Behold the Miracle of Compounding

Editor's note: This story has been updated in 2011.

Compound interest has been called the eighth wonder of the world. And with good reason. It magically turns a little bit of money, invested wisely, into a whole lot of cash. Even Albert Einstein -- a bit of a smarty pants -- is said to have called it one of the greatest mathematical concepts of our time.

But you don't need to be a genius to harness the power of compounding. Even the most average of Joes can use it to make money. Trust me. This is so much easier than the theory of relativity.

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Here's the gist: When you save or invest, your money earns interest or appreciates. The next year, you earn interest on your original money and the interest from the first year. In the third year, you earn interest on your original money and the interest from the first two years. And so on. It's like a snowball -- roll it down a snowy hill and it'll build on itself to get bigger and bigger. Before you know it ... avalanche!

Harness the power

Here are three steps to help you make the power of compound interest or compound earnings work for you. And when I say "work FOR you," I mean it. Once you set up an account, you don't have to do much else. Just sit back and wait for the money to roll in.

1. Start young. When you're in your twenties and thirties, your best friend is TIME. Start rolling your snowball at the top of the hill and you'll have a much bigger mass at the bottom than someone who started halfway down.

Consider this: Amy, a 22-year-old college graduate, saves $300 per month into an account earning 10% per year for six years. (That's the average annual return of the stock market over time.) Then at age 28, she starts a family and decides to stay home with the children full time. By then, Amy had kicked in $21,600 of her own money. But even if she doesn't contribute another cent ever, her money would grow to a million bucks by the time she turned 65.

Compare that to Jason, who put off saving until he was 31. He's still young enough that becoming a millionaire is within reach, but it will be tougher. Jason would have to contribute the same $300 a month for the next 34 years to earn $1 million by age 65. Although Amy invested less money out-of-pocket -- $21,600 over six years vs. Jason's $126,000 over 34 years -- her money had more time to grow, or compound. (See How to Make a Million.)

Bottom line: Getting rich is easier and more painless the earlier you start. Check out our 5 Steps to Start Investing to get started right now.

2. Remember that a little goes a long way. Don't think you have enough money to start investing? You can get into a good mutual fund for as little as $50 a month.

Let's say a 20-year-old stashes $50 a month into a fund earning 10% annually. He'd have $528,000 by age 65. Not bad for practically starting with pocket change! See Top 10 Ways to Save Money to find room in your budget to get started.

A little bit can make a difference elsewhere in compounding, too. For example, if our 20-year-old earned 9% annually instead of 10%, he would amass only $373,000 in the same period of time. That seemingly small 1% difference in performance resulted in 29% less money over the long haul.

That's why, when you're young, you need to invest fairly aggressively. You should invest nearly all your money in stocks or stock mutual funds (as opposed to bonds and other conservative investments) in hopes of netting a bigger return. You'll certainly have ups and downs, but over the long-term, TIME (again, your best friend) will smooth them out for your benefit. Crunch your own numbers with our savings calculator.

3. Leave it alone. The prospect of making a lot of money without doing anything sounds good on paper. But, admittedly, in practice, it can be maddening. Every time you receive your account statement, you watch your balance s-l-o-w-l-y inch up -- or even drop. How on earth are you ever going to get rich at this pace?

Investing is a lot like Heinz ketchup: Good things come to those who wait. You must be patient for compounding to work its awesome power. Remember that as your money earns more, it'll earn even more. You certainly won't get rich overnight this way. But you will get rich if you start young, invest wisely and leave it alone.

A final note

If you invest or save in a regular, taxable account, Uncle Sam will want his share. So make sure you factor that into your saving goal. However, you can invest in tax-sheltered accounts and keep more of the money to yourself. My favorite is the Roth IRA because all your money is tax-free in retirement. See Why You Need a Roth IRA to learn more.

And what about inflation? True, $1 million won't have the same purchasing power in 40 years as it has today, but that's all the more reason to start saving now! The examples above use flat contributions -- $50 per month, for example. But over the years, your income will rise, too. If you increase your savings with each increase in your pay, you'll give your money more fuel to compound, and you'll certainly boost your spending power down the road.

Besides, having a million bucks in 40 years is better than not having a million bucks at all. Start as soon as you can and save what you can to let compounding work its magic.