Future Value of Annuity Calculator
The future value of an annuity asks how much a stream of equal payments will be worth at the end of a schedule. It is the accumulation counterpart to present value. Instead of discounting future cash flows back to today, this calculator grows each payment forward to the final period and adds the results. That makes it a clean fit for recurring contributions, sinking funds, education savings, and any plan where the payment amount is fixed for the entire schedule.
This page is intentionally narrower than the general annuity calculator, which can include an opening balance and can switch between deposits and withdrawals. It is also distinct from the present value of annuity calculator, which values the same style of stream in today’s dollars. If your question starts with a lump sum and asks how much income it can provide, use the annuity payout calculator. If you want standard compound growth for one current balance plus contributions, compare the compound interest calculator.
How the calculation determines calculated
The form takes five inputs: payment amount, interest rate, number of periods, payment timing, and compounding frequency. The calculator requires a nonnegative payment, a nonnegative rate, and a positive integer number of periods. It maps annual, semiannual, quarterly, and monthly compounding to 1, 2, 4, and 12 compounding periods. The annual rate is divided by that count and by 100 to create the effective rate used in the payment schedule.
Then the calculator loops through the payments. Under ordinary end-of-period timing, the final payment has a growth exponent of zero because it is made at the end date. The first payment has the largest exponent because it has the most time to compound. Under beginning-of-period timing, every exponent is one higher, giving every payment one extra period of growth.
Formula
For an ordinary annuity with equal payment PMT, periodic rate r, and number of payments n, the closed-form future value is:
For an annuity due, every payment is made one period earlier:
The schedule uses the equivalent payment-by-payment formula:
For ordinary timing, the time value counts how many periods remain after each payment. For beginning timing, the time value is one period larger. If the interest rate is zero, each payment simply contributes its face amount, so the future value equals payment times number of periods.
This calculator-defined scenario is not a rule, standard, legal conclusion, forecast, or universal convention.
Worked example matching the default inputs
The default example uses a $1,000 payment, 5% interest, 10 periods, end-of-period timing, and annual compounding. Annual compounding makes the periodic rate 0.05. The first payment is made at the end of period 1 and grows for 9 remaining periods, so it contributes $1,000 times 1.05 to the ninth power, or about $1,551.33. The last payment is made at the end of period 10 and contributes exactly $1,000 because it has no time left to grow.
Adding the ten grown payments produces $12,577.89. Total payments are $10,000, so the growth component is $2,577.89 under the calculator’s constant-rate assumption. The result panel reports the rate per compounding period as 5.00% and the payment timing as End.
If the same inputs are changed to beginning-of-period timing, the first payment grows for 10 periods and the final payment grows for 1 period. The total becomes $13,206.79, exactly one additional 5% period applied to the ordinary result.
Future value versus present value
Future value and present value use the same time-value concept from opposite directions. A future value calculation is accumulation-focused: how large can a savings stream become by a target date? A present value calculation is valuation-focused: how much would those future payments be worth if paid as a lump sum today?
That distinction matters for decisions. If you are deciding how much to save each year for a future purchase, future value is the natural view. If you are deciding whether to accept a lump sum instead of promised payments, present value is the natural view. The same $1,000 annual payment stream can have a future value above $10,000 at a positive return while having a present value below $10,000 when discounted.
Ordinary versus due timing
Ordinary annuity timing fits many contribution plans where payments are recorded at period end. Annuity due timing fits payments made at period beginning, such as a deposit made on the first day of every month. With a positive rate, annuity due always creates a larger future value for the same payment, rate, and number of periods because the money is invested earlier.
The timing effect is often modest for one month and large over decades. A beginning-of-month saver contributes the same nominal dollars as an end-of-month saver, but every deposit receives one extra month of return. When the rate is high or the schedule has many periods, that one-period advantage compounds into a noticeable gap.
Insurance product versus accumulation math
This calculator does not quote a fixed, indexed, or variable annuity contract. It does not model surrender periods, guaranteed minimum interest, caps, participation rates, mortality and expense charges, rider fees, tax penalties, or insurer claims-paying ability. It simply values a stream of equal deposits under a constant periodic return.
That simplicity is valuable for planning. You can isolate the effect of payment size, number of periods, rate, and timing before evaluating product features. If a contract illustration uses irregular premiums, bonuses, fees, or guaranteed income benefits, those details need a separate product-specific review.
Tips for better projections
- Use the payment interval as the period count. Ten years of monthly payments means 120 periods, not 10.
- Choose a rate that already reflects expected fees if you are modeling an investment account.
- Run conservative and optimistic scenarios rather than relying on one return.
- Remember that constant returns smooth out volatility; real investments rarely earn the same return every period.
- Compare the payment total with the future value so you can separate savings discipline from investment growth.
Informational note
Future value calculations support planning, but they do not guarantee investment results or insurance benefits. Review risk, liquidity, taxes, fees, and product documents before making financial decisions.