How Does Compound Interest Work? | The Motley Fool (2024)

You might think you need to save money consistently, whether in a savings account, retirement savings plan, or brokerage account, if you want to accumulate more money. But if you save and invest your money wisely over a long period, you could wind up pleasantly surprised at the level of wealth you achieve.

If the idea of watching your money grow before your eyes sounds appealing, it pays to take advantage of the power of compound interest and returns.

Here we'll review what compounded growth entails and show you how a series of relatively modest contributions to a savings or investment account can evolve into a substantial sum over time.

How does compound interest work?

At its core, compounding is the concept of earning interest on interest.

Imagine you put an initial deposit of $1,000 into a savings account that pays 2% interest. That means after a year, your balance will grow to $1,020 without contributing more money.

Now here's the cool part: If you keep that money saved, you'll continue earning interest not just on the initial $1,000, but also on that $20. Assuming your interest rate stays the same, you'll earn $20.40 in interest in your second year, for a balance of $1,040.40.

After 40 years of earning the same interest in that account, your $1,000 will grow to $2,208.04 -- more than double your initial savings, with no extra investment or work.

Generally, you don't just sock away a lump sum of money and come back to it in 40 years. In reality, most people save or invest consistently. With compound interest, your principal (the money you put in) will continue to grow not only by how much you save but also by the interest that's compounding -- a double whammy of savings and interest that could help you grow wealthy over long periods.

What are the benefits of compound interest?

In a nutshell, it can grow your money. Interest means you earn money without needing to do any extra work. Then, the money you earned continues earning even more -- that's compounding. Your money continues to grow, whether you continue to add to it or not.

The downside: If you're being charged compound interest -- say, for a credit card balance -- your debt can grow just as easily (more on that below).

How does compound interest work in the stock market?

Imagine you want to invest your money for a long-term goal, like retirement, and you put $100 a month into a brokerage account or IRA instead of a bank account. These days, a high-yield savings account might pay 4% interest, which isn't bad. But, depending on your investments, the stock market could yield significantly more.

Consider, for instance, an S&P 500 index, which follows the top 500 companies in the U.S. Over the past 30 years, the S&P 500 has delivered a compound average annual growth rate of 10.7% each year -- though returns within a single year can fluctuate quite a bit (and this figure is before inflation). To be conservative, we'll use a 7% return for our calculations.

The following table shows how much money you could wind up with in your brokerage account, depending on how many years you continue to save:

Notice as you get further down the table, the numbers don't just get bigger; they represent increasingly larger gains.

• Our top row shows that in three years, $3,600 in out-of-pocket contributions to an investment account turned into $3,859, representing a $259 gain.
• Look at the third row with a 10-year investment window. A $12,000 out-of-pocket contribution turned into $16,581, representing a $4,581 gain.
• In the very bottom row, $54,000 in contributions turned into $342,920 over 45 years, leaving us with a very substantial and impressive $288,920 gain.

The compounding effect makes these gains possible.

Note that these calculations assume interest is compounded annually -- meaning the interest you earn is only added to your balance once each year. So, for a full year, you only earn interest on your principal investments.

Accounts compound at different intervals. Savings accounts typically compound daily or monthly -- so interest earned on your balance is swept into your balance to earn interest the very next day or every 30 days. Some investment accounts compound interest semi-annually or quarterly. The more frequently your account is compounded, the more you gain.

That total rate of gain per year, with these compounding intervals taken into account, is called the annual percentage yield (APY). When you're charged interest, it's the annual percentage rate (APR).

How long does it take for compound interest to work?

As the table above illustrates, the longer you let your savings or investments sit, the more you benefit from compounding.

You can capitalize on compounding by investing for just a few years, but your gains will be higher if your returns compound for 20 years instead. That's why you're so often encouraged to start saving for retirement as early as possible. The earlier you start saving, the more time you have to compound.

How compounding can work against you

Compounding can work against you when you're charged interest on debt, especially credit card debt.

You can use a credit card for purchases without paying interest as long as you repay the balance by the time it's due. Any remaining balance on the card -- even if you've made the minimum required monthly payment -- accrues interest. Over time, that interest is added to what you owe, and it also accrues interest.

Here's an example: Say you make $1,200 in credit card purchases this month, and you make $100 payments each month (and don't make any other purchases on the card in the meantime). If your credit card's annual interest rate (or APR) is 21%, you'll pay $159 in interest and pay off the balance after 14 months.

If you instead make $50 payments each month, you'll pay $370 in interest and take 32 months to pay off the balance. By paying half the amount, it takes you more than twice as long to repay what you owe, and you pay more than twice the amount of interest -- because of compounding.

This breakdown shows what happens when you pay a $1,200 credit card off over time in $60 increments:

By making $60 payments, you'll pay roughly $290 in interest and finish the debt after two years (or 24 payments). Notice that your interest payments are higher in the beginning and lower toward the end. This happens because your credit card balance is high in the beginning, so the APR will generate a higher interest payment. This is also how many people get stuck in a cycle of debt, as the high interest payments can trap you and make it difficult to pay down your principal.

Remember how earlier we said the more frequently interest compounds, the more it amounts to? Well, some credit card issuers (though not all) compound interest daily, which means for each day you carry a balance past the due date, you're charged interest on interest.

While compound interest can be a powerful tool that works for you when you're saving, it can also very much work against you when you're spending and borrowing.

What is the formula for compound interest?

If you really want to get into the math behind compound interest, here's the formula you need to know:

A = P (1 + r/n) ^ n*t

Here's what these variables mean:

• A is the final sum
• P is your principal
• R is your annual interest rate, written in decimal format
• N is the number of compounding periods per year (for example, interest that compounds annually would be 1)
• T is the number of years your money compounds

Say you invest $3,000 at a 7% APY over 10 years. Here's what you'd end up with:

3,000 (1 + 0.07/1) ^ 1*10

which becomes

3,000 (1.07) ^ 10 (that ^ means "to the power of," in case you're confused)

which then becomes

3,000 (1.967)

which equals $5,901, which is the total amount your investment will grow to, representing a gain of $2,901. Sweet!

Make compound interest work for you

The best way to take advantage of compound interest is to give yourself time -- lots and lots of time.

Many people who retire as millionaires don't have six-figure incomes or family trust funds. Rather, they start saving and investing at a young age and continue doing so consistently over many years. If you invest just $300 a month and get an average annual 7% return, you'll wind up with just over $1 million after 45 years.

It's equally important to not fall victim to compounding. That means understanding how compound interest applies to debt and avoiding scenarios where you're carrying a balance for too long.

If you make a point to use compound interest to your benefit and don't let it work against you, you'll position yourself to make your money work for you throughout your life.