Peter J Wilcoxen > Economic Skills Project


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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:


Solving that for `X` gives the fundamental formula used in present value calculations:


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Peter J Wilcoxen, The Maxwell School, Syracuse University
Revised 04/20/2019