How Does Compound Interest Work?

Compound interest is when the interest you earn on savings or investments accumulates interest on itself. Instead of just earning simple interest — the interest you earn on your original investment — compound interest allows you to earn on both your principal investment and on its earnings. Over time, the interest on interest adds up. That's why compound interest is one of the most important concepts for building long-term wealth. 

What is compound interest? 

Compound interest is interest that is calculated on the principal investment in an account, as well as on any returns earned over time. As brokerage accounts or savings accounts earn interest, those new amounts are added to the original principal amount. Over time, interest accumulates based on the current principal amount — so earlier interest payments are then earning interest, too.  

How does compound interest work?

Your money compounds when you earn interest or returns on money that has already earned interest or returns. For an investor or saver, compound interest multiplies your money at an accelerated rate. That's because compounding interest is calculated on the initial principal as well as all the accumulated interest from previous periods. 

For example, imagine you open a savings account with an initial deposit of $100. Your hypothetical account has a 7% annual percentage yield, or APY, and interest compounds annually.

After one year, you'd have a balance of $107, which is made up of your original $100 plus $7 in gains. When you leave the $107 invested in your account for another year, your balance climbs to $114.50. Your returns in the second year are calculated using the total from your first year, which was $107. You earned another 7% during the second year, for a total of $107 plus $7.50 in returns. 

Savings grow even more after a few years or decades. In 20 years, if you contribute nothing but continue to earn the same APY of 7%, you'd have about $387, or 287% more than your initial investment. That shows why compound interest has been called the eighth wonder of the world, due to its power to grow funds.

However, it's important to understand that compound interest can also work against you. For a borrower, compound interest can rapidly multiply the amount owed. For example, if you don't pay off your credit card debt in full each month, the credit card company adds interest charges daily on your unpaid balance as well as unpaid interest. In other words, the issuer adds more interest on top of what you already owe.

Compound interest formula explained

So how do you figure out how much you can earn with compounding interest? As you might have guessed, there's a mathematical formula for that. Here's what it looks like, and which figures to plug in: 

A = P(1 + r/n)nt

• A is the compound interest earned.

• P is your initial principal or investment. This is the amount you started with in the investing or savings account.

• r represents the returns — or interest rate — you expect to receive. Historically, major market indexes like the S&P 500 typically return about 7% annually. This is an average, so some years will have higher gains and some will have bigger losses. 

• n is the number of compounding periods, or how many times interest compounds per year. Interest typically compounds annually, monthly, or daily. 

• t is the length of time you plan to borrow, invest, or save. For long-term investors, this variable will be decades, rather than months or years. 

Compound interest calculator 

While the compound interest formula shows you how to figure the interest you can expect with compounding, there are easier ways to calculate your potential returns. For example, Acorns' compound interest calculator allows you to enter your own figures and automatically see how compounding interest can work for you. Try out different numbers to see how much your investment could change over time. 

Here's an explanation of the input fields to make the compound interest calculator work for you: 

• Initial deposit: This is your investment on Day 1. 

• Contributions: If you plan to invest regularly, enter an ongoing contribution amount. Using this field will show you how a consistent investment strategy (also known as dollar-cost averaging) may affect your investment's potential growth. 

• Contribution frequency: In this field, enter how frequently you plan to make contributions to your investment account. 

• Average annual return: This is the percentage you expect your investments to grow each year. The stock market fluctuates, so you will likely get a different return each year. A 7% annual return is a common estimate based on market growth over the past century, but you can adjust as you see fit. 

• Years to grow: This figure is the number of years you plan to leave your money invested, also known as your investment horizon. 

3 benefits of compound interest 

Compound interest offers a number of benefits to savers and investors, because it allows you to earn much more than just the simple annual interest rate on your savings and investments.

Long-term growth potential

Investing is a long-term strategy, and compounding interest is one of the reasons why. The earlier you start investing or saving, the more you can benefit from the power of compound interest. That's because over time, your returns will earn returns of their own, increasing the impact of your savings through the long term. Every time you add funds to your investment, you can benefit from growth in the market while earning on previous gains. 

Key to building wealth 

Compounding is key to building wealth over the long term. It allows you to earn on your initial investment as well as on your accumulated gains. 

When you're a new investor, compound interest may not seem like a big deal. But those gains can add up significantly over time. 

In fact, time is the most important factor for compounding. When you think about your long-term goals, 10 years isn't really all that much time. But with 20 or 30 years for your investments to grow and earn returns on returns, compound interest can make a big impact.

Helps you save for retirement

Saving enough money to retire with financial security is a long-term goal for most people, but it's not a goal most people can reach within a few years — or even a decade. However, by starting early, you'll likely have to set aside less money to reach your retirement goal because you'll have the benefit of compounding returns. 

When you start saving early for retirement, you are giving your initial investment and accumulated returns more time to potentially compound. For many savers and investors, the boost from compounding is exactly what they need to make it possible to reach their retirement savings goals.