Annuity-Due Present Value Calculator
A life annuity-due pays at the start of each year while the annuitant survives, and its present value per unit is a-double-dot subscript x. It is the workhorse behind level-premium calculations because premiums are paid at the beginning of each policy year. Using commutation functions, a-double-dot x = Nx / Dx. 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 annuity value and the full present value. Nx and Dx are user-editable inputs because the right mortality table depends on the annuitant.
Annuity-due present value formula
a-double-dot x = Nx / Dx
Present value = payment * (Nx / Dx)
a x (immediate) = a-double-dot x - 1
n-year temporary due = (Nx - N(x+n)) / Dx
Nx is the sum of Dx from age x upward. Dividing by Dx discounts and weights every future survival payment back to the current age.
Annuity-due context
- Annuity-due pays at the start of each period; immediate pays at the end.
- For life annuities, the due value is exactly one unit larger than the immediate value.
- Level net premiums use the annuity-due as the denominator of the equivalence equation.
- Use a consistent mortality table and interest rate for Nx and Dx.
- The annuity value falls as the interest rate rises and as the age rises.
Annuity-due: frequently asked questions
What is a life annuity-due?
A life annuity-due pays a fixed amount at the start of each year for as long as the annuitant lives, beginning immediately. Its actuarial present value per unit is written a-double-dot subscript x. Premiums on life insurance are usually valued as annuities-due because they are paid at the start of each policy year.
How is the present value computed?
With commutation functions, a-double-dot x = Nx / Dx, where Nx is the sum of Dx from age x onward and Dx = v^x times lx. The present value of the annuity equals the annual payment times Nx / Dx.
How does an annuity-due differ from an annuity-immediate?
An annuity-due pays at the beginning of each period; an annuity-immediate pays at the end. For life annuities, a-double-dot x = a x + 1, so the annuity-due value is exactly one payment larger than the immediate value at the same age and interest rate.
Where do Nx and Dx come from?
They are commutation columns built from a mortality table and an interest rate, available from a Society of Actuaries valuation table or computed with our commutation function tool. Because the right table depends on the population, Nx and Dx are user-editable inputs here.
Can I value a temporary annuity-due?
Yes. An n-year temporary annuity-due is (Nx - N at age x+n) / Dx. This page values the whole-life annuity-due Nx / Dx; subtract the later Nx term yourself to make it temporary, as shown in 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.