# IRS Life Expectancy Tables. Calculating Table H.

**Commutation Factors Table H IRS Actuarial Tables.
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If you have seen our basic introductory course on **developing commutation functions**, you must have wondered what good these tables are, especially if you are not an actuary. Well if you are a tax accountant or a tax lawyer you must be familiar with the commutation tables used by the IRS in the US, Table H. Table H contains commutations factors, at various interest rates, that are used in the valuation of annuities, life estates, and remainders. Or in simple words, Income, gifts and estate tax valuations.

A common question that comes is how do you get from Actuarial Life tables to the IRS Table H. If you are trying to reconcile the values what is it that you are missing and needs to change. Here is how we do it.

## Life Expectancy Tables. IRS Table H.

The tables contain values for

Of these three factors the procedure for calculating D_{x} was already addressed in our earlier course as given below:

And l_{x} = number of persons who attain age x according to the mortality table used. For this purpose it is the based on the Life Table 2000CM.

While the calculation of M_{x} is discussed in that earlier post the factors given on IRS website are for The accent at the top of M makes a difference in the calculation. Where M_{x} is used in the calculation of an assurance payable at the end of the year of death, , is used in the calculation of an assurance payable at the moment of death. It is given as:

used in the determination of the present value of an annuity, where the first payment is at the end of a year which then continues annually during the life of the annuitant. , however, is used for the calculation of the actuarial present value of a complete life annuity which makes an adjustment payment for the period of death.

We use the relationships between an assurance payable at the moment of death, a continuous life annuity, and a complete annuity to determine as follows:

The actuarial present value of an assurance payable at the moment of death is given by:

And incase you are wondering what the finished product would look like, here is a small sample.