Compound interest explained, with real examples

Compound interest means earning interest on your interest. Each time interest is added to your balance, the next round of interest is calculated on that larger amount. Early on the effect is small. Over many years it becomes the biggest part of your balance.

A worked example

Put $10,000 in an account paying 5% a year, compounded monthly, and leave it alone for 10 years. The balance grows to $16,470.09. With simple interest, where interest is only ever paid on the original $10,000, you'd have $15,000. The extra $1,470 is interest earned on interest.

The formula

For a single deposit, the balance after t years is:

A = P × (1 + r ÷ n)^{n × t}

where P is the starting amount, r the annual rate as a decimal, and n the number of times interest is added each year. For the example: 10,000 × (1 + 0.05 ÷ 12)¹²⁰ = 16,470.09.

Regular deposits make the biggest difference

Add $200 a month to the same account and after 10 years the balance is $47,526.55. You deposited $34,000 in total, so $13,526.55 is interest.

Stretch the time and the effect grows dramatically. Starting from nothing, $200 a month at 7% for 25 years grows to about $162,000, even though only $60,000 was deposited. Most of that balance is interest earned in the later years.

Does compounding frequency matter?

Less than most people think. Here's $10,000 at 5% over 10 years with different compounding:

Monthly beats yearly by about $180, and daily beats monthly by only $17. The interest rate and the number of years matter far more.

The rule of 72

To estimate how long money takes to double, divide 72 by the annual interest rate. At 6%, money doubles in about 12 years. At 8%, about 9 years. At 3%, about 24 years. It's an approximation, but a remarkably good one for rates between about 4% and 12%.

What this leaves out

Interest is usually taxable, and inflation reduces what each dollar buys, so real growth is lower than the headline numbers. Investment returns also aren't guaranteed the way a savings rate is. This guide is general information, not financial advice.

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