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An annuity certain is an annuity that pays for a fixed, predetermined number of periods regardless of whether the annuitant survives to receive every payment. The number of payments is specified in the contract at inception and does not depend on any person's life or death. Because the payment schedule is deterministic rather than contingent, the present value and future value of an annuity certain can be calculated precisely using standard time-value-of-money formulas.
This distinguishes it from a life annuity, where the number of payments is uncertain because it continues only as long as the named individual lives. An annuity certain is also called a guaranteed annuity or, in formal actuarial notation, a term annuity. Mortgage repayment schedules are a practical example: a 30-year fixed mortgage requires exactly 360 monthly payments regardless of whether the borrower lives to make all of them (the estate or a co-borrower is still obligated to pay).
| Type | Payment Duration | Depends on Survival? |
|---|---|---|
| Annuity certain | Fixed, predetermined number of periods | No — payments continue regardless of the annuitant's survival |
| Life annuity | For as long as the named life survives | Yes — stops at death |
| Perpetuity | Infinite (never ends) | No — independent of any life |
| Contingent annuity | Depends on a specified event | Yes — depends on one or more lives or conditions |
The present value of an annuity-immediate (end-of-period payments) with n periods, payment amount R, and interest rate i per period is: PV = R × [1 − (1+i)^(−n)] / i. This formula discounts each future payment back to the present and sums the results. For an annuity-due (beginning-of-period payments), multiply this result by (1+i) to account for receiving each payment one period earlier.
The present value of an annuity certain is directly useful for pricing loans, bonds, and lease agreements. When a bank offers a mortgage at a given interest rate and monthly payment, the present value of those payments equals the loan principal. Conversely, given a loan amount and interest rate, the formula can be solved for the required payment amount.
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