How to Calculate Compound Interest

Calculates the compound total as principal × (1 + annual rate)^years. Because the interest is added to the principal, the growth accelerates year after year.

Explanation

Compound interest folds each year's interest back into the principal, so the following year earns interest on the interest too. The growth accelerates the longer it runs.

A = P \left( 1 + \dfrac{r}{100} \right)^{n}

$A$ is the total
$P$ is the principal
$r$ is the annual rate in per cent
$n$ is the number of years

The factor $1 + \dfrac{r}{100}$ is how much the money is multiplied by in a single year, applied $n$ times over. The interest earned is $A - P$ .

Example

Take a principal of 1000000 at 3% for 10 years. One year multiplies the money by 1.03, so ten years multiply it by $1.03^{10} = 1.3439\ldots$ . The total reaches $1000000 \times 1.3439\ldots = 1343916.38\ldots$ , meaning about 343916 of interest. Simple interest on the same terms pays only 300000, so compounding is worth roughly 43916 more.

Notes

The calculator compounds once a year. Half-yearly or monthly compounding at the same quoted rate lands on a slightly different total.

For a quick estimate, use the rule of 72: divide 72 by the rate in per cent and you get roughly the number of years needed to double your money. At 3%, that is $72 \div 3 = 24$ years.

The term does not have to be a whole number of years, and a negative rate shrinks the balance instead of growing it. Tax and fees are not included.