Compound Interest Is the Market's Most Powerful Force: Here's How It Actually Works

Why do people invest? It's not just to get a tax break from contributions to a 401(k). The ultimate reason is that we want our money to grow for the future. The way that money grows, and the biggest reason to invest, is the power of compound interest. With compound interest (also called compound returns for stocks), an investment grows over time by earning returns, which then earn additional returns.

Compound interest makes money build upon itself. Your money makes money without you having to work for it. This might sound like magic or an impossible self-propelling perpetual motion machine. But it's not magic; it's math.

Here's how the math of compound interest works, and how it can help your investments grow for years to come.

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Compound interest for stocks: Understanding total return

If you have a savings account at the bank, you're probably familiar with compound interest. If you have $1,000 in a savings account that earns 3% annually, after one year your account balance will grow to $1,030. After a second year, that $1,030 balance will earn 3% again, for a total balance of $1,060.90. In the third year, you will have $1,092.73. The interest earns additional interest. The money builds upon itself.

Earning compound interest (or compound returns) with stocks is a bit more complex, but often more lucrative. That's because stocks earn returns in more than one way. Stocks earn a total return which consists of any share price increase (also called capital gain), plus any dividends or other distributions to shareholders.

For example, if you buy a stock for $100 per share and in one year that stock goes up by $7 and pays a 2% dividend ($2), the stock will deliver a one-year total return of $9, or about 9%. In the second year, let's say the stock price goes up by $3 per share from $107 to $110 and pays the same 2% dividend yield ($2.20). This second year's total return is $5.20, or 4.85%.

Over two years, with $10 per share of capital gains and $4.20 per share of dividends, this stock has gained a total return of $14.20, for a compound annual growth rate (CAGR) of 6.86%.

Stock market returns can vary and are not guaranteed. Not every stock pays dividends. Some mature companies with financially strong balance sheets pay higher dividend yields, while growth stocks tend to pay lower dividends (or no dividends at all) but offer the potential for faster gains in share price. But understanding the total return of a stock or exchange-traded fund (ETF) can show you the full power of compound interest and how it drives long-term growth in your investment portfolio.

How your investments grow with compound interest

Let's say you keep investing money in the stock mentioned in the example above, and it keeps delivering average annual returns of 6.86% (which includes dividends and capital gains from the share price going up). If you're like most long-term investors, you can set up your brokerage account to have your dividends automatically reinvested.

Let's say you keep buying $100 of that same stock every month for 10 years, for a total investment of $12,000. At 6.86% annualized returns for 10 years, your investment would grow to $16,471. Even though you only invested $12,000, your invested money "magically" delivered another $4,471 of gains from compound interest.

Keep in mind that 6.86% is not a very strong rate of return compared to what you could typically earn from the S&P 500 index (SNPINDEX: ^GSPC). This example stock is failing to beat the market. The S&P 500 has delivered a long-term average annual return of about 10% since 1928. Since September 2010, the Vanguard S&P 500 ETF (NYSEMKT: VOO) has delivered average annual total returns of about 15%.

What if you could invest in the Vanguard S&P 500 ETF and earn 15% annualized returns for the next 10 years? Let's say you invest $100 a month ($1,200 per year) in VOO and continue to earn 15% annualized returns. After 10 years your investment would grow to $24,364.

Even though you only put in $12,000 of your own money, your investment in this S&P 500 ETF would double with the power of compound interest. This shows why long-term investing in stocks is often a smart strategy to build wealth. In the long run, with the magical math of compounding, the stock market can make your money work harder for you.

Ben Gran has no position in any of the stocks mentioned. The Motley Fool has positions in and recommends Vanguard S&P 500 ETF. The Motley Fool has a disclosure policy.