How to calculate future value of an annuity, step by step
Future value of an annuity is one number that answers one question: what is a series of equal monthly payments worth at the end of the term, with compound interest? The calculation needs three numbers: your monthly payment, your annual rate and your term in years. On $200 a month at 6% for 20 years, the future value is $92,408.18, the total contributions are $48,000.00 and the interest earned is $44,408.18. So the future value is the monthly payment times the annuity factor, and the annuity factor is one plus the monthly rate to the power of the number of payments, minus one, divided by the monthly rate.
The definition is the value of the payments, grown: each month you put money in, and every payment already in earns interest from then on. The monthly rate is the annual rate divided by 12 — 6% a year is 0.5% a month — and the number of payments is the term in years times 12 — 20 years is 240 payments. If you divide the annual rate by 12 and forget the power, the future value comes out wrong, and everything that follows is built on a number that is not honest.
The worked example, line by line. Step 1 — the monthly rate: 6% ÷ 12 = 0.5% a month. Step 2 — the number of payments: 20 × 12 = 240 payments. Step 3 — the annuity factor: ((1.005)240 − 1) ÷ 0.005 = 462.040895161. Step 4 — the future value: $200 × 462.040895161 = $92,408.18. Step 5 — the total contributions: $200 × 240 = $48,000.00. Step 6 — the interest earned: $92,408.18 − $48,000.00 = $44,408.18. Work it yourself in the future value of annuity calculator.
A note on the rounding: the figures are displayed to two decimals, half-up. The future value is $92,408.18 displayed and $92,408.179032 unrounded, and the interest earned is $44,408.18 displayed and $44,408.179032 unrounded — with fractional inputs it can land a hair either side of a round number, and the calculator prints the unrounded figure so the rounding does not mislead you. The annuity factor is printed to nine decimals, 462.040895161, because at nine decimals the usual rounding guard would itself flip the last digit.
What the answer means
A future value of $92,408.18 means $200 a month at 6% for 20 years ends with $92,408.18 — $48,000.00 of it is the money you put in, 240 payments of $200, and $44,408.18 of it is interest the money earned. That $92,408.18 has to cover everything the annuity grows to: the contributions and the interest together, and the interest is nearly as big as the contributions — almost half the final value is money you never paid in. A $200 payment that grows to $92,408.18 is the ordinary annuity at work: each payment earns interest from the month after it is made, and the interest earns interest of its own. Work it out in the future value of annuity calculator.
Why the last years do most of the work
The last years do most of the work because the interest is charged on the balance already saved, and the balance is biggest at the end. In the second month the $200 already saved earns just $1.00 of interest — the first payment, made at the end of month one, has had only one month to grow. By the last years the balance is tens of thousands of dollars, so the same 0.5% a month is hundreds of dollars of interest a month, and the interest alone is bigger than the payment. The payment never changes, but the interest inside the growth does: it starts at almost nothing and ends up doing nearly half the work. That is why starting early beats saving more later — an extra year at the end, when the balance is largest, is worth far more than an extra year at the start, when the balance is small. Work it out in the future value of annuity calculator.
Future value of an annuity vs compound interest
Future value of an annuity and compound interest answer different questions, and mixing them up is the most common mistake. An annuity grows a series of payments — $200 a month here, and the value is $92,408.18 after 20 years. Compound interest grows money already saved — a lump sum left alone, with no new payments. One is a habit, the other is a balance. The same $200 a month at 6% is an annuity, and the same $200 sitting in an account for 20 years is compound interest on a single deposit — the annuity ends with far more, because 240 payments went in, not one. Use the annuity when you save a little every month, and use compound interest when you want to know what a lump sum becomes. Work it out in the future value of annuity calculator, and check the compound interest calculator before you decide what the answer means.
Annuity vs lump sum
The annuity formula and the lump-sum formula answer different questions too. The annuity formula grows payments — $200 a month here, 240 payments, $92,408.18 at the end. The lump-sum formula grows one deposit — the same $200 paid once would be worth only a few hundred dollars after 20 years, because it is one payment, not 240. One is a stream, the other is a single drop. A $200 monthly payment that grows to $92,408.18 is the same money seen two ways — the annuity formula tells you what the stream is worth, and the lump-sum formula tells you what one payment is worth. Use the annuity when the money goes in every month, and use the lump sum when it goes in once. Work it out in the future value of annuity calculator, and check the future value calculator and the annuity calculator before you decide what the answer means.
Common mistakes
The first mistake is dividing the annual rate by 12 and forgetting the power — only the full formula counts toward the future value, so use the monthly rate and the number of payments together, not the rate alone. The second is confusing the future value with the contributions — a $92,408.18 future value is not $92,408.18 of savings, and $48,000.00 of it is the money you put in. The third is forgetting that the term is in months — a 20-year annuity is 240 payments, not 20, and the formula needs the months. The fourth is assuming the payments earn interest from day one — a payment made at the end of the month earns nothing in that month, and the first payment earns its first dollar of interest in the second month. Work it out in the future value of annuity calculator, and check the annuity calculator and the compound interest calculator before you decide what the answer means.