Future Value Of Annuity Calculator

What this calculator does

Most people do not build savings by putting one large sum away. They build it the slow way, by paying in the same amount again and again. This calculator measures that. Tell it what you put in each period, what rate it earns, and how many periods you keep it up, and it tells you what the whole stream of payments adds up to at the end.

A stream of equal payments at regular intervals is called an annuity, and this tool handles the ordinary kind, where each payment lands at the end of its period. That timing detail is not fussiness. It changes the answer, and it is why a separate annuity due calculator exists for payments made at the start. Here, the assumption is end of period throughout.

Every payment grows for a different length of time

The formula looks forbidding at first glance:

Future value = Payment × [ (1 + rate)^periods − 1 ] ÷ rate

But it is only a shortcut for something simple, and seeing what it stands in for makes the whole tool click. Your payments do not all get the same amount of time to grow. The first one you make has the longest run, and each later one has a little less, right down to the final payment, which lands at the end of the last period and earns nothing at all. It arrives just in time to be counted and not a moment sooner.

So the true calculation is a stack of separate compoundings added together. With 1,000 a period at 6 percent for 10 periods, the first payment compounds for 9 periods and grows to 1,689.48. The second grows for 8 periods, reaching 1,593.85. The ninth grows for a single period, reaching 1,060. The tenth just sits there at 1,000. Add all ten and you get 13,180.79, which is exactly what the formula returns. The formula is not doing anything mysterious. It is saving you from adding up ten different numbers, or three hundred of them.

How to use it

1. Amount of equal payments. What you pay in each period. It has to be the same each time for this calculation to hold.
2. Interest rate per period. The rate earned in one period, not per year, unless your periods are years.
3. Number of periods. How many payments you will make.

Press Calculate for the future value, or Reset to clear the fields. As with any periodic calculation, keep the rate and the periods on the same clock: monthly payments need a monthly rate, which is the annual rate divided by 12, and a period count in months.

A worked example you can check

Say you pay in 1,000 at the end of every period, the money earns 6 percent a period, and you keep it up for 10 periods.

• Total you paid in: 1,000 × 10 = 10,000
• Future value of the annuity: 13,180.79
• Interest earned: 13,180.79 − 10,000 = 3,180.79

So ten payments of 1,000 became 13,180.79. You supplied 10,000 of that and the interest supplied the other 3,180.79, which is about 24 percent of the final pot. That percentage is the number worth watching, because it does not stay at 24.

How much of the pot is yours, and how much the interest made

Every savings total has two parents: the money you put in, and the growth that money earned. Splitting the final figure into those two parts is the single most revealing thing you can do with this calculator, because the balance between them shifts dramatically with time, and the shift is what makes long-term saving worth the patience.

In the ten-period example, your contributions were the senior partner: 10,000 of yours against 3,180.79 of interest, so growth accounted for roughly a quarter of the result. Now stretch the same habit out. Pay in 500 a month at 0.5 percent a month, which is 6 percent a year, and keep going for 240 months, which is twenty years. You will have paid in 120,000. The pot comes to 231,020.45, meaning interest contributed 111,020.45, or about 48 percent of the total.

Read those two together and you can watch the partnership change hands. Over ten periods, growth was a junior contributor. Over twenty years, it very nearly matched everything the saver put in, and had the habit continued it would have overtaken them. The reason is the staggered compounding from earlier: as the years pass, the early payments have been growing for a very long time, and they start throwing off more each period than the new payments you are adding. That is the moment saving stops feeling like pushing and starts feeling like carrying. Working out your own split, total paid in versus what the calculator returns, tells you how close you are to it.

Questions people ask

Does it matter if I pay at the start of the period instead of the end?

Yes. This calculator assumes payments at the end of each period. Paying at the start gives every payment an extra period of growth and produces a larger total, which is what an annuity due calculator works out.

Why does my final payment earn no interest?

Because it arrives at the end of the last period, so there is no time left for it to grow. It is counted in the total at face value.

What rate do I enter for monthly saving?

The monthly rate, which is the annual rate divided by 12, with the number of periods counted in months. Mixing an annual rate with monthly periods gives a badly wrong answer.

What if my payments are not all the same?

Then this formula does not strictly apply, since it assumes equal payments. It still gives a reasonable estimate if you use a typical payment, but the more your contributions vary, the rougher that estimate gets.

References

The definition of an annuity as a stream of fixed periodic payments, and of an ordinary annuity as one in which the first cash flow occurs at the end of the first period, follows OpenStax's finance text, which also derives the future value of such a stream. The idea of projecting what regular contributions accumulate to over time is the basis of the savings goal tool published by the U.S. Securities and Exchange Commission.

1. OpenStax, Principles of Finance, 8.2 Annuities. https://openstax.org/books/principles-finance/pages/8-2-annuities
2. U.S. Securities and Exchange Commission, Investor.gov, Savings Goal Calculator. https://www.investor.gov/financial-tools-calculators/calculators/savings-goal-calculator