Simple interest is interest calculated only on the original principal of the loan or asset.  Compound interest is when interest on a sum of money is periodically added as principal to the previous sum.  Each time this happens, the new interest is calculated based on that new sum, allowing for exponential growth.

Compounding, the act of adding the interest earned to the principal, is done perodically at different intervals depending on the financial institution.  The interest on your savings account might only compound yearly, while the interest on your car loan might compound monthly.

The picture above shows a more complicated calculation to demonstrate how much you will have after so many years with so much money invested with a certain interest rate.  There is a somewhat less accurate, yet much simpler way to get an idea in your head.

 The rule of 72 states that if you divide 72 by a given interest rate for a certain time period, the answer will tell you how many of said time periods it will take for your money to double.  If you expect a given investment to return 10% annually you divide 72 by 10.  The answer is, of course, 7.2.  If you invest $10,000 today at 10%, it will double roughly once every 7.2 years for as long as you have it invested.

If you are 20 now and leave that money until you are 62, and it continues to average ten percent, it will double roughly six times, leaving you with $640,000 for retirement.  Sounds a little more impressive than 10,000 doesn't it?

 The rule of 72 is what I use to keep myself motivated to tuck money away.  Being able to see what you have to gain makes the dry topic of saving and investing more interesting.  It is by no means a perfectly accurate formula, but it is handy to keep in mind when you are sitting there looking at a prospectus or quarterly statement.  It helps give a little perspective as to why you are jumping through these hoops.