Einstein once said that compound interest was "the greatest mathematical discovery of all time." Or maybe Yogi Berra said that. At any rate, Albert and Yogi got it only half right: Compound interest, along with time, is one of the most powerful forces in the universe. And you can quote me on that.

The examples I'm about to give will amaze and delight you, and should give you motivation to open a Drip or IRA or 401(k), or to continue contributing if you already have them. If you're a teacher, you should read this to your class. If you're a parent, you should read it to your kids.

Time saves you money
Imagine you're a 21-year-old, just starting your first post-college job (just play along). The human resources director asks if you want to start contributing to the 401(k) plan. The correct answer? You should jump up and down, hug him, and scream, "YES! YES!"

In almost no circumstance should you not begin saving and investing in that situation.

Let's say you're looking to retire in about 40 years, at the age of 61. You've decided a nest egg of $800,000 will do. By starting now and earning a modest 8% compound annualized growth rate (CAGR) over that time, you'll need to contribute $2,859 each year to reach your goal. If you wait 10 years to start saving, however, you'll have to pump $6,539 into your plan annually, or more than twice as much.

If you're able to achieve a 10% annualized return, roughly what the market has averaged over the years, you'll need to contribute only $1,643 each year, but $4,421 if you wait a decade.

Time makes you a better investor
Using the same example, a person starting at the age of 31 and earning 10% per year can't match the returns of a 21-year-old starter earning 8%. In fact, the 31-year-old would have to earn better than a 12% CAGR in order to be able to contribute the same $2,859 and still reach $800,000 by the age of 61.

Put another way, beginning 10 years earlier in this example is like adding 4% per year to your investing skills, which is huge over the long term. Starting early can forgive poor investing skills.

Here's an even more powerful illustration. (As if you weren't convinced already!) Two 51-year-olds are talking at a party about their 401(k) plans:

EarlyBird Johnson: I've earned a compounded rate of 8% over the past 30 years.
LateComer Larry: What a coincidence, so have I!
EarlyBird: Yes, I started contributing $2,500 a year when I was 21, but had to stop when I was 30. I've not contributed since, although the money continued to grow in my account.
LateComer: I, too, contributed $2,500 a year! However, I didn't start until I was 30. So, now that we're both 51, I've been contributing for 21 years, and you contributed only nine years. How much is in your account?
EarlyBird: Let's see... $169,723. How much is in yours?
LateComer (stunned): Uh.... just $136,142.

The lesson is clear: Never talk to anyone named "EarlyBird" at a party. Oh, yes... and start investing early.

For, you see, gentle investor, the nine-year penalty is even more severe than you think. EarlyBird contributed a total of just $22,500 over the nine years, while LateComer shelled out $62,500 over 21 years -- and still came up well short.

The lesson became even clearer when the two suddenly sober party animals sat down with pencil and calculator. How many more years of $2,500 contributions, LateComer wondered, would it take until he surpassed EarlyBird's total?

Assuming both continued to earn 8% annually, would it take three years? Five years? Well, no. In fact, after 10 more years -- 31 years after EarlyBird stopped contributing and LateComer started -- LateComer will still be behind, $333,034 vs. EarlyBird's $366,415.

Believe it or not, the story is still the same after the 50th year. And the 75th:

Year        EarlyBird                 LateComer
       Savings  |  Cum. Contr.   Savings  |  Cum. Contr.
       ----------------------  -----------------------
  9     $33,716    $22,500         $0          $0
 30     169,723     22,500       136,142     52,500
 40     366,415     22,500       333,034     77,500
 50     791,071     22,500       758,109    102,500
 75   5,417,627     22,500     5,389,275    165,000
 99  34,354,155     22,500    34,354,634    225,000
Assumes 8% CAGR; no adjustment for taxes

It's not until the 99th year, 90 years after LateComer started pumping in $2,500 annually, that he will be able to surpass EarlyBird's total. At that point, LateComer will have contributed a grand total of $225,000, compared to EarlyBird's paltry payout of $22,500. And it's all because of EarlyBird's head start.

The lesson is clear: If you haven't started by now, you might as well forget about it because you'll never catch up. No, wait... I'm just kidding!

The lesson is... start investing early. If you're not socking some money away on a regular basis, start now. Every month you wait to begin will cost you big money many years down the road.

Fool co-founder Tom Gardner once said, "The best time to start investing was yesterday. The next best time is today."

That doesn't mean you should rush right out and buy a bunch of penny stocks, or any stocks you haven't thoroughly researched. But it does mean you should contribute to your 401(k) if you're not already, and invest outside your retirement plan if you can. (With the usual caveat that this is money you won't need for several years... five at least.)

Don't worry about individual stocks; start with an index fund, and move to individual stocks only when -- if -- you're ready to. You can "drip" into an index fund just as well as you can drip into Johnson & Johnson (NYSE: JNJ) or Pepsi (NYSE: PEP).

Remember, time may be the single most important factor to your investing success. An early start means a below-average investor can earn a bigger pile of cash than an excellent investor.

Just get started, because time is money.

Rex Moore would gladly appear at your birthday party, but can't find the time. He owned no companies mentioned in the making of this column. His holdings can be found on his profile page; the Fool's disclosure policy sits patiently here.