Annuity (mathematics)

An annuity is a series of payments made or received at regular intervals. Its value depends on payment amounts, timing, and the interest rate used to discount or accumulate them.

Present value: The value today of future cash flows discounted at a specified rate. An annuity’s present value discounts each scheduled payment back to a common date.
Time value of money: The principle that money available at different times has different economic value. Annuity valuation applies this principle to a sequence of dated payments.
Perpetuity: A stream of equal payments that continues indefinitely at regular intervals. Unlike a finite annuity, a perpetuity has no final payment.
Amortization: The gradual repayment of a debt through scheduled payments of principal and interest. A level-payment loan is valued and divided into principal and interest using annuity mathematics.
Actuarial present value: The expected present value of contingent payments, calculated using probabilities and a discount basis. It extends deterministic annuity valuation to payments that depend on future events.
Future value: The value at a future date of current money or cash flows accumulated at a specified rate. An annuity’s future value accumulates its payments forward to a common date.
Compound interest: Interest calculated on both principal and previously accumulated interest. Compounding determines how payments grow between their dates and the valuation date.
Annuity with payments in advance: A payment stream whose installments are due at the start of each period. Its timing shifts payments earlier than the end-of-period convention used by an ordinary annuity.
Mortgage: A loan secured by real property, commonly repaid through periodic installments. Fixed-rate mortgage payments form an annuity over the loan term.
Mortality table: A statistical table describing survival or death probabilities by age for a population. Life-contingent annuity values rely on estimated probabilities of surviving to payment dates.

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