Compound Interest Calculator

How it works

Compound interest pays interest on the interest already earned. The annual rate is divided by the number of compounding periods in a year, and at the end of every period the balance grows by that periodic rate.

The starting balance and the stream of contributions grow separately and are added together. A contribution made at the start of a period earns interest for that period; one made at the end starts earning in the next period, so the start-of-period option always gives a slightly larger result.

The table shows the balance at the end of each year, what you put in that year, and the interest earned that year, so you can see interest overtake your own contributions as the balance grows.

For a savings account or CD, banks quote the APY, which already includes compounding. With no contributions, entering the APY as the rate with annual compounding matches the bank's figure. Contributions are made once per compounding period, so to model monthly deposits enter the nominal rate with monthly compounding instead. The effective annual rate output converts any nominal rate and frequency into that APY form.

Formula

i = annual rate ÷ n          (n = compounding periods per year)
N = n × years
FV = P × (1 + i)^N + c × ((1 + i)^N − 1) ÷ i
     × (1 + i) when contributions are made at the start of each period
FV = P + c × N               when the rate is 0
APY = (1 + annual rate ÷ n)^n − 1

Example

$10,000 at 5% compounded monthly with $100 added at the end of every month for 10 years grows to $31,998.32. You contribute $22,000 in total ($10,000 to start plus 120 × $100), so $9,998.32 is interest. The 5% nominal rate compounded monthly is an APY of 5.116%.

A $1,000 balance with $100 added at the start of every month at 6% compounded monthly is worth $2,301.40 after one year.

Assumptions and limitations

• The rate you enter is an assumption, held fixed for every year. Real returns on investments vary from year to year and can be negative; savings and CD rates change when they reset.
• One contribution is made every compounding period, always the same amount. With daily compounding that means a contribution every day, so for monthly deposits into a daily-compounding account choose monthly compounding; the difference in interest is small.
• No taxes, fees, withdrawals, early-withdrawal penalties or inflation are taken into account.
• The result is an estimate for planning and is not financial, tax or investment advice.

Frequently asked questions