If you believe that becoming a millionaire is pie-in-the-sky thinking for the average American, think again. All it takes is discipline, patience, and some lifestyle decisions.

Look at these numbers: An individual who can scrounge up $4,000 a year to invest can become a millionaire in 34 years if he or she earns 10 percent annually on the investment after taxes. On the surface, that may seem difficult. However, the Dow Jones Industrial Average has had an average annual return of nearly 11 percent since the 1920s. And 34 years is not really that long. A 30-year-old who starts tomorrow can be a millionaire before age 65.

The numbers are even more impressive if you can save more and get a higher return. For a married couple to save $10,000 a year is not an easy task, but it is possible if they limit the French restaurants and European vacations. If they earn 10 percent annually, they will have $1 million in 25 years.

Let's say that you can't afford to put away $4,000 but are able to save $1,000 a year. The numbers are still impressive. By investing $1,000 a year at 10 percent annually, you will amass nearly $300,000 in 35 years—not $1 million, but not a puny retirement nest egg either.