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Life & Annuity Calculators

Life expectancy, survival odds, and the actuarial value of lifetime income and insurance — computed from the U.S. Social Security Administration period life table.

1 · Life Expectancy & Survival

Remaining life expectancy at your age, and the probability of reaching a target age.

Life expectancy — years remaining
Expected age at death
Chance of reaching age
Survivors per 100,000 at your age
ₜpₓ = l₍ₓ₊ₜ₎ ⁄ lₓ

2 · Life Annuity & Insurance Pricing

The actuarial present value of $1/year for life, and the price of life insurance, at a chosen interest rate.

Annuity factor äₓ ($1/yr for life, due)
Value of income /yr for life
Whole-life insurance factor Aₓ
Single premium for benefit
Level annual premium
äₓ = Σ vᵗ·ₜpₓ  ·  Aₓ = Σ vᵗ⁺¹·ₜpₓ·q₍ₓ₊ₜ₎

3 · Early / Delayed Income — Actuarial Reduction

If lifetime income normally starts at a target age, taking it earlier (or later) is adjusted so the value is actuarially fair.

Actuarially-fair adjustment factor
Adjusted benefit at claim age
Change vs full benefit
Annuity factor at claim age
Deferred value factor to normal age
F = ₍ₙ₎Eₐ · ä₍NRA₎ ⁄ äₐ

4 · Mortality Curve

Annual probability of death (qₓ) by age, log scale — the classic actuarial curve.

Male Female

Source & method. Mortality rates (qₓ) and life expectancy (eₓ) are the U.S. Social Security Administration 2021 Period Life Table (public domain); survivors (lₓ) are derived from qₓ. Annuity and insurance factors use standard life-contingency formulas with annual discounting and a benefit paid at the end of the year of death. A period table reflects one year's mortality across all ages and does not project future improvement, so it understates the life expectancy of people alive today. Educational use only — not financial, insurance, or retirement advice.