How Compound Interest Can Help You Retire a Millionaire -- Even on a Modest Income

"Money makes money. And the money that money makes, makes money." That quotation, attributed to Benjamin Franklin, is all about the power of compounding, whether it's compound interest or the compounded growth of stocks.

The phenomenon of compounding is available to us to help us build fat retirement savings accounts. Here's a look at how you might use it.

Image source: Getty Images.

Get inspired first

Before explaining more about compounding, here's a little inspiration: Know that plenty of people of very limited means have been able to become millionaires or multimillionaires thanks to compounding.

I've written about these extraordinary ordinary people before -- people such as these.

Ronald Read: Mr. Read was a Vermonter who worked as a janitor and a gas station attendant. He lived frugally and quietly invested his money. According to a Wall Street Journal report, he owned at least 95 different stocks when he died in 2014, including JPMorgan Chase, CVS Health, and Procter & Gamble -- and he reportedly collected $20,000 monthly in dividends from them! Mr. Read made news when he donated $6 million to his local library and hospital.

Here's more inspiration -- look at how you might amass a million or millions -- if you sock away $1,000 per month into stocks:

Source: Calculations via Investor.gov's calculator.

See? Over long periods, even relatively small investments can grow like gangbusters.

It's all math

The magic of compound growth is dependent on three factors:

• How much you can invest.
• How quickly your money grows.
• How many years your money has to grow.

Here's a closer look at each.

How much you can invest

You may not be able to sock away $1,000 per month, but whatever you can invest can help you eventually amass substantial sums. If you can invest more than $1,000 each month, I encourage you to do so -- especially because your earliest invested dollars are your most powerful ones, with the most time in which to grow for you.

If you can only invest, say, $300 per month now, don't fret. You may be able to up that to $500 in the next few years, and perhaps a few years later you could be socking away $1,500 monthly.

How quickly your money can grow

Your money's growth rate matters a lot, too, of course. The table above models three different growth rates: 8%, 10%, and 12%. I like to assume 8% when I do my own retirement planning, in order to be a bit conservative -- since the stock market doesn't always deliver big annual returns. Over many decades, though, it has averaged annual returns near 10% over long periods.

If you want to aim for faster growth, you might put some of your money in some growth stocks, understanding that they're not guaranteed to soar. Some might be very overvalued, and some might even implode. (Still, if you take the time to learn more about them, you might do well.) Don't put too much in any one or two stocks, though -- our Foolish investing philosophy suggests buying into around 25 or more companies and aiming to hang on to your shares for at least five years.

A less volatile and very effective way to build long-term wealth is via a simple, low-fee index fund -- such as one that tracks the S&P 500 index or an even broader index. Here are a few to consider:

• Vanguard S&P 500 ETF (NYSEMKT: VOO)
• Vanguard Total Stock Market ETF (NYSEMKT: VTI)
• Vanguard Total World Stock ETF (NYSEMKT: VT)

How many years your money has to grow

Finally, there's time. The table above shows the crazy power of time. Your investment account might grow by $1,000 or $3,000 per year in your first years, but later on, it could be growing by $100,000 or $500,000 per year. That's the power of compounding at work!

The secret to success

Compounding is one very effective secret to success -- and another one is diligence. If you're not investing significant (to you) sums regularly for many years, you won't get the amazing results above.

So make a plan -- and then stick to it.

JPMorgan Chase is an advertising partner of Motley Fool Money. Selena Maranjian has positions in Procter & Gamble. The Motley Fool has positions in and recommends JPMorgan Chase, Vanguard S&P 500 ETF, and Vanguard Total Stock Market ETF. The Motley Fool recommends CVS Health. The Motley Fool has a disclosure policy.