You have $100 to open a savings account at XYZ Bank on January 1. The annual interest rate is 5%. How much will you have in five years?
Well, if the bank simply gave you 5% of your $100 at the end of the year, you would have $105 on December 31. If you left the $105 in the account to earn another 5% next year, at the end of that second year, you would have: $105 x 1.05 = $110.25. Not only did you earn interest on your original $100 in year two, you earned interest on year one's interest. That is, it compounded. If you carried this out another eight years, here's what your account might look like:
At the end of 10 years, you would have $162.89 in the account just for doing nothing. But it gets better. The example above assumes the bank pays interest on the balance at the end of the year (that is, the interest compounded annually). In the real world, a bank would usually pay you interest on your account balance at the end of every month (that is, the interest compounds monthly). The bank simply divides the annual interest rate (5% in our case) by 12 months, and applies that rate to your balance at the end of each month. So in year one, let's see what happens:
Notice that when the bank compounded the balance annually, you only had $105.00 at the end of year one. But if the bank compounds monthly, you have $105.12 at the end of year one. It may not sound like much, but consider the effect on a $500,000 beginning balance: At the end of 10 years, the investor has $814,447.13 if the interest compounds annually, but she has $823,504.75 -- a full $9,057.62 more -- if the interest compounds monthly.
Compounding doesn't just affect how much interest investors earn; it affects how much interest investors pay. For example, if that $1,000 savings account had really been a $1,000 loan to you from XYZ Bank, the amount of interest you pay would be influenced by how often the bank compounded the rate. The important lesson here is that the more frequently compounding occurs, the more interest is earned (or paid) on a balance. Some credit cards even compound interest daily, which greatly affects the borrower's balance owed.