Future Value of Annuity Calculator

Future value = payment × [(1 + i)ⁿ − 1] ÷ i × (1 + i if payments are at the beginning of each period) (i = annual rate ÷ payments per year; n = years × payments per year)

Payment

The periodic payment — the amount deposited each period, the same amount every time, which is what makes this an annuity rather than a series of arbitrary deposits

Annual rate

The nominal annual rate, which is divided by the number of payments per year before anything else happens — 7 percent a year becomes 0.5833… percent a month on the default case

Years

How long the payments continue, multiplied by the payments per year to give the number of deposits

i

The rate per period — the annual rate divided by the payments per year, and the rate each individual deposit actually compounds at

n

The number of payments, which is also the number of compounding periods

Use it to answer what a regular savings plan will be worth, and specifically to see the split between what you contributed and what the growth added — that split is the honest way to look at any long-horizon plan, because it tells you how much of the outcome depends on the rate rather than on you. It is also the right tool for the reverse question of what a series of withdrawals will leave behind, with the sign of the payment flipped, and for comparing two plans that differ only in timing: paying into an account on the first of the month rather than the last is worth 1,519.37 over twenty years on the default numbers, which is not nothing and costs nothing. Two things to get right before trusting the answer. The rate is a nominal annual rate that the page divides evenly across the year, so it earns exactly the stated rate over twelve months of monthly compounding but not over twelve months of some other frequency — and it is a constant, so a plan that steps its contributions up over time is not this calculation. And the timing setting is not cosmetic: the difference between an ordinary annuity and an annuity due is one whole period of interest on every payment, which compounds to more than half a percent of the final balance over twenty years.

1. 500 a month for 20 years at 7%, paid at the end of each month

   1. The rate per period: 7% ÷ 12 = 0.5833…% a month
   2. The number of payments: 20 × 12 = 240
   3. Total contributed: 500 × 240 = 120,000
   4. Future value: 500 × [(1.005833…)²⁴⁰ − 1] ÷ 0.005833… = 260,463.33
   5. Earnings: 260,463.33 − 120,000 = 140,463.33

   The earnings exceed the contributions, and that crossover is the whole point of a long-horizon plan: 140,463.33 of the final balance is money the account produced rather than money you paid in. Note also that the first deposit earns interest for 240 periods and the last one for a single period, which is why the future value is not simply the contributions grown at 7 percent for twenty years. Paying the same 500 at the beginning of each month instead — the next example — adds one more period of interest to every one of those 240 payments.

2. The same plan as an annuity due — 261,982.70

   1. Everything is identical except that each 500 goes in at the start of the month rather than the end
   2. Every one of the 240 payments therefore earns one extra month of interest
   3. That is the ordinary-annuity answer multiplied by (1 + 0.005833…) : 260,463.33 × 1.005833… = 261,982.70
   4. Earnings rise to 261,982.70 − 120,000 = 141,982.70

   The 1,519.37 difference is one month of interest on the entire balance, and it is worth having: it costs nothing but the timing of the transfer. The same gap appears in every plan, and it is proportionally larger the higher the rate and the longer the term — which is why the setting is on the page rather than buried in the assumptions.

3. 5,000 a month for 10 years at −5% — the account shrinks

   1. The rate per period: −5% ÷ 12 = −0.4166…% a month
   2. The number of payments: 10 × 12 = 120, so 600,000 contributed
   3. Future value: 5,000 × [(0.995833…)¹²⁰ − 1] ÷ (−0.004166…) = 472,923.09
   4. Earnings: 472,923.09 − 600,000 = −127,076.91

   The formula is the same one and it handles a negative rate without a special case, which is the point of showing it: 600,000 paid in over ten years ends at 472,923.09, so the account is worth 127,076.91 less than the deposits. The order of the payments matters more here than anywhere else — the early deposits lose the most because they have the longest to fall.

The rate is a single constant for the whole term, and that is the assumption most likely to be wrong over a long horizon: a twenty-year plan does not have a twenty-year rate, and feeding this calculator an average rate produces a figure that no actual sequence of returns would have produced, because a bad year early costs more than a bad year late. It is a nominal annual rate divided evenly across the year, so with monthly payments it compounds monthly, and the same annual rate quoted with a different compounding frequency would give a different answer — this page does not convert between them. Payments are equal and evenly spaced, so a plan that increases its contribution with inflation, skips a year, or adds a lump sum at the start is outside it. It ignores tax entirely: contributions to a tax-advantaged account, the tax on the growth, and the difference between pre-tax and after-tax contributions all change what the balance is worth to you and none of them appear. It ignores fees, which compound against you exactly the way the return compounds for you, and it ignores inflation, so the final figure is in the currency of the contributions rather than in today's purchasing power — 260,463.33 in twenty years is not 260,463.33 today. It assumes the account never has a withdrawal, an early-withdrawal penalty or a required minimum distribution taken out of it. Finally, it treats all periods as complete: it cannot handle a first payment that arrives partway through a year or a term that ends between payments, and it does not model the actual calendar, so the interest credited on a real account will differ slightly from this on any given date.

What is the future value of an annuity?

It is what a series of equal payments made at fixed intervals will be worth at the end of the term, with each payment having earned interest for however long it was in the account. On the default case, 500 a month for twenty years at 7 percent comes to 260,463.33, of which 120,000 is the contributions and 140,463.33 is interest. The payments must be equal and evenly spaced — a series of irregular deposits is a different calculation.

How do I calculate the future value of an annuity?

Divide the annual rate by the number of payments per year to get the rate per period, multiply the years by the payments per year to get the number of payments, then use payment × [(1 + i)ⁿ − 1] ÷ i. On the default numbers: i is 7% ÷ 12 = 0.5833…% and n is 240, so 500 × [(1.005833…)²⁴⁰ − 1] ÷ 0.005833… = 260,463.33. If the payments come at the beginning of each period rather than the end, multiply the result by (1 + i) and you have the annuity due.

What is the difference between an ordinary annuity and an annuity due?

When the payment lands inside the period. An ordinary annuity pays at the end, an annuity due at the beginning, and a beginning payment earns one extra period of interest on every single deposit. On the default plan that is the difference between 260,463.33 and 261,982.70 — 1,519.37, or exactly one month of interest on the whole balance. Rent and most loan payments are ordinary annuities; a deposit you make on the first of the month into your own account is an annuity due, and choosing that timing is free money.

Does it matter how often I make the payments?

Yes, twice over, and the two effects can pull in opposite directions in how you read them. The annual rate is divided by the number of payments per year, so paying monthly compounds monthly and earns slightly more on the same annual rate than paying annually does. And the frequency changes how much you deposit in total if you hold the payment size fixed rather than the annual amount. At 1,000 a payment for ten years at 5 percent: annual payments give 12,577.89 on 10,000 contributed, and semiannual payments give 25,544.66 on 20,000 contributed — the second is larger because twice as much money went in, not because the rate behaved differently.

Can the future value be less than what I paid in?

Yes, whenever the rate is negative, and the calculator handles it without a special case. 5,000 a month for ten years at −5 percent means 600,000 of contributions ending at 472,923.09, so the account is worth 127,076.91 less than you put in. The order of the deposits matters in that case: the earliest payments have the longest to fall and lose the most, so the same total deposited over the same term produces a worse result the earlier it goes in.

What rate should I use for the future value of an annuity?

The one you can actually expect to earn, held constant for the whole term — and it is worth being conservative, because the figure is highly sensitive to it and the sensitivity grows with the term. Use a nominal annual rate and let the calculator divide it by the payment frequency; do not pre-convert it yourself. If you are comparing against an inflation-adjusted goal, remember the answer is in the currency of the deposits and not in today's purchasing power, so a nominal rate that looks healthy can be a thin real return.

Why is the interest more than my contributions?

Because of how long each payment stays in. Every deposit earns interest for a different number of periods — the first for the full 240 on the default plan and the last for one — so the account is not simply your contributions grown at 7 percent for twenty years. When the term is long enough and the rate high enough, the total earnings pass the total contributions, and on the default case they do: 140,463.33 of interest against 120,000 paid in. That crossover is a function of time more than of the rate, which is why starting early matters more than contributing more.

• Appendix J to Part 1026 — Annual Percentage Rate Computations: the end-of-period contribution convention used for the ordinary annuity case here — Consumer Financial Protection Bureau regulation, via the Electronic Code of Federal Regulations (United States)
• Annuities — Investor.gov glossary (a series of payments made at fixed intervals, and the contract built on one) — U.S. Securities and Exchange Commission, Investor.gov (United States)
• Compound Interest Calculator — the SEC's own tool for a lump sum, useful as the contrast to a series of payments — U.S. Securities and Exchange Commission, Investor.gov (United States)