Picture this:

Imagine if your portfolio doubled as an ATM machine, cranking out cash while you were sleeping, watching television, or reading the paper.

Every month a steady stream of payments flowed straight into your brokerage account. In some cases earning 10%, 25%, even 50% in returns on your original investment.  

As fantastic as it sounds, this is exactly what it's like to own some dividend-paying stocks. Of course, you don't build a double-digit income stream overnight. But with time, even a tiny yield can become a monster payout. It's the irrefutable math of investing.

ConocoPhillips (COP 0.39%) is a great example of what the power of compound growth can do for a stock's yield. Over the past ten years the company has increased its dividend at a 16% compounded annual clip. If you had bought and held the stock over that time, the annual yield on your investment would be almost 15% today. 

Take a look at the chart below to see what I'm talking about. This simple table shows the incredible power of small dividend hikes compounded over time. In this hypothetical investment, I assumed you purchased ConocoPhillips shares at around $18.44 near the beginning of 2003. 

The Power of Compounding in Action

YearDividend per ShareYield on Cost
2013 $2.70 14.64%
2012 $2.48 13.47%
2011 $2.01 10.91% 
2010 $1.64 8.89% 
2009 $1.46 7.90% 
2008 $1.43 7.77% 
2007 $1.25 6.78% 
2006 $1.10 5.95% 
2005 $0.90 4.88% 
2004 $0.68 3.70% 
2003 $0.62 3.37% 

Source: Yahoo! Finance

Let's play out this hypothetical investment out another 10 years. Assuming ConocoPhillips can continue to grow its dividend at a 10% annual clip, the yield on our original investment will grow to 38% by 2024. That's the magic of compound growth in action. 

ConocoPhillips is a good example of this process, but there are plenty of other companies in the energy sector that have generated similar returns. 

Take ExxonMobil (XOM 0.39%) for example. Many income investors skip over this stock because of its meager 2.6% yield. But over the past decade, the company has grown its dividend at a 10% compounded annual rate. Had you bought and held the stock over that time, your yield on cost would be 7%. 

Chevron (CVX 0.57%) has done even better. Over the past decade the company has increased its dividend at an 11% annual clip. If you had held the stock over that time, the yield on your original investment would be 11.5% today. 

The great thing about the oil patch is that these companies are sitting on million of barrels of oil. No matter how much money the Fed prints, the real value of that oil isn't changing as a result. 

Of course, a decade ago none of these stocks had yields that would blow your socks off. But through compounding small gains over time, almost all of these companies now yield in the double digits. 

This common sense type of investing doesn't require extensive education. You certainly don't need an MBA. Just some basic arithmetic will do.

You don't necessarily need smarts either -- just enough observation skills to identify wonderful businesses.

What does it require? The only skill you really need is patience. Anyone can achieve these types of results so long as they are willing to compound their profits over decades and don't fuss over daily fluctuations. Unfortunately, patience is a rare commodity on Wall Street.

Foolish bottom line
The returns generated by ConocoPhillips are evidence that even a small yield can become big given enough time. That's not a lesson most investors want to hear. But it's the irrefutable math of investing.