Annuity Calculator
Find the monthly or yearly income a lump sum pays over a set term, the lump sum a target income needs, or what regular deposits grow to. Level or rising payments.
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About this toolWhat is the Annuity Calculator?
An annuity is a series of equal (or steadily rising) payments over a fixed number of periods. This annuity calculator answers the three questions people ask about one: how much income can this lump sum pay me, how big a lump sum do I need for the income I want, and what will regular deposits grow to.
You choose monthly, quarterly, semi-annual or annual payments, whether each payment is made at the end of the period (an ordinary annuity) or the start (an annuity due), an optional yearly increase to keep up with inflation, and an amount to leave over at the end. The drawdown chart and table show the balance, interest and payments year by year until the money runs out.
- Payout from a lump sum, lump sum needed, and growth of deposits
- Ordinary annuity or annuity due
- Monthly, quarterly, semi-annual or annual payments
- Optional yearly payment increase and remaining balance
- Year-by-year drawdown chart and schedule
How to use the Annuity Calculator
- Choose what to calculate: the payout from a lump sum, the lump sum needed for a payout, or the growth of regular deposits.
- Enter the lump sum or the payment, the annual interest rate and the number of years.
- Pick the payment frequency and whether payments are made at the end or start of each period.
- Optionally add a yearly increase and an amount to leave at the end.
- Read the result and the drawdown chart, or switch to the table for year-by-year interest and payments.
Worked examples
Income from $500,000
Input
$500,000 at 5% for 25 years, monthly, ordinary
Output
$2,922.95 a month; $876,885 paid out in total
Interest pays for $376,885 of the total. As an annuity due (payments at the start of each month) the payment drops to $2,910.82.
Inflation-linked income
Input
Same, with payments rising 2.5% a year
Output
First payment $2,278.99 a month, rising each year
Starting about $640 lower buys protection against rising prices. By year 25 the payment has grown to about $4,100.
How much for $4,000 a month for 30 years?
Input
$4,000 a month, 5%, 30 years, then the same with a 3% yearly increase
Output
$745,126 for level payments; $1,060,004 if payments rise 3% a year
Indexing the income to inflation raises the lump sum needed by over 40%, a useful reality check for retirement targets.
Background and insight
For level payments the maths is the present value of an annuity: PMT = PV × i / (1 − (1 + i)^−n), with i the rate per period and n the number of payments. The rate per period here is the annual rate divided by the number of payments a year, the convention used by financial calculators when payments and compounding share a frequency. A $100,000 lump sum at 6% over 20 years pays $716.43 a month, the same figure as the monthly payment on a 20-year $100,000 loan at 6%, because a payout annuity is a loan in reverse.
An annuity due pays at the start of each period, so the first payment leaves immediately and each payment is smaller by a factor of (1 + i). Rising payments are handled by discounting each payment separately, PV = Σ PMT × (1 + g)^year × (1 + i)^−t, which is exact even when the growth rate equals the interest rate (where the textbook growing-annuity formula divides by zero).
This is a time-value-of-money calculation. A life annuity bought from an insurer is priced on mortality tables, fees and the company's own investment assumptions, and it pays for as long as you live rather than for a fixed term, so its quote will differ. The calculator is the right tool for a period-certain annuity, a planned drawdown of savings or checking whether an insurer's quote is reasonable.
Common use cases
Planning retirement drawdown
See how long a pot lasts at a given withdrawal, or the withdrawal that empties it on a chosen date.
Comparing an annuity quote
Compare an insurer's period-certain offer with what the same lump sum would pay at a market interest rate.
Lottery and settlement payouts
Value a stream of payments against a lump-sum option at your own discount rate.
Finance coursework
Check ordinary annuity, annuity due and growing annuity problems with a full schedule.
Tips and limitations
- The rate is the return the remaining balance earns while it is paid out. Use a cautious rate for money you rely on.
- A level payment loses buying power every year. A 2% to 3% yearly increase is a simple hedge, at the cost of a lower first payment.
- Taxes are not modelled. Payouts from pre-tax accounts are taxable income; part of a purchased annuity's payment may be a tax-free return of principal.
- If you need income for life rather than for a set term, look at life annuity quotes or plan for a longer term than you expect to need.
Frequently asked questions
How much does a $500,000 annuity pay per month?
Over 25 years at 5%, a $500,000 lump sum pays about $2,923 a month with payments at the end of each month. Over 20 years at the same rate it pays about $3,300. A life annuity from an insurer is priced differently and depends on your age.
What is the difference between an ordinary annuity and an annuity due?
An ordinary annuity pays at the end of each period, an annuity due at the start. Because annuity-due payments leave the account one period earlier, each payment is smaller by a factor of (1 + i), and the present value of a given payment stream is larger by the same factor.
How do you calculate an annuity payment?
Use PMT = PV × i / (1 − (1 + i)^−n), where PV is the lump sum, i the interest rate per period and n the number of payments. For $100,000 at 6% a year paid monthly for 20 years, i = 0.005 and n = 240, giving $716.43.
How much do I need to buy an annuity of $2,000 a month?
For a fixed 20-year term at 5%, about $303,000. At 4% it is about $330,000, and over 30 years at 5% about $373,000. Enter your own term and rate in Lump sum needed mode.
What is a growing annuity?
An annuity whose payments rise by a fixed percentage, here once a year. It costs more up front than a level annuity with the same first payment, but the income keeps more of its value as prices rise.
Does this annuity calculator include fees and life expectancy?
No. It is a pure time-value calculation for a fixed term. Insurance annuities add mortality pooling, fees and the insurer's rates, and riders such as guaranteed withdrawal benefits are priced separately.
Is there an in-depth guide to the Annuity Calculator?
Yes. “401(k), Roth IRA and Annuities: The Maths Behind Retirement Accounts” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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