Method 9 is based on commutation functions, and is provided to match results from older computer systems. Commutation functions are based on the traditional actuarial principles and are shortcuts to simplify the actuarial present value computation.
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Note: |
With advances in computing power, commutation functions are no longer necessary; instead, it is better to rely on the principles of a discounted cash flow as described in Methods 0, 1, and 2 above. |
Fractional Ages
Using commutation functions, the present value
formula is
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for integral 𝑥
and 0 ≤ 𝑡 ≤ 1 |
Assuming 
and 
are linear functions of 𝑡 for integral age 𝑥 and 0 ≤ 𝑡 ≤ 1,
then it follows that 
and 
and 
are also linear functions of 𝑡, thus we have the
following:
and therefore 
is easily calculated.
Payments more frequently that annually
Using commutation functions, the present value
formula is
and by using the Woolhouse method we have
