How the calculation works
Value a level series of payments at two different dates
An annuity in interest mathematics is a series of level payments made at regular intervals. Present value answers what that entire payment stream is worth today at the selected discount rate. Future value answers what the same stream accumulates to at the end of the term.
An ordinary annuity assumes payments occur at the end of each period. An annuity due assumes they occur at the beginning, giving every payment one extra period of interest.
For an annuity due, multiply either ordinary-annuity value by (1 + r).
Present value of an annuity
Present value discounts every future payment back to today. The farther away a payment is, the more heavily it is discounted when the rate is positive. This calculation is useful for valuing installment streams, leases, structured payments, and other level cash flows.
Future value of an annuity
Future value accumulates each payment forward to the end of the term. Earlier payments earn interest for more periods than later payments, which is why beginning-of-period payments produce a larger future value than otherwise identical end-of-period payments.
Annuity due versus ordinary annuity
The two structures differ only by one period of timing. Multiplying an ordinary-annuity present or future value by (1+r) produces the corresponding annuity-due value at the same rate and number of payments.
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