Method 8 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 |
where 
and 
are
functions of 
which is calculated by assuming a uniform distribution of deaths (UDD)
throughout the year of age 𝑥.
Payments more frequently that annually
Using commutation functions, the present value
formula is
and by using the Woolhouse method we have
