Annuity present value
By Jude Wallis
The present value of an annuity is the single amount today that is worth the same as a fixed series of equal future payments, discounted at a chosen rate.
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It answers the question a pension buyout or a lottery choice actually poses: what is a run of payments worth right now. Each payment is discounted for the time until it arrives and the discounted amounts are added, which the annuity factor does in one step.
Timing has to be declared. An ordinary annuity pays at the end of each period; an annuity due pays at the start, and every payment is discounted one period less, which makes it worth more. The frequency of the rate must match the payments too, so a monthly stream is discounted at a monthly rate rather than an annual one.
Remove the end date and the same idea becomes a perpetuity, where the factor collapses into a single division. The annuity present value calculator discounts the stream, present value is the underlying idea, and ordinary against due annuities is the timing question.