Definition
Annuity factor is the present value today of an income stream that pays one unit of currency at each of a specified series of future dates, computed at a chosen discount rate and, in actuarial applications, weighted by survival probability.
Why it matters
Annuity factor is the central computational primitive that converts income streams into single figures and vice versa, which makes it the workhorse of every retirement income calculation. Once the annuity factor for a specific configuration is known, dividing a premium by the annuity factor produces the annual income that premium can support, and multiplying an annual income need by the annuity factor produces the capital required to fund it. The whole vocabulary of lifetime income analysis rests on this operation.
How it works
Annuity factor is computed by discounting each future payment of one unit back to the present at the chosen discount rate and summing across all payments. For a stream of one dollar per year over twenty years at a 3 percent discount rate, the annuity factor is approximately 14.88, meaning $14.88 today produces one dollar per year over the twenty-year stream. For lifetime income arrangements, each future payment is additionally weighted by the probability that the recipient will be alive to receive it, producing an actuarial annuity factor that is smaller than the corresponding fixed-period figure because the survival probabilities discount future payments beyond what the discount rate alone does. The lower actuarial annuity factor is the arithmetic reason that mortality pooling produces higher income per dollar of premium than fixed-period drawdown: the pool pays out to those who survive, and the actuarial annuity factor reflects only survivorship-weighted years. A larger annuity factor corresponds to a lower income yield per dollar of premium; a smaller annuity factor corresponds to a higher one.
In practice
Every income quote an individual receives from a lifetime income product is the reciprocal of an annuity factor: the annual income per dollar of premium is one divided by the annuity factor for that arrangement at those parameters. A professional can compute the actuarial annuity factor for an individual's specific configuration and set it alongside the quoted income to reveal the implicit annuity factor the product is using; the gap between the two reflects insurer costs, margin, and product features. Individuals evaluating quotes across products can compute a rough implicit annuity factor themselves by dividing the premium by the annual income; the resulting figure allows a like-for-like comparison across products with different presentation formats.
Related terms
- Present value
- Actuarial present value
- Cost of income
- Discount rate
- Pooling multiplier
- Frictionless pool
- Solo drawdown
- Mortality credits