A whole life annuity due makes beginning-of-period payments while the annuitant is alive, so valuation combines interest and survival probabilities.
A whole life annuity due is a life-contingent payment stream that pays at the beginning of each period while the annuitant is alive. The first payment is made immediately, assuming the annuitant is alive on the valuation date, and later payments occur only if the annuitant survives to their payment dates.
This is primarily an actuarial cash-flow concept. A retail annuity contract may contain similar lifetime-income features, but actual benefits depend on the contract, payout option, guarantees, expenses, and insurer.
For annual unit payments to a person currently age (x):
| Payment time | Payment if alive | Probability of reaching date | Present-value weight |
|---|---|---|---|
| 0 | 1 | 1 | 1 |
| 1 | 1 | ({}_1p_x) | (v,{}_1p_x) |
| 2 | 1 | ({}_2p_x) | (v^2,{}_2p_x) |
| … | … | … | … |
Here, ({}_kp_x) is the probability that a person age (x) survives for (k) years, and (v=(1+i)^{-1}) is the one-period discount factor at annual effective interest rate (i).
The first payment is immediate. It is therefore not discounted and does not depend on surviving an additional year.
The standard annual whole life annuity-due factor is:
For a payment of (B) each year:
Where:
The summation is written to infinity because no fixed maximum payment count is assumed in the model. In practice, mortality tables end at a limiting age, and software or commutation functions perform the calculation.
An annuity due certain has a known number of payments. Its value depends on payment, rate, term, and beginning-of-period timing.
A whole life annuity due does not have a known payment count at issue. Each possible future payment is multiplied by the probability that the annuitant will be alive to receive it. Replacing this structure with a fixed (n)-period factor ignores longevity uncertainty.
Consider a hypothetical whole life annuity due paying $10,000 annually. Assume a 4% annual effective discount rate and the following illustrative survival probabilities:
| Payment time | Survival probability | Discounted probability weight |
|---|---|---|
| 0 | 1.00 | 1.000000 |
| 1 | 0.98 | 0.942308 |
| 2 | 0.95 | 0.878328 |
| 3 | 0.91 | 0.808987 |
For these first four payment dates only:
This is not the value of the full whole life annuity. The complete calculation must add every later survival-weighted payment supported by the mortality basis. The example shows how each term is constructed without inventing a full mortality table.
| Structure | First payment | When payments stop | Key additional feature |
|---|---|---|---|
| Whole life annuity due | Immediately | At death | Survival-contingent |
| Whole life annuity immediate | End of first period, if alive | At death | No time-0 payment |
| Temporary life annuity due | Immediately | Earlier of death or fixed term | Survival plus term limit |
| Annuity certain due | Immediately | After fixed number of payments | Not survival-contingent |
| Life with period certain | Per contract | Death, subject to guaranteed minimum period | Some payments may continue after death |
| Joint-and-survivor annuity | Per contract | Based on survival of either covered person | Two-life probabilities and possible benefit change |
For annual unit payments, the relationship between whole life due and whole life immediate is:
The 1 represents the immediate time-0 payment. Do not automatically use the fixed annuity-certain adjustment ((1+i)) for life-contingent streams; survival weighting changes the relationship.
Higher survival probabilities increase the expected number of payments and generally increase actuarial present value. The relevant table may depend on the covered population, valuation purpose, improvement assumptions, and applicable standards.
A higher discount rate reduces the present value of later expected payments. Interest and mortality assumptions must use compatible payment periods.
Monthly or quarterly payments require frequency-specific valuation rather than blindly dividing an annual payment or factor. Timing within the year affects value.
A period-certain guarantee, installment refund, cash refund, or death benefit can create payments after the annuitant dies. Those benefits require additional cash flows and probabilities.
Pricing or contract value may include expenses, capital requirements, margins, taxes, commissions, options, and insurer assumptions beyond the benefit’s actuarial present value.
The Society of Actuaries’ Actuarial Present Value study note presents the whole life annuity-due factor as the sum of discounted survival probabilities. Its notation distinguishes whole-life, temporary, deferred, due, and immediate payment structures.
For retail products, the U.S. Securities and Exchange Commission’s Investor.gov annuity guide explains that costs, risks, features, withdrawal consequences, and insurer financial strength must be considered. An actuarial formula alone does not determine product value or suitability.
This article is educational and does not provide personalized actuarial, investment, tax, insurance, legal, or retirement advice.