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Future Value of Ordinary Annuity Calculator

An ordinary annuity pays at the end of each period. Enter your payment, rate, term and frequency to see what those end-of-period payments grow into over time.

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The Concept

What is the future value of an ordinary annuity?

An ordinary annuity is a series of equal payments made at the end of each period — the end of every month, quarter or year. Its future value is what that whole stream of payments grows into once each one has earned compound interest through to the end of the term. The earliest payments compound the longest and contribute the most, which is why the final total dwarfs the sum of the payments themselves.

End-of-period timing is the standard convention, which is exactly why it is called “ordinary.” If your payments instead arrive at the start of each period, that is an annuity due and grows slightly more — you can switch to it on the general future value of annuity calculator. To layer these payments on top of an opening lump sum, use the future value calculator.

The Timing

Why “ordinary” means end of period

The only thing that separates an ordinary annuity from an annuity due is when each payment is made:

  • Ordinary annuity — payment at the end of the period. Each payment starts compounding one period after it is counted.
  • Annuity due — payment at the beginning of the period, so every payment gets one extra period of growth.

Because ordinary payments arrive later within each period, an ordinary annuity always ends up a little smaller than the equivalent annuity due. Over 20 years, $500 a month reaches about $260,463 as an ordinary annuity versus about $261,983 as an annuity due — a difference of roughly $1,500 that comes purely from timing.

How To

How to use this calculator

Four inputs define the result, all assuming end-of-period payments:

  • Payment amount — the fixed sum you contribute at the end of each period.
  • Annual interest rate — the yearly rate of return you expect.
  • Number of years — how long you keep contributing.
  • Payment frequency — monthly, quarterly or annually. Interest compounds at the same frequency.

The result splits the future value into what you paid in and the interest earned on top, and the year-by-year breakdown shows the balance building period after period.

The Formula

The ordinary annuity formula

The future value of an ordinary annuity is:

FV = PMT × [ ((1 + i)n − 1) ÷ i ]

where PMT is the payment per period, i is the periodic interest rate (the annual rate divided by the number of periods per year), and n is the total number of payments. The term in brackets is the ordinary annuity factor — it sums up the growth of every individual payment into one multiplier, with each payment compounding for one period less than the payment before it. An annuity due simply multiplies this result by an extra (1 + i). The single-sum version this builds on is covered in the future value formula guide.

Example

Example: $500 at the end of each month

Here is how $500 paid at the end of every month grows as an ordinary annuity at 7 percent, compounded monthly, over different terms. The interest portion overtakes the payments as the term lengthens.

TermFuture valuePaid inInterest earned
10 years$86,542$60,000$26,542
20 years$260,463$120,000$140,463
30 years$609,985$180,000$429,985

Over 30 years the $180,000 you pay in becomes about $609,985 — more than two-thirds of the final balance is interest, all from letting each end-of-period payment compound for the years that follow.

Real World

Where ordinary annuities show up

End-of-period payments are everywhere in personal finance, which is why the ordinary annuity is the default case:

  • Bond interest. Coupon payments are typically paid at the end of each period, making a bond's income stream a classic ordinary annuity.
  • Regular investing. Many people contribute to an investment or retirement account at month-end, after being paid.
  • Loan and mortgage payments. Amortized loans are built on end-of-period payment math, the same structure viewed from the borrower's side.

Whenever the money moves at the close of the period rather than the start, the ordinary annuity is the right model — and this calculator gives you the future value directly.

Assumptions

Assumptions behind the numbers

  • End-of-period payments. Every payment is made at the close of the period — the defining feature of an ordinary annuity.
  • Equal, on-time payments. Each payment is the same size and made on schedule for the full term.
  • A constant rate. The same rate applies every period; real returns vary, so treat the result as an estimate.
  • Payments only. There is no opening lump sum — for that, use the future value calculator.
  • Nominal figures. Results are not adjusted for inflation or tax.
FAQ

Frequently Asked Questions

It is what a series of equal payments made at the end of each period grows into after earning compound interest. Contributing $500 at the end of every month for 20 years at 7 percent builds to about $260,463 — $120,000 of it your own payments and the rest interest. The calculator works it out from your payment, rate, term and frequency.
The word ordinary refers to timing: each payment is made at the end of the period rather than the beginning. This is the standard assumption for most recurring payments, from bond coupons to loan-style contributions. When payments instead come at the start of each period, it is called an annuity due.
FV = PMT × [((1 + i) to the power of n, minus 1) ÷ i], where PMT is the payment, i is the periodic interest rate (the annual rate divided by periods per year), and n is the total number of payments. The bracketed part is the annuity factor, which rolls every payment's individual growth into a single multiplier.
At 7 percent compounded monthly, $500 paid at the end of each month grows to about $86,542 in 10 years, $260,463 in 20 years, and $609,985 in 30 years. Because the payments arrive at period-end, each one compounds for one period less than it would in an annuity due.
Only the timing. An ordinary annuity pays at the end of each period; an annuity due pays at the beginning, so every payment compounds one extra period and the total is a little higher. The same $500 a month over 20 years reaches about $260,463 as an ordinary annuity versus about $261,983 as an annuity due.
Use it whenever payments land at the end of the period, which covers most regular saving and investment plans as well as things like bond interest. If your payments are made at the start of each period instead, switch to the annuity-due option on the future value of annuity calculator.
Learn

The concepts behind the numbers — read the full library in the Learn hub.

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The engine that makes each end-of-period payment grow, explained with examples.

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The future value of an annuity due formula is FV = C × [((1+r)^n − 1)/r] × (1+r).

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Disclaimer

Important disclaimer

This page is provided for informational and educational purposes only. It does not constitute financial, investment, tax, legal, or accounting advice, and should not be treated as a substitute for advice from a licensed professional.

Any figures, examples, or calculator results shown are estimates based on stated assumptions — not guarantees. Actual returns, rates, and outcomes will vary. Read our full disclaimer before acting on any results.