Annuity Calculator – Grow a Balance or Draw a Steady Income
An annuity is simply a series of regular, equal (or steadily rising) payments. You either pay money in to build a balance, as with a savings plan, or draw money out of a balance as income, as with a pension pot or an insurer's payout annuity. This annuity calculator links the five quantities involved, starting amount, regular payment, ending balance, time and rate of return, and solves for whichever one you leave blank. It works at any payment frequency, handles yearly increases, deferred income and perpetuities, and shows a full payment schedule.
Future value of an annuity, worked through
With a per-period rate i and N payments, the future value of a starting amount S plus contributions PMT is FV = S(1+i)^N + PMT × ((1+i)^N − 1) / i. Saving 500 a month for 20 years on top of 10,000 at 7% compounded monthly gives i = 0.07/12 = 0.5833% and (1+i)^240 = 4.038739. The starting amount grows to 40,387.39 and the contributions to 260,463.33, for a final balance of 300,850.72. You put in 130,000, so 170,850.72 (56.8%) is interest. From year 9 onward the balance earns more interest each year than you contribute.
The payout formula, worked through
Drawing income runs the same maths in reverse. To use up a balance B over N payments, PMT = B / a_N, where a_N = (1 − (1+i)^−N) / i is the annuity factor. For 300,000 over 25 years at 5% compounded monthly, a_N = 171.0600, so the income is 1,753.77 a month. Total income is 526,131.04: your own 300,000 comes back, plus 226,131.04 of interest.
Ordinary annuity vs annuity due
In an ordinary annuity payments happen at the end of each period; in an annuity due they happen at the start. Contributions made earlier earn one more period of growth, so the future value is multiplied by (1 + i). Income drawn earlier leaves less behind to earn, so the same 300,000 pays 1,746.49 instead of 1,753.77.
Payout rate is not your return
Insurers often quote a payout rate: first-year income divided by the premium. Because part of every payment is your own money coming back, the payout rate overstates the return. 100,000 that buys 600 a month for 20 years has a 7.20% payout rate but an implied return of only 3.886%. Use Implied return to check any quote.
Perpetuities, growing income and deferral
A perpetuity pays forever, so it can only pay the interest: PMT = B × i. At 4% a year, 500,000 supports 1,636.87 a month. If the income must rise by g each year, the balance must grow just as fast, which gives the Gordon formula B = PMT / (r − g): 500,000 at 4% with 2% yearly rises pays 10,000 in year one. Deferring the start lets the balance compound first: 100,000 left for 10 years at 5% becomes 164,700.95, which pays 1,086.95 a month for 20 years instead of 659.96 if it started today.
Compounding frequency vs payment frequency
The rate you enter is compounded on its own schedule, which need not match the payments. The calculator converts it to a per-payment rate with i = (1 + R/m_c)^(m_c/m_p) − 1, the standard financial-calculator handling when P/Y ≠ C/Y. 7% compounded annually becomes 0.5654% a month, not 0.5833%.
FV, PMT, PV, NPER and RATE use signs for direction: money you pay in is negative and money you receive is positive. The calculator shows the matching formula with your numbers so you can reproduce each level-payment result.What this tool does not model
It does not model lifetime (mortality-based) annuities, variable or indexed returns, fees and surrender charges, or taxes. Results are in nominal money; for income that keeps pace with inflation, set the yearly increase to the inflation rate. For loans, use a loan EMI calculator instead.