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11.6: Future and Present Annuity Factors- Mathematical Formulas

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    Let’s “put on the table” the formal mathematical formulas for ordinary annuities’ factors. Remember: a “factor” is a multiplier (for the given cash flows). These formulae will be useful when your tables do not have a particular interest rate that you need, and especially when you need to calculate a fractional rate, e.g., 10.23%.

    Key: PVAF – Present Value Annuity Factor. FVAF – Future Value Annuity Factor.

    11.5.png

    Example 1: R = 0.10; N = 5; P = 2

    Solution 1: [(1) ÷ (0.10/2)] – [(1) ÷ (0.10/2) (1 + 0.10/2) 5 × 2] = 7.72173493

    *This multiplier should be the same as in your Present Value Annuity Table.

    Example 2: R = 0.095; N = 5; P = 2

    Solution 2: [(1) ÷(0.095/2)] – [(1) ÷(0.095/2) (1 + 0.095/2) 5 × 2] = Fill in your answer

    *This multiplier is not in your Present Value Annuity Table. Compare the two solutions.

    11.6.png

    Example 3: R = 0.10; N = 5; P = 2

    Solution 3: [(1 + 0.10/2)5 x 2– 1] ÷0.10/2 = 12.57789253554883

    *This multiplier should be the same as in your Future Value Annuity Table.

    Example 4: R = 0.1012; N = 5; P = 2

    Solution 4: [(1 + 0.1012/2) 5 x 2– 1] ÷0.1012/2 = Fill in your answer

    *This multiplier is not in your Future Value Annuity Table. Compare the two solutions.

    This page titled 11.6: Future and Present Annuity Factors- Mathematical Formulas was last modified on Fri, 19 Aug 2022 16:16:52 GMT and is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Kenneth S. Bigel via source content that was edited to the style and standards of the LibreTexts platform.