a single dollar
amount in the future. This is in
contrast to the “annuity” type of problem that represents a stream of equal
dollar amounts or a “stream of unequal payments” problem.
The
FV $ amount may either be a cash inflow or a cash outflow.
Future
values are calculated using compound rates of return. Even if not stated, the
Future Value calculation process implicitly assumes that a compound interest (or
compound return) processes have been used to arrive at this future dollar
amount.
Unless
stated otherwise, a future value calculation assumes that the FV occurs at the
end of the future time period.
The
formula for calculating the future value of a single dollar amount is as
follows:
or
Where:
FV = Future Value
PV = Present Value
i
= annual interest rate or annual rate of return
n
= number of compounding periods
FUTURE
VALUE INTEREST FACTOR (FVIF)
A
FVIF is the interest rate factor that is used to take a dollar value stated at
the present time and restate that value as a future value.
It reflects both the applicable interest rate (or rate of return) per
period and the number of periods the compound return is being earned.
The
formula for a FVIF is as follows:
A
small set of future value interest factors is presented in the Future Value
Interest Factor Table.
The
FVIF Table is sometimes referred to as the Future Value of a Dollar Table
or a Compound Value of a Dollar Table.
FUTURE VALUE INTEREST FACTOR (FVIF) TABLE
|
|
i =
1% |
2% |
3% |
4% |
5% |
6% |
7% |
|
# of periods |
|
|
|
|
|
|
|
|
1 |
1.0100 |
1.0200 |
1.0300 |
1.0400 |
1.0500 |
1.0600 |
1.0700 |
|
2 |
1.0201 |
1.0404 |
1.0609 |
1.0816 |
1.1025 |
1.1236 |
1.1449 |
|
3 |
1.0303 |
1.0612 |
1.0927 |
1.1249 |
1.1576 |
1.1910 |
1.2250 |
|
4 |
1.0406 |
1.0824 |
1.1255 |
1.1699 |
1.2155 |
1.2625 |
1.3108 |
|
5 |
1.0510 |
1.1041 |
1.1593 |
1.2167 |
1.2763 |
1.3382 |
1.4026 |
|
6 |
1.0615 |
1.1262 |
1.1941 |
1.2653 |
1.3401 |
1.4185 |
1.5007 |
|
7 |
1.0721 |
1.1487 |
1.2299 |
1.3159 |
1.4071 |
1.5036 |
1.6058 |
|
8 |
1.0829 |
1.1717 |
1.2668 |
1.3686 |
1.4775 |
1.5938 |
1.7182 |
|
9 |
1.0937 |
1.1951 |
1.3048 |
1.4233 |
1.5513 |
1.6895 |
1.8385 |
|
10 |
1.1046 |
1.2190 |
1.3439 |
1.4802 |
1.6289 |
1.7908 |
1.9672 |
|
11 |
1.1157 |
1.2434 |
1.3842 |
1.5395 |
1.7103 |
1.8983 |
2.1049 |
|
12 |
1.1268 |
1.2682 |
1.4258 |
1.6010 |
1.7959 |
2.0122 |
2.2522 |
|
13 |
1.1381 |
1.2936 |
1.4685 |
1.6651 |
1.8856 |
2.1329 |
2.4098 |
|
14 |
1.1495 |
1.3195 |
1.5126 |
1.7317 |
1.9799 |
2.2609 |
2.5785 |
|
15 |
1.1610 |
1.3459 |
1.5580 |
1.8009 |
2.0789 |
2.3966 |
2.7590 |
Example
of use of FVIF table:
Using the table FVIF value; the FVIF value for n = 5 and i = 7% is 1.4026. This value is the same as the 1.4025517 calculated above and rounded to 4 decimal places.
Be sure to see the text book assignments for more information on this topic.