Life Annuity Present Value Calculator
This calculator computes the actuarial present value (APV) of a whole life annuity that pays a fixed annual amount as long as the annuitant lives. The APV is the sum of each annual payment multiplied by two discounting factors: the probability of surviving to receive that payment (from the SSA Period Life Table) and the present value discount factor for the time value of money. This is the standard actuarial method used to price immediate annuities and value defined-benefit pension liabilities. Enter the annuitant's age and sex, the annual payment amount, and the discount rate. The calculator projects survival probabilities from the SSA table and accumulates the discounted expected payments.
Life annuity present value formula
APV = sum of [Payment x (k)p(x) x v^k]
where v = 1/(1 + i), (k)p(x) = survival probability for k years
Life expectancy = sum of (k)p(x) for k = 1 to max age
The survival probability k-p-x is the product of annual survival rates from age x to age x+k-1. The discount factor v^k converts a payment k years in the future to its present value.
Life annuity valuation explained
- Older annuitants have a smaller APV because fewer expected payments remain and survival probabilities are lower.
- Higher discount rates reduce APV by making distant payments worth less today.
- Females have higher APVs than males at the same age because they have lower mortality and thus more expected payments.
- Insurers use annuitant mortality tables (lighter mortality than SSA) and add expense loads, so actual annuity prices differ from this estimate.
- The APV equals the fair economic value of the annuity; if the market price exceeds APV at your discount rate, the annuity is relatively expensive.
Life annuity present value: frequently asked questions
What is the actuarial present value of a life annuity?
The actuarial present value (APV) is the sum of all expected annuity payments, each discounted for the time value of money and the probability that the annuitant is still alive to receive it. Formally: APV = sum of (payment x k-p-x x v^k) for k from 1 to maximum age minus current age, where v = 1/(1+i) is the discount factor and k-p-x is the k-year survival probability.
What discount rate should I use?
Use the expected investment return of the assets backing the annuity. Insurers typically use a rate consistent with high-grade bond yields. For Social Security or pension planning, rates between 3 and 5 percent are common in government actuarial analyses.
What is the difference between a life annuity and a term annuity?
A life annuity pays as long as the annuitant lives, regardless of duration. A term annuity pays for a fixed number of years regardless of whether the annuitant survives. A life annuity carries longevity risk for the insurer; its present value depends on mortality assumptions.
Why does the annuity value decrease with higher interest rates?
Higher discount rates reduce the present value of future payments more heavily. At a 6 percent discount rate, a payment 20 years from now is worth only about 31 cents per dollar today, versus about 55 cents at 3 percent. So higher rates always reduce the present value of any future income stream.
How accurate is this calculator?
This calculator uses the SSA 2021 Period Life Table, which represents US population-average mortality. Actual annuity pricing uses proprietary annuitant mortality tables (which have lower mortality than the general population, since annuitants self-select for better health) and may include load factors. Treat this as an educational planning estimate.
Official sources
- Social Security Administration: SSA 2021 Period Life Table.
- Society of Actuaries: SOA Mortality Table Research.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.