The Maxwell School

Syracuse University

Syracuse University

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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:

`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`

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URL: https://wilcoxen.maxwell.insightworks.com/pages/4817.html

Peter J Wilcoxen, The Maxwell School, Syracuse University

Revised 04/20/2019

URL: https://wilcoxen.maxwell.insightworks.com/pages/4817.html

Peter J Wilcoxen, The Maxwell School, Syracuse University

Revised 04/20/2019