The future value of an annuity is what a series of equal payments is worth at the end, interest included. Put $500 a month into an account earning 6% for 20 years, and you'll have $231,020 from $120,000 paid in.
The calculator assumes each payment lands at the end of its month and interest compounds monthly. In textbook terms, that's an ordinary annuity. Paying at the start of each month instead makes it an annuity due.
Ordinary annuity or annuity due?
P is the payment, i the rate per period and n the number of payments. Here a period is one month. So i is the annual rate divided by 12, and 20 years means 240 payments.
Paid at the start, every payment earns one extra period of interest. So an annuity due is always worth more, by exactly one period's interest on the final balance.
Paying earlier adds a month's interest, not a year's
How much that's worth depends on the length of the period. In the OpenStax finance textbook, $3,000 a year at 4% for five years grows to $16,248.98. Paid at the start of each year, it reaches about $16,898.93, which is 4% more.
With monthly payments the step is much smaller. At 6% a year, one month's interest is 0.5%. On the $231,020 above, paying at the start of each month adds just $1,155 (231,020 × 0.005). You'd only gain a full 6% if you paid once a year.
Your first payments do most of the work
Early payments compound for longer, so they end up worth far more than late ones. Here's the same $500 a month at 6%, split in two:
| $500 a month at 6% | Years of payments | Paid in | Value at the end of year 20 |
|---|---|---|---|
| All 240 payments | 20 yr | $120,000 | $231,020 |
| Only the last 120 payments | 10 yr | $60,000 | $81,940 |
The last 120 payments are worth $81,940 when year 20 ends. So the first 120 are worth $231,020 − $81,940 = $149,080, or 64.5% of the total. Both halves cost you the same $60,000.
A higher rate pays off more than in proportion
Interest compounds on earlier interest, so the result bends upward as the rate rises. Here's $250 a month for 30 years, $90,000 in all:
| Annual rate, $250 a month for 30 years | Future value | Interest earned | Growth on the $90,000 paid in |
|---|---|---|---|
| 2% | $123,181 | $33,181 | 36.9% |
| 4% | $173,512 | $83,512 | 92.8% |
| 6% | $251,129 | $161,129 | 179.0% |
| 8% | $372,590 | $282,590 | 314.0% |
Going from 4% to 8% doubles the rate but more than triples the interest, from $83,512 to $282,590. Small differences in the rate you assume move the answer a lot over long periods.
Which rate should you enter?
Enter a yearly interest rate that leaves compounding out. That's how U.S. banking rules define an interest rate. The calculator divides it by 12 and compounds monthly. So 6% works out to (1 + 0.06 ÷ 12)^12 − 1 = 6.17% a year.
An annual percentage yield (APY) already includes compounding. If your 6% is an APY, convert it first: 12 × (1.06^(1/12) − 1) = 5.84%.
| A 6% APY, $250 a month for 30 years | Rate entered | Future value |
|---|---|---|
| APY typed in as the rate | 6% | $251,129 |
| Converted to a monthly-compounded rate | 5.84% | $243,579 |
Typing the APY in as the rate overstates this 30-year result by $7,550. The gap grows with the rate and the number of years.
When the formula doesn't fit
It needs equal payments at equal intervals and one fixed rate. If your payments rise each year, the growing annuity calculator values that stream as a lump sum now. The present value of annuity calculator does the same for level payments.
Paying once a year, at the end of each year? Entering a twelfth of that amount each month gives the money extra months of interest. The result runs high.
An annuity from an insurer is a different product
In finance math, "annuity" simply means a stream of equal payments. FINRA uses the word for a contract with an insurance company, which promises periodic payments now or later. Such contracts carry fees, including surrender charges and mortality and expense risk charges. This calculator models none of them.
FINRA notes that the money grows tax-deferred. Withdraw before age 59½, and you may face a 10% tax penalty. To project a contract with a starting premium, use the deferred annuity calculator.