Before the time of powerful computers, actuaries used “commutation functions” as a means of computation short-cuts. This worked well enough when using a static mortality table and a single constant interest rate, but with the increasing use of mortality with projected generational improvement and interest rates that vary with time (spot rates or forward rates), commutation functions are no longer applicable, practical, or useful. However, many legacy computer systems and worksheets are based on commutation functions, so they are included in EAC PV Tools.

·        The Society of Actuaries has developed a study note on commutation functions.

·        The Social Security Administration has a paper on commutation functions.

The symbol (𝑥) denotes a life aged (𝑥).

Basic commutation functions for annuities

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2.   

3.   

Basic commutation functions for life insurance

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6.   

Present value using commutation functions

7.    present value of a life annuity of 1 per year, paid at the beginning of the year

8.    present value of a life insurance of 1 payable at the end of the year of death

Excel functions

Click here to see the various Excel functions to handle commutation functions.