Compound Interest: What It Is, Formula, Examples

What Is Compound Interest?

By Matthew Frankel, CFP – Updated Oct 9, 2025 at 1:37 AM

Key Points

Compound interest grows by reinvesting earnings, creating larger interest over time.
Increasing compounding frequency (e.g., monthly) can significantly accelerate investment growth.
Compound earnings combine dividends and value increases, enhancing overall returns.

When it comes to calculating interest, there are two basic choices: simple and compound. Simple interest simply means a set percentage of the principal amount every year.

For example, if you invest $1,000 at 5% simple interest for 10 years, you can expect to receive $50 in interest every year for the next decade. No more, no less. In the investment world, bonds are an example of an investment that typically pays simple interest.

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Multiple stacks of pennies growing larger each stack. — undefined

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Simple and compound interest on a $10,000 investment portfolio at 10% interest over time. Calculations by author.

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Note that 10% is, roughly, the long-term annualized return of the S&P 500. It was 9.65% for the 30-year period through 2022. Returns like this, compounded over long periods, can result in some pretty impressive performances.

It's also worth mentioning that there's a very similar concept known as cumulative interest. Cumulative interest refers to the sum of the interest payments made, but it typically refers to payments made on a loan. For example, the cumulative interest on a 30-year mortgage would be how much you paid toward interest over the 30-year loan term.

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A graphic showing and explaining the formula used to calculate compound interest. — Image source: The Motley Fool.

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With "A" as the final amount, here's what all the other variables mean:

Principal (P): The starting balance on which interest is calculated. For example, if you decide to invest $10,000 for five years, that amount would be your principal for the purposes of calculating compound interest.
Interest rate (or expected rate of return in investing) expressed as a decimal (r): For calculation purposes, if you expect your investments to grow at an average rate of 7% per year, you would use 0.07 here.
Compounding frequency (n): How frequently you're adding interest to the principal. Using the example of 7% interest, if we were to use annual compounding, you would simply add 7% to the principal once per year. On the other hand, semiannual compounding would involve applying half of that amount (3.5%) twice a year. Other common compounding frequencies include quarterly (every three months), monthly, weekly, or daily.
Time (T): The total time in years. In other words, if you're investing for 30 months, be sure to use 2.5 years in the formula.

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$10,000 invested at 8% interest compounded annually, quarterly, and monthly. Calculations by author.

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A hypothetical example of how to calculate compound interest. — Image source: The Motley Fool.

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About the Author

Matt Frankel, CFP, is a contributing Motley Fool stock market analyst and personal finance expert covering financial stocks, REITs, SPACs, and personal finance. Prior to The Motley Fool, Matt taught high school and college mathematics. He holds a bachelor’s degree in physics from the University of South Carolina, a master’s degree in mathematics from Nova Southeastern University, and a graduate certificate in financial planning from Florida State University. He won a SABEW award for coverage of the 2017 Tax Cuts and Jobs Act. He is also regularly interviewed by Cheddar, The National Desk, and other TV networks and publications for his financial, stock market, and investing expertise.

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