What is an annuity?
An annuity, in the plain mathematical sense used on this page, is a series of equal payments made at equal intervals — the same amount, on a regular schedule, for a set number of periods. Saving a fixed sum every month toward a goal, paying a fixed installment, and receiving a fixed pension-style income are all annuity patterns. This calculator answers the two questions people ask most often about such a pattern. First, if you keep making a known payment, what will those payments grow to by the end — their future value? Second, working backwards, if you need a particular amount by a particular date, how large must each payment be? Choose the direction at the top of the calculator; the fields and the headline answer follow your choice.
The word annuity is also used for insurance products that pay an income, often for life. Those contracts add fees, guarantees and insurer-specific terms on top of the core mathematics. This page covers the core mathematics only — the growth of a level payment series at a fixed rate — which is also the engine inside savings plans, sinking funds and the regular-investment math in the Investment Calculator and the SIP Calculator.
The annuity formula
Annuity due = ordinary annuity × (1 + i)
Where P is the payment per period, i is the interest rate per period (the yearly rate divided by the payments per year), and n is the total number of payments. If the rate is zero, the future value is simply P × n. To find the payment needed for a target, the same formula is rearranged: payment = target × i ÷ ((1 + i)n − 1), with an extra division by (1 + i) for an annuity due.
Ordinary annuity versus annuity due
The only difference between the two types is when each payment lands. In an ordinary annuity the payment is made at the end of each period — the pattern of loan installments and of most end-of-month saving. In an annuity due the payment is made at the start of each period — the pattern of rent, insurance premiums and many lease payments. Because every due payment sits in the account for one extra period, it earns one extra period of interest, and the whole future value is exactly the ordinary-annuity value multiplied by (1 + i). The gap looks small per payment, but across hundreds of monthly payments it is real money, and it is why two savers paying identical amounts can end with different balances purely because one pays on the first of the month and the other on the last.
Worked example
Pay $1,000 once a year for 10 years at 5%, as an ordinary annuity. The periodic rate is 5% and there are 10 payments, so the future value is $1,000 × ((1.05)10 − 1) ÷ 0.05 = $12,577.89. You paid in $10,000 of your own money; the other $2,577.89 is interest — interest earned not on one lump sum, but on a growing stack of payments, the later ones contributing almost nothing and the earliest contributing the most. Switch the same plan to an annuity due and each payment gains one extra year of growth: $12,577.89 × 1.05 = $13,206.79. Run the calculator backwards with a $20,000 target instead, and it will tell you the yearly payment that target requires at the same rate and term.
What changes the result most
Three levers drive an annuity, and they are not equal. The number of payments matters most, because early payments compound for the longest time — extending a plan usually beats raising the payment by the same proportion. The rate matters next, and its effect grows with the term. The payment size scales the result in direct proportion: double every payment and you exactly double the future value, interest included. Frequency interacts with all three — monthly payments start compounding sooner than yearly ones — which is why this calculator asks how many payments you make per year rather than assuming a schedule for you.
Worked example
Paying $1,000 a year for 10 years at 5% as an ordinary annuity grows to $12,577.89 — $10,000 of payments plus $2,577.89 of interest. As an annuity due, with each payment made at the start of the year, the same plan grows to $13,206.79.
How to use this calculator
- Choose the direction: grow a known payment to its future value, or find the payment needed to reach a target value.
- Enter the payment per period (or, in payment mode, the target future value you need to reach).
- Enter the yearly interest rate, the number of years, and how many payments you make per year.
- Choose ordinary annuity if payments land at the end of each period, or annuity due if they land at the start.
- Read the future value, then compare what you paid in with the interest earned — and try the other timing to see the start-of-period advantage.
Sinking funds and saving for a known bill
The payment mode of this calculator is exactly the sinking fund calculation businesses and homeowners use for a known future cost: a roof replacement in eight years, a tax bill, a machine that must be replaced at a set date. Instead of facing the whole sum at once, you set aside the level payment the formula gives you, and interest quietly covers part of the target — the longer the runway, the larger the share interest covers and the smaller your own payments need to be. The same backwards logic helps households: name the goal and the date first, then let the formula, not a guess, set the monthly amount.
Annuities, lump sums and honest limits
An annuity spreads contributions over time, so it will always finish behind an equal total invested as a lump sum on day one — the lump sum compounds in full from the start. What the annuity gives you instead is feasibility: most goals are funded from monthly income, not from a windfall. Two limits apply to every figure on this page. The rate is held fixed for the whole term, while real savings and investment returns move around, and no taxes, fees or inflation are deducted. Treat the result as the clean mathematical answer at the rate you entered, then test a lower rate to see how much of your plan depends on optimistic returns.