How to Calculate Compound Interest, Step by Step

With compound interest, you earn interest on your interest. Each time it is added, the balance grows and the next interest is figured on the bigger amount. That is why the numbers grow faster over time than with simple interest.

Try it with your own problem ↓

The steps

Identify P (the starting amount), r (the yearly rate as a decimal), n (how many times a year it compounds) and t (the years).
Write the formula: A = P × (1 + r/n)^n×t.
Work out r/n and add 1, then work out n × t.
Raise (1 + r/n) to the power n × t with a calculator.
Multiply by P. The interest earned is A − P.

A worked example

You put $1,000 in an account at 5% compounded monthly for 10 years. How much do you have?

P = 1,000, r = 0.05, n = 12 (monthly), t = 10.
r/n = 0.05 ÷ 12 = 0.0041667, so 1 + r/n = 1.0041667.
n × t = 12 × 10 = 120.
1.0041667¹²⁰ ≈ 1.647009.
A = 1,000 × 1.647009 ≈ 1,647.01.

You would have about $1,647.01, so you earned $647.01 in interest. With simple interest it would be $1,500.

Try it with your own problem

Open the free The Money Jar with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: $1000 at 5% compounded monthly for 10 yearsOpens The Money Jar with this example

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Common mistakes

Using 5 instead of 0.05. Turn the percent into a decimal.
Forgetting to divide the rate by n. A monthly rate is the yearly rate divided by 12.
Multiplying instead of raising to a power. The exponent n × t is how many times it compounds.
Rounding the rate early. Keep every digit until the end.

Questions people ask

What is the difference between simple and compound interest?

Simple interest is only on the starting amount: P × r × t. Compound interest also earns interest on the interest.

Does compounding more often help?

Yes, a little. The same 5% for 10 years gives $1,628.89 compounded yearly, $1,647.01 monthly and $1,648.66 daily.

What is APR versus APY?

APR is the stated yearly rate. APY is what you actually earn after compounding, so it is a bit higher.

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