Actuarial present value

The actuarial present value (APV) is the expected value of the present value of future payments whose timing or amount depends on uncertain events such as survival or death.

In actuarial science, APVs are used to value benefits and premiums for products such as life insurance and life annuities under stated assumptions about interest and about survival and death probabilities, often taken from a life table.

APVs can be defined in discrete or continuous time depending on the payment timing and modelling convention, and are commonly expressed using standard actuarial notation for life-contingent contracts.

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