What is the difference between APR and APY?

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For loans or investments that involve compounding interest, there are two popular interest rate related terms.

1) Annual Percentage Rate, or APR, is a measure of how much interest will be on an annual basis without taking into account compound interest.

2) Annual Percentage Yield, or APY, is the same interest rate measure, but accounts for compound interest - a better measure of how much you will actually pay in interest. Banks and credit card issuers often express credit card interest rates in APR, in order to better hide just how much interest would cost.

Fortunately, calculating APY is a relatively simply matter, as is APR. Here are some examples so that you can calculate APR versus APY:

• APR = Period Rate x Periods per Year

Let's say a credit card company offers a 13% interest rate, and they express that rate in terms of APR with a monthly billing cycle.

• 13% = Period Rate x 12
• The Period Rate is 13%/12, or 1.083% per month.
• APY = (1 + Period Rate) ^Periods Per Year - 1
• APY = (1 + 0.01083)^12 -1
• APY = 13.8%

That extra 0.8% makes a difference in how much you pay each month. How much of a difference? Compare the payments on a $1,000 balance over the span of a year. Assuming you carry the balance consistently, you'd pay $130 in interest on a 13% APR but $138 in interest on a 13% APY.

Likewise, banks will publish the APY on an investment option (like a Certificate of Deposit, or CD) to make it look better than it is. Take a 4.5% APY CD from a bank. This looks like a very competitive, high savings rate, doesn't it? Let's break it down with some high school algebra:

• 4.5% = (1+Period Rate)^12 -1
• 4.5% + 1 = (1+Period Rate)^12
• ((4.5% + 1)^(1/12))-1 = Period Rate
• Recalling APR = Period Rate x Periods (in this case, 12): 4.4% APR

In this case, you're not getting the interest rate you thought you were based on an advertisement. If you were comparing this to, say, a 1 year Treasury note, and the note had a 4.45% APR, you could have purchased the higher APY CD without knowing you would have made less money by the end of the year!

There was a lot of math in this article, and that's okay - it's important to know the difference between APR and APY, and how they can be switched in advertisements from financial institutions. That way, when it comes time to shop around for rates, you can compare apples to apples. Here are two rules of thumb:

• APR is a better measure of interest rates for investments
• APY is a better measure of interest rates for debts and loans

Incidentally, student loans, including student loan consolidation, are calculated differently, as they do not feature compounding interest.