| Mathematics of the FV | Formula Using a FV Factor |
|---|---|
FV = PV x (1.00 + i)n
|
FV = PV x [FV factor]
|
FV = $10,000 x (1.00 + 0.02)8
|
FV = $10,000 x [FV factor for n=8, i=2%]
|
FV = $10,000 x (1.02)8
| |
FV = $10,000 x 1.172
|
FV = $10,000 x 1.172 ← future value factor
|
FV = $11,720
|
FV = $11,720
|
Future value factors are available in future value tables, such as the abbreviated version shown here:
i=1%
|
i=2%
|
i=3%
|
i=4%
|
i=5%
|
i=6%
|
i=8%
|
i=10%
|
i=12%
| |
|---|---|---|---|---|---|---|---|---|---|
n = 0→
|
1.000
|
1.000
|
1.000
|
1.000
|
1.000
|
1.000
|
1.000
|
1.000
|
1.000
|
n = 1→
|
1.010
|
1.020
|
1.030
|
1.040
|
1.050
|
1.060
|
1.080
|
1.100
|
1.120
|
n = 2→
|
1.020
|
1.040
|
1.061
|
1.082
|
1.103
|
1.124
|
1.166
|
1.210
|
1.254
|
n = 3→
|
1.030
|
1.061
|
1.093
|
1.125
|
1.158
|
1.191
|
1.260
|
1.331
|
1.405
|
n = 4→
|
1.041
|
1.082
|
1.126
|
1.170
|
1.216
|
1.262
|
1.360
|
1.464
|
1.574
|
n = 5→
|
1.051
|
1.104
|
1.159
|
1.217
|
1.276
|
1.338
|
1.469
|
1.611
|
1.762
|
n = 6→
|
1.062
|
1.126
|
1.194
|
1.265
|
1.340
|
1.419
|
1.587
|
1.772
|
1.974
|
n = 7→
|
1.072
|
1.149
|
1.230
|
1.316
|
1.407
|
1.504
|
1.714
|
1.949
|
2.211
|
n = 8→
|
1.083
|
1.172
|
1.267
|
1.369
|
1.477
|
1.594
|
1.851
|
2.144
|
2.476
|
n = 9→
|
1.094
|
1.195
|
1.305
|
1.423
|
1.551
|
1.689
|
1.999
|
2.358
|
2.773
|
n = 10→
|
1.105
|
1.219
|
1.344
|
1.480
|
1.629
|
1.791
|
2.159
|
2.594
|
3.106
|
n = 11→
|
1.116
|
1.243
|
1.384
|
1.539
|
1.710
|
1.898
|
2.332
|
2.853
|
3.479
|
n = 12→
|
1.127
|
1.268
|
1.426
|
1.601
|
1.796
|
2.012
|
2.518
|
3.138
|
3.896
|
i= the interest rate per period with the interest added and compounded at the end of each period
We highlighted the factor used in our computation. As you can see, the future value factor of 1.172 is located where n = 8, and i = 2%.
Our future value of 1 table is unique in that we have an additional row: n = 0. Most FV of 1 tables omit the row for n = 0, and begin with the row n =1. There should be no difference in FV factors other than minor rounding differences.
To appreciate the usefulness of the FV of 1 table, focus on the column with the heading of i = 10%. This column tells you that the present value of 1.000 is 1.000 at time period 0—the present time. As you move down the 10% column, the next row (where n = 1) shows that the future value will increase by 10% to 1.100. Continuing down the 10% column, you see that at the end of two periods (n = 2) the future value is 1.210, an increase of 0.110 (1.100 x 10%). The next figure down indicates that at the end of three periods the future value is 1.331, which is an increase of 0.121 (1.331 – 1.210; and 1.210 x 10%).
The FV of 1 table provides the future amounts at compound interest for a single amount of 1.000 at various interest rates. These factors should make the future calculations a bit simpler than calculations using exponents.
The 10% column of the future value table can be used to determine the future value of a single $1.00 invested today at 10% interest compounded annually. The single $1.00 amount will grow to $3.138 at the end of 12 years. The FV table also provides some insight as to the future cost of items that are expected to increase at a constant rate. For example, if a cup of coffee presently costs $1.00 and the cost is expected to increase by 10% per year compounded annually, then a cup of coffee will cost $3.138 per cup at the end of 12 years.
We can also use the factors for amounts greater than $1. For example, if the monthly cost of a family’s health insurance plan is $1,000 at the present time and it is expected to increase by 10% per year compounded annually, then the monthly cost at the end of 12 years will be $3,138.
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