The Maxwell School
Syracuse University
Syracuse University
The present value of a future payment `F_T` at time `T` answers the question “How much would need to be deposited in a bank account today in order to have a balance equal to `F_T` at that date?”
At an interest rate of `r`, an initial deposit of `X` dollars will grow over time as shown below.
| Date | Balance |
| 0 | `X` |
| 1 | `X+rX=X(1+r)` |
| 2 | `[X(1+r)](1+r)=X(1+r)^2` |
| 3 | `X(1+r)^3` |
| ... | ... |
| T | `X(1+r)^T` |
In order to have the target amount, `F_T` at `T`, the deposit `X` would need to satisfy the equation:
`X(1+r)^T=F_T`
Solving that for `X` gives the fundamental formula used in present value calculations:
`X=(F_T)/(1+r)^T`