In spite of all the people who shop for the best interest rate, there are only few who have actually done the math. Understanding how interest rates work can help you see how important differences in rates can be.

It is important to remember that the amount of money that you owe increases with compound interest. This means that your interest will get added to your principal, and you will pay interest on the interest you owed from the month before (and the month before that, and so on).

Here is how compound interest works. If you took $10,000 and left it in a savings account at 20% annual compound interest, after 10 years you would have $61,917. After 20 years, $383,375. After 30 years, $2,373,763. 40 years, $91,004,381. And 50 years, $563,475,143.

If you account for, say, five percent inflation, that money would have a $10,732,859 in today's dollars. That's some return on an initial investment of $10,000!

This is the way the credit card companies make their money. Be very wary of compound interest, at least when you are paying it instead of receiving it!

Let's work through a more realistic example. Say you have an average unpaid credit card balance of $1,000 at 15% APR. If that principal stays at the same amount (i.e., your purchases equal your payments), you will owe $150 for interest in the first year. This $150 is added to the principal, and then interest is charged on that. The second year, keeping the principal at $1,000, you'd owe another $172.50, for a total of $1322.50. It goes on, and the next three years would see debts of $1,520.88, $1,749, and $2,011.35. So, five years later, your debt will be twice the amount that you originally borrowed!

If you let this kind of situation go on long enough, you'll end up paying on that credit card for years and still not clearing the debt.

There might not seem to be that much difference between 15% APR and 12% APR. But that three percent difference is significant. At 12% APR, the same scenario would calculate out this way over five years: $1120, $1254.40, $1404.93, $1573.5, and $1762.34. There is a savings of $249.01 from the three percent difference–almost a quarter less interest.