Compound Interest Formula: How to Calculate It Step by Step

What compound interest means

Compound interest is interest earned on both your original amount and on the interest that has already been added. Because each period's interest becomes part of the base for the next period, growth speeds up over time.

Simple interest, by contrast, is calculated only on the original amount. Over long periods, the gap between the two can be large.

The compound interest formula

The standard formula for the final balance is:

• •A = P × (1 + r / n) ^ (n × t)
• •A is the final amount, P is the starting amount (principal), r is the annual rate as a decimal, n is the number of times interest compounds per year, and t is the number of years.
• •To find only the interest earned, subtract P from A.

Worked example: $10,000 at 5% for 10 years

With annual compounding (n = 1), the balance is 10,000 × 1.05 ^ 10, which is about $16,288.95. The interest earned is about $6,288.95.

With monthly compounding (n = 12), the balance is 10,000 × (1 + 0.05 / 12) ^ 120, which is about $16,470.09. More frequent compounding gives a slightly higher result.

The Rule of 72 shortcut

To estimate how long it takes to double your money, divide 72 by the annual rate. At 5%, 72 / 5 = 14.4 years. It is an approximation, but it is useful for quick mental checks.

Common mistakes

The Compound Interest Calculator handles the conversions and shows the final balance instantly.

• •Entering 5 instead of 0.05 for the rate in the formula.
• •Forgetting to multiply n by t in the exponent.
• •Ignoring taxes, fees, and inflation, which reduce real returns.