What Is Compound Interest?

Compound interest definition

Compound interest is the money your bank pays you on your balance — known as interest — plus the money that interest earns over time. It’s a way to make your cash work for you. How quickly your money grows is determined by your savings rate, bank balance and the number of times per year your bank pays interest, or “compounds.”

How compound interest accounts work

• Say you put $5,000 in a savings account with an annual percentage yield of 4% and your account compounds interest monthly. If you don’t make additional deposits, after one year, your balance would grow by about $204.

• In future months, that extra $204, along with the original deposit of $5,000 (sometimes referred to as the “principal”), will continue to earn interest. Without touching your account, if you continued to earn a 4% APY, you’d have $5,636 at the end of three years.

• If you make monthly contributions of $100 during the same three-year period, those additional deposits will earn interest, too. After three years, you would have contributed a total of $8,600. But with monthly compounding, you’d actually accumulate $9,455 by the end of the third year.

You don’t need large amounts of cash to experience the benefits of compound interest. Say you start with $10 and save $10 each month for three years in a savings account that earns a 4% APY. At the end of that time, you’d have $393. Even better, $23 of that amount would come from interest, meaning it’s money that your own funds earned.

» See how fast your own savings could grow? Use the NerdWallet compound interest calculator

You can take advantage of the power of compound interest as long as you have an account that offers a return, but you’ll want to find the best interest rates. The national average rate for savings accounts is currently 0.43%, but some institutions offer much more. Some online accounts, for example, have rates more than 10 times the national average. 

» Looking for more options? Read NerdWallet’s list of best high-interest savings accounts

Compound interest savings account example. Here’s a chart that shows how a $5,000 balance could grow over a period of three years. This assumes you make $100 monthly contributions and earn a 4% APY. You can find similar competitive rates with the best savings accounts.

Banks typically reserve the right to raise or lower the interest rate on a savings account at any time. If you want to earn compound interest at a consistent rate for a specific timeframe, consider opening a certificate of deposit. You can read NerdWallet’s primer on CDs to learn more.

The difference between simple interest and compound interest

Simple interest occurs when your bank pays interest on your original balance. It is easy to calculate simple interest: Start with the balance and then multiply it by the interest rate for your selected time period. That amount is what the bank deposits to your account at the end of the term.

Compound interest occurs when the interest you earn on your money starts to earn interest, too.

In the first example above, if you wanted to know how much simple interest you'd earn, you could calculate $5,000 multiplied by 4%. You’d get $200 earned in simple interest, for a total balance of $5,200. But with monthly compounding, the interest earnings add a little bit to the balance, too. So after a year, you'd actually earn about $204, for a total of about $5,204. It may not seem like it’s making much of a difference, but it adds up after time.

The higher the rate and your balance, and the more often the balance compounds, the more you’ll earn. Many online savings accounts are attractive because they compound daily instead of monthly. Marcus by Goldman Sachs (read review here) and American Express (read review here) have such accounts.

You can calculate how much you could earn with NerdWallet's compound interest calculator. You can adjust the compound frequency to calculate your balance with daily, monthly or annual compounding. You can also factor in additional deposits to your account.

» Learn more about the role of compound interest: Read about APY vs. interest rate

What is the compound interest formula?

Here is how to compute monthly compound interest without a calculator: Use the formula A=P(1+r/n)^nt, where:

A = ending amount P = original balance r = interest rate (as a decimal) n = number of times interest is compounded in a specific time frame t = time frame

In the example above, we know the ending amount is about $5,204 because we used a compound interest calculator. But here is how it looks if we use the formula:

A = ending amount P = $5,000  r = 0.04 (in our example, we used a 4% annual percentage yield) n = 12 (in our example, interest compounds monthly for one year, so it compounds 12 times) t = 1 (in our example, the time period is one year)

A = $5,000(1 + 0.04/12)^(12 x 1) A = $5,000(1 + 0.003333)^12 A = $5,000(1.003333)^12 A = $5,000x1.0407 A = $5,203.70, or about $5,204