Annuity Present Value Calculator

What the annuity present value calculator does

An annuity is a stream of fixed payments at regular intervals: a pension paid each year, a settlement paid in instalments, a bond's coupons, or rent on a lease. Enter the payment per period, the discount rate per period and the number of periods, and the annuity present value calculator converts the whole stream into one figure in today's terms. That present value is the amount which, invested today at your rate, would exactly reproduce every payment.

Why a future payment is worth less

Money you hold today can be invested and grow, so a dollar promised next year is worth less than a dollar now; you give up the return you could have earned in the meantime. The further away a payment is, the more it is discounted. A payment in one year is reduced slightly; one in twenty years is reduced heavily. The calculator discounts each payment according to how long you wait for it and adds up the results.

The formula

For an ordinary annuity, with each payment at the end of the period:

PV = PMT × (1 − (1 + i)^(−n)) ÷ i

PMT is the payment per period, i the discount rate per period and n the number of periods. The bracketed part is the annuity factor, a single multiplier that covers all the discounting. At a zero rate the result is PMT × n, since every payment counts at face value.

The calculator also shows the discount: the raw total of the payments minus their present value. That is the value lost to waiting, and it grows with the rate and with the number of periods. The donut chart splits the raw total into the part that survives discounting and the part lost to time.

Choosing the discount rate

Small changes in the discount rate move the answer a lot. The rate is the return you could earn on the money if you had it now, so it reflects both interest rates in general and the risk of the payments. A safe, government-backed stream is usually discounted at a low rate; a risky or uncertain one at a higher rate. Run the calculator with a cautious rate and an optimistic one and treat the value as somewhere between. If a small change in the rate changes your decision, the choice is finely balanced.

Where it helps

When offered a lump sum now or instalments later, compare the lump sum with the present value of the instalments, not their raw total. A pension quoted as an annual amount, or a settlement paid over several years, can be reduced to one present value and compared with other options. A bond's price is largely the present value of its coupons, and a lease can be valued the same way.

Reading the results

The present value is an estimate, not a market price. It depends on the rate you choose and assumes the payments are certain and evenly spaced. Risk, tax or inflation adjustments can change the picture. The discount shown beside the raw total is a reminder that a larger sum paid later is not always the better deal.

This article is general information only and is not financial advice.

About This Annuity Present Value Calculator

Use this annuity present value calculator to get an instant estimate based on the figures you enter. Adjust the inputs above to match your situation, or browse all our calculators to plan your next step.