Q&A: What does APR mean?

Question

My bank is currently offering a 3 month CD that pays a 4% APR. Does that mean if I buy a $5,000 CD, it will pay me $200 after 3 months?

Answer

The CD will not pay you $200. It will pay you $50.16.

APR Defined

APR is an abbreviation that stands for Annual Percentage Rate. The key point to emphasize is ANNUAL. This is the rate of return for a given investment spread over a year. Since this particular CD is only open for 3 months, we have to convert the annual rate. We will convert it to a monthly rate, and then add up the interest earned over 3 months. To convert an annual rate to a monthly rate, simply divide it by twelve. This means that 4% APR is the same as a 1/3% monthly rate. 1/3% of $5,000 is $16.66 each month, and for three months that gives us a total interest earned of $50.

Other Rates

Anyone notice something strange here? In the short answer, I said that the CD would pay $50.16, but in the previous section we figured it would pay only $50. What’s the difference? The difference comes from the power of compound interest.

The calculation of $50 in the APR section was a calculation of SIMPLE interest earned, but our CD pays COMPOUND interest. What’s the difference? See, in the first month, the CD will earn $16.66. This means that starting month 2, our CD has a value of $5,016.66. 1/3% of $5,016.66 is $16.72. The interest earned went up because the interest from the first period also earned interest. In the third month, our CD is worth $5,033.38. 1/3% of $5,033.38 is $16.78. So after our interest has earned interest, we are left with $5,050.16. Pretty cool, huh?

Simple VS Compound Interest

But what if there were an easier way to calculate the effect of compound interest? Sure, $0.16 is not a large amount to be off, but what if you were calculating your mortgage, or your retirement? The effect of compound interest is much stronger over longer periods of time. Fortunately, there is usually a very easy way to determine the exact effect of compounding. This is done through the use of effective rates. An effective rate is a rate that factors in the effect of compounding to allow you an easy way to figure your exact return from an investment. There are many types of rates, from nominal to real to effective, from yields to rates, and it can be very confusing to determine which number you should be most concerned with. Well fear not. Below is a quick list of the most common terms you will find used in the financial world to describe interest rates:

APR
The annual percentage rate is the interest rate that is used to calculate the payment on a loan or an investment. This number is based on simple interest, and does not include the effects of compounding interest. Therefore, it can be used to give only an estimate of interest earned/paid.
APY
The annual percentage yield is the annual rate that factors in the effects of compounding on your interest earned/paid. It is used to calculate the precise amount interest on an investment or loan. If you want to know exactly what your investment will pay, use the APY as your interest rate. In the case of the above example, you could use the APY of the CD (which the bank probably provides) instead of the APR and calculate the interest the same as we did in the “APR Defined” section. This would provide you the precise interest earning of the CD. APY is more frequently used for interest that you.
EAR
You will usually see this one on the same page as the APR for a loan, credit card, etc. You may have noticed that the EAR is always higher than the APR. This is because the EAR is the effective annual rate, and it takes into account the effect of compounding interest, fees, charges, and time. This is the rate you should use when comparing two loans. And remember that the EAR is the true cost of the loan, not the APR. The APR understates the true cost of the loan.

Is everyone thoroughly confused? Well, don’t stress about all these terms too much. You don’t have to memorize all these terms and what they mean and how to calculate them. What you need to be focused on is just one thing: Effective rates tell you the true cost of a debt, and APY tells you the true gains of an investment. When looking at a loan, look for the effective rate. It will probably be listed simply as the EAR. A CD or savings account may or may not tell you the APY, but you can at least use the APR to get a close estimate of your investment gains. If you are fortunate enough to be given the APY of the account, then use that instead of the APR to get a much more accurate picture of exactly how much interest you will earn.

Posted on 11 Dec 2008