Guides / Savings and investing

How Compound Interest Works, With a Worked Example

Compound interest is interest earned on your interest. The longer money stays invested, the more the growth speeds up. It is also a reminder that debt grows the same way.

The formula

The value after t years is A = P × (1 + r / n) raised to the power n × t, where P is the starting amount, r is the annual rate as a decimal, and n is the number of times interest is added each year.

A worked example

Put 10,000 in an account that pays 7% a year, with interest added once a year, for 10 years. The growth factor is 1.07 to the power of 10, which is about 1.9672. The final value is about 19,671.51, so the interest earned is about 9,671.51.

Does the frequency matter?

Yes, but less than the rate and the time. The same 7% added monthly gives slightly more than adding it once a year, because each month's interest starts earning too. The gain from monthly compounding is small compared with leaving the money invested for longer.

Compound interest works against you too

Unpaid credit card balances and some loans compound the same way. A balance that is not paid down keeps adding interest to the amount owed.

Limits of the calculation

The formula assumes a fixed rate and no extra money added or withdrawn. Real returns on investments vary and can fall, and fees and taxes reduce the result. Treat the figure as an illustration, not a promise.

Try it yourself

The Compound Interest Calculator shows the end value and the interest earned for any amount, rate, time and compounding frequency.