Present Value of an Annuity Calculator

An annuity is a stream of equal payments made at regular intervals: a pension, a bond's coupon payments, a structured settlement, a trust's annual distribution. Present value of an annuity answers what that entire stream of future payments is worth today, in one lump sum, discounted at a given rate.

This is the same underlying math behind valuing a charitable remainder annuity trust's payment stream or pricing a bond's coupons, generalized here to a fixed number of periods rather than a life contingency or a specific coupon schedule.

How does this calculator work?

Enter the equal payment amount received each period, the annual discount rate, the number of years, how many payments occur per year, and whether payments arrive at the end of each period (ordinary, the common case) or the beginning (annuity due).

The calculator discounts each future payment back to today and sums them, using the standard annuity present value formula.

A level stream is worth less than its raw total because later payments are discounted harder, the same logic that prices a bond's coupons and mirrors a lump-sum present value. Reverse the question, how a stream grows toward a future date, and you have the future value of an annuity.

Worked example

A stream of $1,000 per month for 10 years, discounted at a 6% annual rate, payments at the end of each month.

Payment per period

$1,000

Total payments (undiscounted)

$120,000

Present value

$90,073.45

Discount

$29,926.55

How the numbers work

Even though you'll receive $120,000 in total over 10 years, that stream is only worth $90,073.45 today, because later payments are discounted more heavily than earlier ones. A payment 10 years out is worth much less today than one arriving next month.

The gap between the undiscounted total and the present value ($29,926.55 here) grows with the discount rate and the length of the stream. A longer or more heavily discounted annuity is worth proportionally less today relative to its face total.

Whenever you're comparing a lump sum offer against a stream of future payments, such as a lottery payout, a pension buyout, or a structured settlement, this present value is the number that puts both on equal footing.