Let's say you're a brand-spankin' new 22-year-old college graduate who, as a lovely gift, receives a cool $20,000 from Uncle Ernie, who blew off college and opted to make a fortune selling Beanie Babies "back in the day."

Let's further say that Ernie, smart fella that he is, advises you that the Beanie Baby gold rush is over and that instead of investing your (or rather, his) not-so-hard-earned moola in additional furry critters, you ought to plow it into the market, perhaps via dirt cheap S&P trackers such as the Vanguard 500 (FUND:VFINX).

Ernie also thinks rock-solid actively managed mutual funds might be a good way to go and that given your age, you might also consider racy growth stocks. You may experience some turbulence, he points out, but the likes of eBay (NASDAQ:EBAY), Broadcom (NASDAQ:BRCM), and Amazon.com (NASDAQ:AMZN) all boast five-year earnings-growth forecasts in excess of 20% -- and stock prices significantly below their respective 52-week highs. Starbucks (NASDAQ:SBUX) and EchoStarCommunications (NASDAQ:DISH) look pretty intriguing right now, too.

Say uncle!
Flash forward 40 years and let's also assume that, thanks to Ernie's sound counsel, you've managed to beat the market's historical average by a bit, notching an annualized return on that gift of $20,000 of 11%.

The payoff? Well, let's just say you'll be able to buy a round (or several) at the 19th hole while offering a series of toasts to your favorite uncle, the Beanie Baby kingpin whose generous graduation gift morphed into a nest egg of some $1.3 million by the time you turned 62.

Impressive, no?

It's a miracle
That growth owes to what Albert Einstein once reportedly described as "the greatest mathematical discovery of all time" -- the miracle of compound interest. In truth, there's nothing miraculous about it; it's just basic math. As your nest egg grows, that 11% return operates on a bigger and bigger stash of cash, resulting in the transformation of a relatively modest sum of start-up money into a fortune you can bank on -- literally.

The trick, of course, is that you've gotta get going. Give that $20,000 just 20 years to compound and, at the same 11% growth rate, you'll wind up with a little more than $160,000. Give it 10, and you'll be looking for someone else to pick up the bar tab: $56,788 is the not-so-magic number.

Step by step
The bottom line? When it comes to investing, time really is on your side -- or at least it can be if you decide to put "paying yourself first" at the top of your priority list. That's the first step; the second is putting your money to work intelligently, allocating your assets in a way that's consistent with your timeline and tolerance for risk while providing the maximum bang for your investment buck.

The Fool is full of ideas on that front, and if you're an investing newbie, I'd encourage you to check out GreenLight, a new service designed with beginning investors in mind. Since our debut earlier this year, we've zeroed in on such hot topics as choosing a broker, growth stocks, valuation, and an alternative approach to S&P index investing that provides greater diversification and better returns to boot.

If you'd like to sneak a peak at GreenLight, just click here. A risk-free guest pass to the service is yours for the taking. There's no obligation to stick around if you find it's not your cup of tea, so go ahead and give GreenLight a whirl. And be sure to let us know what you think on our members-only boards: Those come free with your guest pass, too.

Shannon Zimmerman runs point on the Fool's Champion Funds newsletter service, and at the time of publication didn't own any of the securities mentioned above. Starbucks, Amazon.com, and eBay are Stock Advisor recommendations. You can check out the Fool's strict disclosure policy by clicking right here.