Joint Life Annuity Calculator
A joint-life annuity pays while both annuitants survive and stops at the first death; a last-survivor annuity pays until the second death. The two are tied together by the inclusion-exclusion identity a-double-dot last survivor = a-double-dot x + a-double-dot y - a-double-dot xy. This calculator takes the two single-life annuity-due values and the joint-life annuity-due value (from a valuation table or our commutation tool) and the annual payment, then returns the last-survivor annuity value and the present values of the joint and last-survivor benefits. Every annuity value is a user-editable input.
Joint and last-survivor annuity formula
Last-survivor a-double-dot = a-double-dot x + a-double-dot y - a-double-dot xy
PV joint-life = payment * a-double-dot xy
PV last-survivor = payment * last-survivor a-double-dot
The joint-life status pays only while both live; the last-survivor status pays while at least one lives. The identity follows from adding the two single statuses and removing the double-counted joint period.
Joint life context
- Joint-life annuities are the cheapest of the three because payments cease at the first death.
- Last-survivor annuities are the most expensive because they pay the longest.
- Pension joint-and-survivor options are valued with these statuses.
- The single-life values must use the same interest rate as the joint value.
- Correlated mortality between the two lives is captured in the joint commutation column.
Joint life annuity: frequently asked questions
What is a joint-life annuity?
A joint-life annuity pays while both annuitants are alive and stops at the first death. A last-survivor annuity pays until the second (last) death. The two are linked by a-double-dot last survivor = a-double-dot x + a-double-dot y - a-double-dot xy, where xy denotes the joint-life status.
How is the last-survivor value computed?
By the standard inclusion-exclusion identity: the last-survivor annuity-due equals the sum of the two single-life annuities-due minus the joint-life annuity-due. This calculator applies that identity to the three values you enter and multiplies by the annual payment for the present value.
Where do the single and joint annuity values come from?
Each single-life annuity-due is Nx / Dx from a mortality table; the joint-life annuity uses a joint commutation column built from the two lives' survival. Compute them from a Society of Actuaries valuation table or our commutation tool. They are user-editable inputs because the right table depends on the annuitants.
Why does a last-survivor annuity cost more than a joint-life annuity?
Because it keeps paying after the first death, until the second death, so payments are expected for longer. The identity makes this explicit: the last-survivor value exceeds either single life value, while the joint-life value is the smallest of the three.
Can I use this for a pension survivor benefit?
Yes. Many pensions value a joint-and-survivor benefit using exactly these statuses. Enter the annuity values for the member and spouse and the joint status; the payment is the annual benefit. This is an educational tool, not a plan valuation.
Official sources
- Society of Actuaries: SOA multiple-life and annuity 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.