Work out the regular payments a sum of money can pay at a fixed interest rate, the amount you'd need for a payout you want, or how long it lasts. Payments can rise each year.
The annuity formulas
With a yearly rate R and k payments a year, the rate per period is i = R ÷ k (the rate compounds once per payment period). For n level payments at the end of each period:
PV = PMT × (1 − (1 + i)⁻ⁿ) ÷ i PMT = PV × i ÷ (1 − (1 + i)⁻ⁿ)
For payments at the start of each period (an annuity due), multiply PV by (1 + i), or divide PMT by (1 + i). How long a lump sum lasts:
n = −ln(1 − PV × i ÷ PMT) ÷ ln(1 + i)
Growing annuity. When payments rise by g each year (and stay level within the year), Calcist adds up each payment's present value directly: PV = Σ PMT × (1 + g)year ÷ (1 + i)period.
Worked example
$100,000 at 5% a year, paid monthly for 20 years: i = 0.05 ÷ 12 = 0.4167%, n = 240. PMT = 100,000 × 0.004167 ÷ (1 − 1.004167⁻²⁴⁰) = $659.96 a month. Paid at the start of each month, it's 659.96 ÷ 1.004167 = $657.22. If you take $1,000 a month instead, the money lasts 129 full payments, about 10 years 9 months, plus a final $628.96.
This is the math, not an insurance quote
An annuity you buy from an insurance company is priced differently. A life annuity pays for as long as you live, so the insurer prices in how long people your age are expected to live, along with its costs and profit. That means the payout can be higher than a fixed-term calculation for an older buyer, and you give up access to the lump sum. Fees, surrender charges and riders vary widely. Use this calculator to understand the time value of money, then compare real quotes.
Limitations
A planning estimate, not financial, tax or investment advice. Every assumption is listed under the result.
Sources
How we checked this
Before every update, this calculator is run in a real browser with these known answers, and it must match all of them:
- $100,000 at 5% for 20 years pays $659.96 a month ✓
- Paid at the start of each month (annuity due): $657.22 ✓
- Payments rising 3% a year start at $515.71 ✓
- $1,000 a month for 25 years at 4% needs $189,452.48 ✓
- $100,000 at 5% paying $1,000 a month lasts 10 years, 9 months, then $628.96 ✓
- 0% rate: $1,000 a month for 10 years needs $120,000 ✓
- Payment below the interest lasts forever ✓
- 0% rate: $100,000 at $1,000 lasts n = PV ÷ PMT = 100 periods ✓
- 0% rate payout: interest earned is $0, not −$0 ✓
Last checked October 26, 2026. Spotted something wrong? The math is done in your browser with the formula shown on this page, so you can check any result by hand.
Questions people ask
How do I calculate an annuity payment?
PMT = PV × i ÷ (1 − (1 + i)⁻ⁿ), where i is the rate per period and n is the number of payments. $100,000 at 5% monthly for 20 years pays $659.96 a month.
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 pays at the start. Because each payment comes one period sooner, an annuity due's payment is smaller for the same lump sum, by a factor of 1 + i.
How much do I need for $1,000 a month?
At 4% for 25 years, about $189,452. At 0% it would be $1,000 × 300 = $300,000, so interest covers the difference.
What is a growing annuity?
One whose payments rise each year, often to keep up with inflation. The first payment is smaller than a level annuity's, but later ones are bigger.
Why is an insurance company's quote different?
A life annuity pays until you die, so the insurer uses life expectancy and includes its costs. This calculator uses a fixed number of years and a fixed rate, with no fees.