Annuity-Immediate Present Value Calculator
A life annuity-immediate pays at the end of each year while the annuitant survives, the standard arrears form for payout annuities. Its present value per unit is a subscript x, and with commutation functions a x = N(x+1) / Dx, which equals Nx / Dx minus one. This calculator takes the commutation columns Nx and Dx for the annuitant's age (from a valuation table or our commutation function tool) and the annual payment, then returns the per-unit value and the full present value. Nx and Dx are user-editable inputs because the appropriate mortality table depends on the annuitant.
Annuity-immediate present value formula
a-double-dot x = Nx / Dx
a x (immediate) = a-double-dot x - 1 = N(x+1) / Dx
Present value = payment * a x
n-year temporary immediate = (N(x+1) - N(x+n+1)) / Dx
The immediate value omits the payment at time zero that the annuity-due includes, which is why it is exactly one unit smaller.
Annuity-immediate context
- Immediate annuities pay in arrears; due annuities pay in advance.
- For life annuities the due value always exceeds the immediate value by exactly one unit.
- Payout annuities and pension benefits are commonly valued as immediate annuities.
- Use a consistent mortality table and interest rate for Nx and Dx.
- The value falls as the interest rate rises and as the age rises.
Annuity-immediate: frequently asked questions
What is a life annuity-immediate?
A life annuity-immediate pays a fixed amount at the end of each year for as long as the annuitant lives, with the first payment one year after issue. Its actuarial present value per unit is written a subscript x. It is the standard form for payout annuities that pay in arrears.
How is the present value computed?
Using commutation functions, a x = N(x+1) / Dx, which is equal to Nx / Dx minus 1. The present value of the annuity equals the annual payment times a x. This calculator derives a x from the Nx and Dx you enter.
How does it differ from an annuity-due?
An annuity-immediate pays at the end of each period; an annuity-due pays at the beginning. For life annuities the relationship is a-double-dot x = a x + 1, so the immediate value is exactly one payment smaller than the due value at the same age and interest rate.
Where do Nx and Dx come from?
They are commutation columns from a mortality table and an interest rate, available in a Society of Actuaries valuation table or from our commutation function tool. Because the right table depends on the population, Nx and Dx are user-editable inputs here.
Can I value a deferred or temporary annuity?
Yes. A temporary immediate annuity for n years is (N(x+1) - N(x+n+1)) / Dx, and a deferred annuity shifts the starting Nx term. This page computes the whole-life immediate value; adjust the Nx terms yourself per the formula block.
Official sources
- Society of Actuaries: SOA annuity and valuation study materials.
- U.S. Social Security Administration: SSA Office of the Chief Actuary life tables.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.