# formulas of annuity

## Regular Annuity Formulas

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These are the main formulas that are needed to work with regular annuity cash flows (Definition/Tutorial). Please note that these formulas work only on a payment date, not between payment dates. This is the same restriction used (but not stated) in financial calculators and spreadsheet functions.

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height="90" width="80%">\[Pmt = \frac{{P{V_A}}}{{\left[ {\frac{{1 - \frac{1}{{{{\left( {1 + i} \right)}^N}}}}}{i}} \right]}}\]

To solve for | Formula |
---|---|

Future Value | \[F{V_A} = Pmt\left[ {\frac{{{{\left( {1 + i} \right)}^N} - 1}}{i}} \right]\] |

Present Value | \[P{V_A} = Pmt\left[ {\frac{{1 - \frac{1}{{{{\left( {1 + i} \right)}^N}}}}}{i}} \right]\] |

Periodic Payment when PV is known | |

Periodic Payment when FV is known | \[Pmt = \frac{{F{V_A}}}{{\left[ {\frac{{{{\left( {1 + i} \right)}^N} - 1}}{i}} \right]}}\] |

Number of Periods when PV is known | \[N = \frac{{ - \ln \left( {1 - \frac{{P{V_A}}}{{Pmt}}i} \right)}}{{\ln \left( {1 + i} \right)}}\] |

Number of Periods when FV is known | \[N = \frac{{\ln \left( {1 + \frac{{F{V_A}}}{{Pmt}}i} \right)}}{{\ln \left( {1 + i} \right)}}\] |

Discount Rate | Can only be calculated through a trial and error process |

Variable | Definition |
---|---|

$$FV$$ | Future Value |

$$PV$$ | Present Value |

$$i$$ | Discount Rate |

$$N$$ | Number of Periods |

$$Pmt$$ | Payment (per period) |

$$ln$$ | Natural logarithm function (log base e) |

Category: Annuity

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