The formula used to discount a future value to a present value today is as follows:
Where:
PV = Present Value
FV = Future Value
r = rate
t = time
Assume you would like to have a future lump sum of $10,000. How much would you have to invest today, if the initial contribution grew at required rate of 7.00% for five years? Plugging those values into the formula would yield the following:
The amount that is required today, in order to have $10,000 in the future will decrease as a function of either a longer time-frame, or a higher discount rate. Using Excel, we can model the amounts required given a specific time-frame or rate:
| Year | FV | rate | PV |
| 5 | $ 10,000.00 | 7.00% | $ 7,129.86 |
| 10 | $ 10,000.00 | 7.00% | $ 5,083.49 |
| 15 | $ 10,000.00 | 7.00% | $ 3,624.46 |
| 20 | $ 10,000.00 | 7.00% | $ 2,584.19 |
| 25 | $ 10,000.00 | 7.00% | $ 1,842.49 |
| 30 | $ 10,000.00 | 7.00% | $ 1,313.67 |
The data can be represented visually as well:
Viewing the chart above, you can see that the initial investment required today, decreases exponentially as a function of time.
Using an HP12C calculator, the present value can be calculated using the following keystrokes:
[10,000][FV]
[7][i]
[5][n]
[PV]
A copy of the Excel model can be found here
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