It is often purported that Albert Einstein referred to compound interest as the greatest force on earth. Strong words from one of the smartest men to ever live. Although this article's intention is not to ponder Einstein's most compelling views, we do intend to demonstrate the importance of understanding the difference between Annual Percentage Rate (APR) and Annual Percentage Yield (APY) and how one takes compounding into account while the other does not can affect the amount you pay on a loan or the amount you receive as a lender.

What is Compounding?
At its most basic, compounding refers to earning interest on previous interest. All investors want to maximize compounding on their investments, while at the same time minimize it on their loans. (For more detail on this subject, see Investing 101: The Phenomenal Concept Of Compounding.)

Compounding is especially important in our APR vs. APY discussion because many financial institutions have a sneaky way of quoting interest rates that use compounding principles to their advantage. Being financially literate in this area will help you spot which interest rate you are really getting.

Defining APR and APY
APR is the annual rate of interest without taking into account the compounding of interest within that year. Alternatively, APY does take into account the effects of intra-year compounding. This seemingly subtle difference can have important implications for investors and borrowers. Here is a look at the formulas for each method:

 
For example, a credit card company might charge 1% interest each month; therefore the APR would equal 12% (1% x 12 months = 12%). This differs from APY, which takes into account compound interest. The APY for a 1% rate of interest compounded monthly would be [(1 + 0.01)^12 – 1= 12.68%] 12.68% a year. If you only carry a balance on your credit card for one month's period you will be charged the equivalent yearly rate of 12%. However if you carry that balance for the year, your effective interest rate becomes 12.68% as a result of the compounding each month.

The Borrower's Perspective
As a borrower, you are always searching for the lowest possible rate. When looking at the difference between APR and APY, you need to be worried about how a loan might be "disguised" as a lower rate than it really is.

For example, when looking for a mortgage you are likely to choose a lender that offers the lowest rate. Although the quoted rates appear low, you could end up paying more for a loan than you originally anticipated. Banks will often quote you the Annual Percentage Rate (APR).

As we learned earlier, this figure does not take into account any intra-year compounding either semi-annual (every six months), quarterly (every three months), or monthly (12 times per year) compounding of the loan. The APR is simply the periodic rate of interest multiplied by the number of periods in the year. This may be a little confusing at first, so let's look at an example to solidify the concept: