11.6 Future and Present Annuity Factors: Mathematical Formulas

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.

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.

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. 

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Introduction to Financial Analysis Copyright © 2022 by Kenneth S. Bigel is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.

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