Future Value of Annuity: How to Calculate It

This calculator works out the future value of an ordinary annuity—the total amount you’ll have at the end of a series of equal payments, each earning compound interest. You enter the payment amount, the interest rate per period, the number of periods, and (optionally) whether payments are made at the end or the beginning of each period. The result is the future value, shown as a single dollar figure, which is the sum of all payments plus all the interest they earn.

Formula

The future value of an ordinary annuity (payments at the end of each period) is:

FV = PMT × [((1 + r)ⁿ − 1) / r]

Where:

• FV = future value of the annuity (in dollars, or any currency unit)
• PMT = payment amount per period (same currency unit)
• r = interest rate per period, expressed as a decimal (e.g., 5% = 0.05)
• n = number of periods (e.g., months, quarters, years)

If payments are made at the beginning of each period (an annuity due), multiply the result by (1 + r):

FV_due = FV_ordinary × (1 + r)

The calculator uses the same formula, converting the percentage rate to a decimal internally. It also handles the annuity-due case with the timing selector.

Worked Example

Using the default values: payment = $1,000 per period, interest rate = 5% per period, number of periods = 10, payments at the end of each period.

Step 1: Convert the interest rate to a decimal: 5% = 0.05.

Step 2: Calculate (1 + r)ⁿ = (1.05)¹⁰.

1.05¹⁰ = 1.6288946268 (approximately).

Step 3: Subtract 1: 1.6288946268 − 1 = 0.6288946268.

Step 4: Divide by r: 0.6288946268 / 0.05 = 12.577892536.

Step 5: Multiply by PMT: 1,000 × 12.577892536 = $12,577.89.

So the future value is $12,577.89, which matches the calculator’s output. If the payments were made at the beginning of each period, you would multiply by (1.05) to get $13,206.79.

When to Use This Calculator

You would use a future value of annuity calculation whenever you want to know how much a series of regular, fixed payments will grow to over time, given a constant interest rate. Common situations include:

• Estimating the balance of a retirement account after making monthly contributions for 20 years.
• Calculating the future value of a sinking fund—a reserve where you deposit a fixed amount each period to meet a future expense.
• Comparing savings plans that involve regular deposits versus a lump sum.
• Understanding how much you’ll accumulate if you invest a fixed amount each month at a given return.

The calculator is also useful for educational purposes—to see how compounding amplifies regular savings. For instance, saving $200 per month at 6% annual interest compounded monthly for 30 years yields about $201,907, but the total contributions are only $72,000. The rest is interest.

Note that this formula assumes the interest rate stays constant and payments are exactly equal. Real-world investments often have variable returns, and you may adjust contributions over time, so treat the result as an estimate, not a guarantee.

How to Read the Result

The future value figure represents the total amount you will have after the last payment is made and the final period’s interest is credited. It includes both your contributions and the accumulated interest.

If you are comparing different plans, look at the future value in today’s dollars—but remember that inflation will reduce the purchasing power of that future amount. For example, $12,577.89 ten years from now will not buy as much as $12,577.89 today if inflation averages 3% per year. To account for inflation, you could use a real rate of return (nominal rate minus inflation rate) in the calculation.

The result is also sensitive to the timing of payments. With an annuity due (payments at the beginning), you get one extra period of interest on each payment, which increases the future value. The difference grows with higher rates and longer terms.

Common Mistakes and Pitfalls

One frequent error is mixing up the interest rate period. If you make monthly payments, the interest rate must be the monthly rate, not the annual rate. For example, an annual rate of 6% compounded monthly means r = 0.06/12 = 0.005 per month. Using 6% directly in the formula would drastically overstate the result.

Another common mistake is forgetting to convert the percentage to a decimal. Entering 5 instead of 0.05 in the formula will produce a nonsensical result. The calculator handles this conversion for you, but if you use the formula manually, always divide the percentage by 100.

Rounding too early can also skew results. In the worked example, we carried many decimal places. If you round (1.05)¹⁰ to 1.63, you get a future value of $12,600—a difference of $22.09. For long terms, rounding errors can be substantial.

Finally, be clear about whether payments are at the beginning or end of the period. Most textbook problems assume ordinary annuities (end of period), but many real-world payments (like rent or insurance premiums) are due at the beginning. Using the wrong timing changes the result by a factor of (1 + r).

Limits of the Formula

The future value of an annuity formula assumes a constant interest rate over the entire term. In practice, interest rates fluctuate, especially over long periods. If you are planning for retirement, a fixed-rate annuity (like a CD ladder) might match the assumption, but stock market investments will not.

The formula also assumes payments are made exactly on time and are equal in amount. If you skip a payment or change the amount, the formula no longer applies directly. You would need to calculate each payment’s future value separately and sum them.

Another limitation is that the formula does not account for taxes or fees. Investment returns are often taxed, and some accounts charge maintenance fees, which reduce the actual future value. For a more accurate estimate, you would need to adjust the interest rate to an after-tax, after-fee rate.

Finally, the formula gives a nominal future value. To compare with today’s purchasing power, you must adjust for inflation. Using a real rate of return (approximately nominal rate minus inflation) can give a more meaningful result for long-term goals.

Annuity Due vs. Ordinary Annuity

The distinction between an ordinary annuity and an annuity due is crucial. An ordinary annuity has payments at the end of each period—think of a loan repayment or a savings deposit made at month’s end. An annuity due has payments at the beginning of each period—like rent, which is paid on the first of the month.

The future value of an annuity due is always higher than an ordinary annuity with the same payment, rate, and term, because each payment earns interest for one extra period. The factor is simply (1 + r). For example, with the default values, the ordinary annuity gives $12,577.89, while the annuity due gives $13,206.79—a difference of $628.90.

When using the calculator, select “Beginning” if your payments are made at the start of each period. Many financial calculators have a “begin” mode for this purpose. If you are unsure which type you have, check the terms of your contract or the timing of your deposits.

Frequently Asked Questions

What is the difference between future value and present value of an annuity?
Future value tells you how much a series of payments will be worth at a future date, after earning interest. Present value tells you how much that series of payments is worth today, discounted at a given rate. Future value uses compounding; present value uses discounting.

How do I calculate the future value if payments are monthly but the interest rate is annual?
Divide the annual interest rate by 12 to get the monthly rate, and use the number of months as the number of periods. For example, 6% annual becomes 0.5% per month (0.005 as a decimal). Then apply the formula with n = number of months.

Can this calculator handle payments at the beginning of the period?
Yes. Use the “Payment timing” dropdown to select “Beginning”. The calculator multiplies the ordinary annuity result by (1 + r) to give the annuity due future value.

What if I want to know the future value of a lump sum, not a series of payments?
That is a different calculation: FV = PV × (1 + r)ⁿ, where PV is the present lump sum. This calculator is specifically for annuities—regular payments. For a lump sum, you would use a compound interest calculator.

Is the future value guaranteed?
No. The formula assumes a constant interest rate and timely payments. Real-world investments can go up or down, and rates change. The result is an estimate, not a promise.

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in pmt | Payment per period | $ | 1000 | 0
in rate | Interest rate per period | % | 5 | 0
in n | Number of periods | periods | 10 | 0
sel when | Payment timing | End=0, Beginning=1
out fv | Future value | $ | pmt * ((pow(1 + rate/100, n) - 1) / (rate/100)) * (1 + (rate/100)*when) | 2