Basic Examples (3) 

Compute the commutation functions for a mortality table that goes from 1 to 0 in five periods and a discount rate of 0.9:

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Do the same computation as immediately above but return the values as a nested Association in which the outer keys represent years. The result is converted into a Dataset to aid visualization:

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Do the same computation as immediately above, but assume the starting age for the mortality vector is age 20:

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Scope (3) 

Exact values will be provided where rational numbers are used for the inputs:

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The function works on symbolic arguments:

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By adjusting the discount rate, the function can be used for mortality tables that go by time units other than a year. Compute the commutation functions of a mortality table that goes by 10-year periods when the annual discount rate is 0.95:

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Options (2) 

Changing the "ReturnForm" option changes the form of the output:

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Changing the "InitialTime" option changes the keys of the "TimeAssociation" return form; the values of each association remain the same:

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Applications (8) 

Get the commutation functions for males based on "U.S. Historical Population Mortality Rates 2000-2017 for 2017" and a discount rate of 0.95:

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Use the commutation dataset to compute the value of an "increasing annuity" issued to a 60 year old male that pays $1 its first year, $2 its second year, and one additional dollar each year thereafter:

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For a person aged 33, compute the net single premium for a 20-year term insurance payable at the end of the year of death, where $1 is paid if the death occurs in the first year, $2 is paid is the death occurs in the second year, and so on:

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Use the commutation dataset to plot the level annual premium for a term life insurance policy of 20 years as a function of the issue age of the insured:

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Use the commutation dataset to compute the annual level premium (paid at the beginning of the year) per $1 of whole life coverage for a purchaser with issue age of 25:

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Use the same dataset to plot the retrospective reserve on this policy according tothe attained age of the insured:

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Compute the net single premium needed to fund a life insurance policy of $1,000,000 on a 61 year old male for 10 years, with death benefits paid at the end of the year of death:

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Do the same computation using the commutation dataset but make the notation more transparent:

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Properties and Relations (1) 

The resource function MortalityConvert permits use of mortality data provided as a hazard or probability instead of as survival:

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Neat Examples (1) 

Determine the amount an insurer would be willing to pay to rid itself of a $1,000,000 insurance policy issued to a 25 year-old priced under the mortality table contained in "U.S. Historical Population Mortality Rates 2000-2017 for 2017" when the insurer becomes aware that the insured’s hazards are 80% greater than contained in the table:

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