If there were an eighth wonder of the world, we'd nominate the equation for compound interest: Your money x (1 + i)^n. (If you're not a math geek, don’t worry; we're going to decipher that for you.)

Albert Einstein (or maybe it was Yogi Berra) called this deceptively simple formula the "greatest mathematical discovery of all time." We call it your ticket to financial independence.

That's right, just three straightforward inputs can change your life: the amount of money you invest; the rate of return you get; and how much time you have to let your money grow.

Hate math but like money? Read on. Since words cannot adequately describe the magical nature of compound interest, let's try a few visuals.

Here's how a single $1,200 investment grows over time in four savings scenarios.

How a single $1,200 investment grows

*Based on the stock market's historical rate of return.

you can see, simply socking away one lump sum and leaving it put could turn $1,200 into nearly $40,000 over 40 years. Not only have you earned interest, but you've earned interest on your interest. And all you had to do was invest your first paycheck.

That said, let’s be honest: $37,691 ain’t what it used to be. So let’s make one small revision and invest $1,200 every year. Behold compound interest in a mildly caffeinated state.

A more compelling table than the previous one

Now we're at half a million. Not bad, right? Still, we think you can top it. In fact, it’s not a stretch to get near that magical $1 million milestone. Just save $2,500 a year (a mere $208 a month), and at 9% you’ve got a million dollars in 40 years. Or stick with the $1,200 annual contribution but improve your investing skills (which the rest of this series will show you how to do). If you are able to best the stock market’s average annual returns by a mere 3 percentage points, the $1 million prize is yours. 

If we could, we would cue a soaring chorus of angels opening the doors to usher you into the Valhalla of investing … but we misplaced that file somewhere on our hard drive.

And the best part about compound interest is that it works the same for everyone, whether you have $20 to invest or $200,000. Go ahead, tinker with this compounding calculator to see what we mean. If you don't believe you can become a millionaire with just the resources you have right now, keep reading.

The amazing tale of the Mississippi washer woman Oseola McCarty was born in Mississippi in 1908. For nearly 75 years, she lived in the same simple house, washing other people's clothes for a living and putting whatever money she could into savings accounts at local banks.

In the summer of 1995, Oseola made local and then national headlines when she donated $150,000 to the University of Southern Mississippi to establish a scholarship fund. "I just figured the money would do [scholarship recipients] a lot more good than it would me," she said. It soon came out that this washer woman had managed to amass nearly one quarter of a million dollars over her lifetime.

Time -- a key part of the compounding equation -- helped turn her meager early investments into hundreds of thousands of dollars.

-Motley Fool