The Difference Between APR and APY

If you've done any sort of comparison shopping to find the best rates on savings accounts or loans, you've likely seen the initials APR and APY after the interest rate. You usually see APR after interest rates quoted for loans, and APY after interest rates quoted for investments (savings accounts, checking accounts, certificiates of deposit, etc). What's the difference?

Before we get into the differences, let's define what they stand for. APR stands for Annual Percentage Rate and APY stands for Annual Percentage Yield. Now that we have that out of the way, we can begin investigating the difference between the two.

Believe it or not, the two terms were not made up just to confuse people. There is a valid reason for the difference - compound interest.

What Is Compound Interest?

Simply put, compound interest is interest earned or charged on previous interest. If you are investing, this is a good thing. You want to earn compound interest. If you are borrowing, this is a bad thing. You do not want to pay compound interest.

Compound interest is a bit tricky because there are two factors that really affect how it is calculated. The first, obviously, is the interest rate. By convention, interest rates are usually quoted on a per-year basis. For example, if we say something pays 12% interest, it's assumed to be 12% interest per year. But another factor determines how much money you will have at the end of one year - the compounding period or compounding frequency. Think of the compounding frequency as how often your accrued interest gets added to your principal and thus earns more interest.

Let's look at an example. Suppose we have $100 and we invest that in a product that pays 12% per year, compounded monthly. Our compounding period is a month, so at the end of each month, we are paid our interest and that gets added to our principal that we earn interest on the following month. Because interest rates are quoted on a per-year basis, to do our math, we need to convert that to a per-month basis. Twelve percent per year is equal to one percent per month.

The following table illustrates our balance for the first 3 months. Notice that in the second month, we get paid interest on the interest we earned in the first month. Likewise, in the third month, we get paid interest on the interest we earned in the second month.

Month	Starting Balance	Interest Earned	Ending Balance
1	100	1	101
2	101	1.01	102.01
3	102.01	1.0201	103.0301

Using a compound interest calculator like the one found here, we can see that after one year, our balance will be $112.68.

This is where the difference between APR and APY comes into play. In this case, 12% is our APR - the annual percentage rate. But if we just figured out 12% of $100, that is $12, so at the end of the year, we'd expect to have $112. When we take into account the monthly compounding, we end up with more money - $112.68. The amount we actually get, or yield, is larger due to compounding. To account for this, we use the annual percentage yield figure, or APY. In this case, our APY is 12.68%.

Note that the compounding period has a direct influence on APY. In our example, if we changed our compounding period from monthly to daily, our APY becomes 12.747%. The more often we add that accrued interest to our principal, the more money we make. Likewise, a longer compounding period results in a lower APY. If our investment was compound quarterly (every 3 months), the APY drops down to 12.55%.

You can play around with various compounding periods to see the effect on APY using this calculator. Note that if your compounding period is one year, your APR and APY will be equal. (In this case, the interest is often referred to as simple interest, rather than compound interest.)

APY gives consumers an easy way to compare to investments. for example, if you were asked to choose between two investments where one paid 12.2% compounded monthly and one paid 12.5% compounded semi-annually, it would be somewhat tedious to figure out which one will earn you the most money. But if we look at the two investments in terms of APY, it becomes easy. The first has an APY of 12.905 and the second has an APY of 12.890 (which can be found using the calculator linked to above). All other things being equal, the first investment will generate more money for us, so that's the one we should choose, even though the quoted interest rate is lower.

Which Do I Pay Attention To - APR Or APY?

My examples so far have been using investments - situations where we are earning money - but these terms also apply to loans and interest we might be charged by a lender. You may have noticed that the APY figure is almost always higher than the APR figure. This leads to an interesting advertising phenomenon: For products where the consumers pay interest, the lower APR figure is often often quoted. For products where consumers earn interest, the higher figure, APY, is often quoted. Here's two examples from Bank Of America's website:

Advertisement for a loan

 

Advertisement for a savings account

In general, you always want to pay attention to the APY figure. If you are investing, you want that number to be as high as possible. If you are borrowing, you want it to be as low as possible. You may need to read the footnotes or small print disclosures to find it, but it should be provided somewhere. If you are comparing two products, make sure you are comparing apples to apples - APY to APY and not APR to APY.

Credit Cards

I've written previously about how you should not carry a balance on your credit cards, but here's another reason to not do that: You're paying a higher interest rate than you think. The interest rate listed on your credit card statement is quoted as APR, but the amount you are actually paying, the APY, is almost a full point higher! And, not surprisingly, they don't make it easy for you to find out.

Here's an example from my Discover credit card. This is on my statement:

This is in the fine print on my statement:

No details, but it sure sounds like are going to be compounding daily. To find out for sure, you can call the number listed, or dive into your cardmember agreement document you received when you signed up for the card. (You did save that, right? Me neither. Luckily, we have the internet.) Here's what they say:

Yup. They describe it, rather than flat out say it, but by adding the accrued interest to your balance each day, they are compounding daily. Now let's hop back to our APR to APY calculator and see what that does to our 11.99% APR interest rate:

Yikes!! That's almost a full percentage point higher! Don't carry a balance, folks.