What is the future value of an annuity formula?

FV = P × [(1 + r)n − 1] ÷ r for deposits at the end of each period, where P is the deposit, r the rate per period and n the number of deposits.

How much interest do I earn on regular deposits?

Subtract the total deposited (P × n) from the future value. The calculator shows both numbers.

Ordinary annuity or annuity due?

Ordinary if you pay at the end of each period (most savings plans and loans); annuity due if you pay at the beginning (rent, many insurance premiums).

Can I use an annual rate with monthly deposits?

Convert first: monthly rate = annual rate ÷ 12 and n = years × 12. The result assumes monthly compounding.

Future Value of Annuity Formula

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Future Value of an Annuity Calculator

The future value of an annuity is the balance you build by depositing the same amount every period and letting it compound. The first deposit earns interest for n − 1 periods, the second for n − 2, and the last one, made on the final day, earns nothing. Adding those growing deposits gives a geometric series whose sum is P × [(1 + r)ⁿ − 1] ÷ r.

Formula

FV = P × (1 + r)ⁿ − 1r

Where

FV: future value of the payment stream (payments at the end of each period)
P: payment per period
r: interest rate per period, as a decimal
n: number of payments

Calculator

Payment per period (P)

Rate per period (r) (%)

Annual rate ÷ payments per year.

Number of payments (n)

Result and step-by-step solution

Future value of the annuity

32,775.87

120 payments of 200.00 (total paid in 24,000.00), of which 8,775.87 is interest.

Convert the rate to a decimal
r = 0.5% = 0.005
Growth term
(1 + r)ⁿ = (1 + 0.005)¹²⁰ = 1.819397
Annuity factor
1.819397 − 10.005 = 163.879347
Multiply by the payment
200.00 × 163.879347 = 32,775.87

How to use the formula

This is the formula behind savings plans, retirement contributions and sinking funds. Make sure the payment, the rate and the number of periods use the same frequency: 200 a month for 10 years at 6% a year means P = 200, r = 0.5% and n = 120, which is the default example on this page. The result is 32,775.87, of which 24,000 came from deposits and 8,775.87 from interest.

If deposits are made at the start of each period, every payment gets one extra period of growth; use the future value of an annuity due. To work backwards from a savings target to the deposit you need, use the sinking fund formula.

Frequently asked questions

What is the future value of an annuity formula?: FV = P × [(1 + r)ⁿ − 1] ÷ r for deposits at the end of each period, where P is the deposit, r the rate per period and n the number of deposits.
How much interest do I earn on regular deposits?: Subtract the total deposited (P × n) from the future value. The calculator shows both numbers.
Ordinary annuity or annuity due?: Ordinary if you pay at the end of each period (most savings plans and loans); annuity due if you pay at the beginning (rent, many insurance premiums).
Can I use an annual rate with monthly deposits?: Convert first: monthly rate = annual rate ÷ 12 and n = years × 12. The result assumes monthly compounding.

Last reviewed: September 26, 2026. Calculations run in your browser and were checked against numpy-financial, SciPy and published spreadsheet examples.