Professor Jeremy Siegel wrote a book and he called it, The Future for Investors. I read it and wept.

A chart on page 126 shows how $1,000 invested in stocks back in 1871 would be worth about $250,000 today. Ah, but if I'd only reinvested those dividends! That $1,000 would have ballooned to nearly $8 million.

But what's so "accidental" about that?
After all, haven't I just described a fairly obvious way to invest? Sure, back in 1871, and even in the 1940s and 1950s. Back then, investors actually bought stocks for the streams of cash flow they provided in return -- their dividends.

You may even recognize that as the very definition of the word "investing." But sometime in the early-1960s, things took a nasty turn. Suddenly a new generation of "investors" bought stocks solely to sell them to somebody else at a higher price. Sound familiar?

It should, because by 1987, unless you were retired (or hopelessly out of date), dividends were an afterthought. And by the go-go '90s, any self-respecting company with the gall to pay one stood accused of being "mature" or worse, washed up and entirely out of ideas.

Enter my accidental uncle
By 1965, hotshot brokers were hocking the American dream of "capital appreciation." Back then, it was the Nifty 50, mega oil and chemical conglomerates, and consumer monsters like PepsiCo (NYSE:PEP), Philip Morris, and Johnson & Johnson (NYSE:JNJ).

But these stocks also happened to pay dividends. And that's how my uncle accidentally got rich. The "cheaper" these hot stocks got during the bear market of the '70s, the BIGGER his dividends got as a percentage of the new shares he bought. That's right, my uncle got rich. in the worst market in half a decade!

Because even as he was missing the boat on "new economy" wonders like computer giant IBM (NYSE:IBM), he was locking in some of the highest dividend yields in history and ended up with thousands and thousands of shares of stock. Then, when the market finally turned in 1981... shocker! The stocks went up... the dividends went up... and the rest is history.

But Uncle, how'd you ever afford so many shares?
That's a funny story best told by example. Earlier we talked about Pepsi, Philip Morris, and Johnson & Johnson, so let's start with those.

Pepsi -- $2,000 invested in Pepsi as recently as 1980 is now worth more than $150,000. You would have started with 80 shares, but by reinvesting dividends, you would have 2,800 shares today.

Philip Morris -- $2,000 invested in Philip Morris (now Altria (NYSE:MO)) in 1980 is worth just under $300,000 today. You would have started with 58 shares. Today, thanks to stock splits and reinvesting dividends, you would have more than 4,300 shares.

Johnson & Johnson -- $2,000 invested in Johnson & Johnson in 1980 would be worth close to $140,000 today. You would have started with only 13 shares of stock. Today, thanks to reinvestment and splits, you would own more than 2,000 shares.

Believe it or not (I didn't believe it myself), if you'd bought those three stocks and reinvested your dividends, you'd have a portfolio now worth close to $600,000 after starting with an investment of only $6,000. And that's if you never added another penny.

Surely, it's too late for you and me?
Not even close. And I'm going to prove it using nothing more than a modest IRA rolled over from my stint in corporate America and a dividend nut named Mathew Emmert. Mathew has convinced me that he can help me beat the market and lower my risk by owning dividend-paying stocks.

So, with Mathew's help, I'm stuffing my old rollover IRA full of dividend payers. I've already bought a handful, including beaten-down Pfizer (NYSE:PFE) and Bank of America (NYSE:BAC) with its ridiculous 4.6% yield. I have a few bucks left to put to work.

The only rules are that every stock will offer a better-than-average dividend -- Microsoft (NASDAQ:MSFT) and its 1.3% yield need not apply -- and all dividends must be reinvested. That's why I opted to conduct this little experiment in my IRA instead of my brokerage account. This way, I can avoid the taxman until... well, later.

This is something you might want to try
If you've read my past columns, you know I have a portfolio of small caps, exchange-traded funds, and a handful of non-dividend-paying fliers. I invest this way for a number of reasons, but mainly because I've convinced myself I have a knack for it and... let's be honest, it's fun.

But we all have to grow up sometime and start playing the odds. That's why I've turned to Mathew and his Motley FoolIncome Investor newsletter service for advice on my most important investment. I have a hunch that in 30 years, I'll be glad I did. Maybe I'll accidentally get rich like my uncle.

As for the Wizard of Wharton, I don't think he offers stock picks. But Mathew Emmert does. If you want to see what Mathew's picking now, enjoy 30 days of free access to Income Investor. You won't pay a cent, and if you do subscribe, you can probably cover the cost with your dividend checks (though I'd recommend you reinvest those). To learn more, click here.

Fool writer Paul Elliott owns Pfizer and Bank of America. Pfizer and Microsoft are Motley Fool Inside Value picks, andBank of America is an Income Investor recommendation. The Motley Fool isinvestors writing for investors.