What the Annuity Calculator does
This annuity calculator solves any one of the five annuity values - payment, present value, future value, interest rate or number of payments - from the other four. It works both ways round: a payout annuity that draws a regular income from a lump sum, and a savings annuity that builds a balance from regular deposits, with payments at the end of each period or at the start.
Alongside the answer it prints the full schedule, period by period, with the interest earned and the balance left, so you can see exactly when a pot runs down or a target is reached. The arithmetic matches the spreadsheet PMT, PV, FV, NPER and RATE functions.
How to use it
- Choose Payout if you are drawing an income from a sum of money, or Savings if you are paying in to build one.
- Choose what to solve for. That field disappears; fill in the others. Enter all amounts as positive numbers - the direction choice takes care of signs.
- Set how many payments a year and whether they fall at the start of each period.
- Read the answer, the interest earned and the schedule. For a payout, the balance line shows when the money runs out.
Reading the results
For a payout, the payment is the level amount the pot can support for the number of payments while earning the rate, leaving the ending balance you set (0 means spend it all).
Interest earned is the part of the money that came from growth rather than from the starting amount or deposits. In a long payout, interest can pay for a large share of the income.
The rate is a nominal annual rate divided evenly across the payments. The effective annual rate beside it shows what that means once compounding is included.
Worked example: a 25-year income from 250,000
A retiree has 250,000 and wants a monthly income for 25 years (300 payments), assuming 5% a year, leaving nothing at the end. The monthly rate is 0.05 / 12 = 0.416667% and 1.00416667^300 = 3.48150.
The payment is 250,000 x 0.00416667 / (1 - 1 / 3.48150) = 1,041.67 / 0.712767 = 1,461.48 a month. Over 300 payments that is 438,443 drawn, of which 188,443 is interest earned on the money still invested.
Turn it round: with 180,000, drawing 1,500 at the start of each month at 4%, the money lasts about 152.8 payments - 12.7 years - with a smaller final payment. And to save 50,000 in 18 years at 6%, a saver needs 129.08 a month, the same answer as the spreadsheet PMT example.
Formulas and scoring rules
- Rate per payment
i = annual rate / payments per year- The annuity identity
PV x (1 + i)^n + PMT x (1 + i x type) x ((1 + i)^n - 1) / i + FV = 0Spreadsheet sign convention: money you pay is negative, money you receive positive. type = 1 for payments at the start.- Payout payment
PMT = (PV x (1 + i)^n - FV) x i / (((1 + i)^n - 1) x (1 + i x type))- Number of payments
n = ln((PMT x (1 + i x type) / i - FV) / (PMT x (1 + i x type) / i - PV)) / ln(1 + i)No answer when the payment does not exceed the interest.- Rate
Solved numerically (Newton, then bisection); never guessed- Effective annual rate
(1 + i)^(payments per year) - 1
Annuity calculations versus annuity products
In finance maths, an annuity is any series of equal payments at equal intervals: a loan, a savings plan and a pension income are all annuities. An insurer's lifetime annuity is a product that pays for as long as you live, priced using mortality tables, insurer costs and guarantees that this calculator does not know about.
So use this page to understand what a sum of money can support at a given rate for a fixed term, or to check a quote's implied rate. Do not treat its answer as a quote for a lifetime annuity.
Limitations: what the result does not prove
- It assumes a constant interest rate and equal payments. Rising payments need the present value calculator's growth option.
- A fixed term is not a lifetime. The money runs out at the end of the term whatever your age.
- Taxes, charges and inflation are ignored unless you build them into the rate.
- Solving for the rate may have no answer if the amounts are inconsistent; the page says so instead of guessing.
Privacy: where your data goes
Everything you paste, type or drop is processed in this browser tab. It is not uploaded, logged, stored or sent to analytics. Session recording and tag-manager scripts are switched off on this page.
Standards and sources
- Microsoft Support - PMT function
- Microsoft Support - NPER function
- Microsoft Support - RATE function
Frequently asked questions
How much income can a lump sum provide?
Choose Payout, solve for Payment, and enter the lump sum, the rate you expect and the number of payments. 250,000 at 5% over 25 years supports 1,461.48 a month when the balance is allowed to reach zero at the end.
When should I tick the annuity due (payments at the start) option?
Tick it when each payment is made at the start of its period. Payments of an ordinary annuity are made at the end of each period; payments of an annuity due at the start. Rent and insurance premiums are usually due; loan repayments and most pension incomes are ordinary. Ticking the box changes every formula by a factor of (1 + i).
How long will my savings last if I withdraw a fixed amount?
Choose Payout and solve for Number of payments. With 180,000 at 4% and 1,500 taken at the start of each month, the money lasts about 153 months. If the withdrawal is less than the monthly interest, the pot never runs out and the page says so.
How do I find the interest rate of an annuity quote?
Choose Solve for Interest rate and enter the price (present value), the payment and the number of payments. The result is the rate that makes them consistent, which you can compare with deposit or bond rates for the same term.
Why must amounts be entered as positive numbers?
To avoid sign mistakes. Spreadsheets need money out to be negative and money in positive; here the Payout or Savings choice sets those signs for you, and the schedule shows the direction of every payment.
Can I leave some money at the end of a payout?
Yes. Enter the balance you want left as the future value. The payment falls so that the pot still holds that amount after the last payment - useful for keeping a reserve or leaving a sum to someone.
Last reviewed by the A2Z.Tools team against the sources listed above.
