Annuity Calculator

What this calculator tells you

An annuity is a series of equal payments made at regular intervals over a fixed period. A pension that pays a set amount each year, a lease with fixed yearly rent, and a promised fixed payment from a contract are all annuities. This calculator finds the present value of such a series: how much those future payments are worth in money today, given the return you could earn elsewhere.

The idea behind present value is that money available now can be invested and grow, so a payment due in the future is worth less than the same amount today. The discount rate you enter is the return you could reasonably expect from an alternative use of the money. A higher rate means future payments are worth less today; a lower rate means they are worth more.

How the result is worked out

The calculator assumes each payment arrives at the end of its year. The present value is the sum of each payment divided by one plus the discount rate, raised to the number of years until that payment. The closed form used here is PV = PMT × (1 − (1 + r)⁻ⁿ) ÷ r, where PMT is the yearly payment, r the discount rate and n the number of years. When the rate is zero, the value is simply the payment multiplied by the number of years.

A worked example

Suppose you are offered 1,000 a year for five years, and your alternative return is 5%. Each payment is discounted separately: the first is worth about 952, the second about 907, and so on. Added together, the five payments are worth about 4,329 today. The undiscounted total is 5,000, so the difference of about 671 is the cost of waiting.

Why the discount rate matters most

The result is sensitive to the discount rate, so it is worth testing a range. Try the rate you could earn on a savings account, the rate on a bond of similar length, and a higher rate reflecting the risk you are taking. If the answer changes a lot across that range, the decision depends heavily on your assumption, and it is worth checking the reasoning behind it.

Limits of the calculation

Annuity contracts often include terms that change the value: inflation adjustments, guarantees that last only for a set period, survivor benefits, and fees. None of these are modelled here. Taxes on each payment and any charge for early exit are also excluded. The calculator treats the rate and the payments as known, which they rarely are for a long contract.

Use the figure as a starting point for comparing offers on a like-for-like basis, using the same discount rate for each. Read the contract for any feature that changes how much you actually receive, and consider the protection offered if the provider runs into difficulty.

Using the result

Present value is most useful for comparing options. If a lump sum offer is higher than the present value of the annuity at a rate you trust, the lump sum may be the better choice for you; if it is lower, the annuity may be worth more. This comparison also depends on your need for regular income, your health and how long you expect to live, which the calculator cannot judge.