"Get a new mortgage at 5.25% (5.38% APY) Today!" Look familiar? I'm sure it does. We can't get quotes for loans these days without seeing two interest rates (thank your federal regulators). It's often confusing. Will I pay 5.25% on my loan or will I pay 5.39% on my loan? The answer is both.

It all depends on the math, but we'll get to that in a second. In our interest rates above (borrowed from a bank's current special), the 5.25% is the APR. APR stands for Annual Percentage Rate. This is the rate on your loan if interest is compounded once a year. APY stands for Annual Percentage Yield; this is the rate you'll pay annually once the magic of compounding interest is added in. Make sense? No dude we need more.

Let's start with compounding interest. What is it? Compounding interest is the interest one earns on interest already earned. Say you have $10 in a savings account that pays 10% every month. After the first month you'll receive $1, giving you a total of $11 in the account. After the second month you'll receive $1.10. Why not just another $1? Because you are now getting 10% of $11, not 10% of $10. This brings your total to $12.10 after month 2. Month 3 will yield another $1.21 in interest, giving you a total balance of $13.31. Below you'll find a table that includes an entire year at 10% per month.

So now that you know how compound interest works, we can look at how the rates work on an annual basis. Since the monthly rate was 10%, then the annual rate should be 120% right? Well, we can check that easily by taking our original amount of $10, multiplying it by 120%, which gives us interest earned and adding the $10 from the original balance. $10 X 120% + $10 = $22. $22? That isn't the $31.38 we have in the table. What is the annual rate used to calculate an ending balance of $31.38? Take $31.38 and subtract the beginning balance of $10 and divide by $10 to get the percentage in growth. Add in 100% for the original balance and you have the total yield for the year. It looks like this ($31.38 - $10) / $10) = 213.8% yield + 100% = 313.8% growth. You can check this by multiplying $10 times the percentage rate of 313.8%.

That may have been difficult to follow. There are two snippets to pull out of all that mess: 120% and 213.8%. Spoiler Alert: 120% is the APR and 213.8% is the APY.

Let's look at this a different way. Your bank tells you that on day one you deposit the $10 and on day 365 they'll give you the $10 back plus 120% in interest. This would give you $22. But banks don't work on annual schedules like that. They pay interest monthly. So instead your bank tells you at the end of each month they'll give you 10% (120% / 12 months). On day 365 you're looking at the balance of $31.38.

The Annual Percentage Rate, is the quoted rate they'll divide by 12 to calculate interest each month. The Annual Percentage Yield is what the rate looks like when you included the compounded interest. Go back to the mortgage example: 5.25% APR and 5.38% APY. Those numbers are much closer than my example. That's because I used an outrageous interest rate (10% per month) to illustrate the point. But since you're so smart now, you can look at a table with the mortgage rates and see how it works in the real world. For simplicity, we are assuming you aren't making any payments to decrease the balance of your mortgage. Your mortgage is $100,000:

Compound interest works on loans too. The interest that was charged each month was 5.25% / 12 months = .4375%. But once you look at the annual picture, over the 12 months I was charged a total of 5.38% worth of interest.

Banks are required to make this distinction when offering you quotes on loans. But it's important that you understand the difference when you get the quote. Why? What if the mortgage officer quoted you 5.38% and you thought it was APY when actually he was giving you APR? 5.38% APR works out to about 5.52% APY and a loss of $200 a year on the $100,000 mortgage. $200 doesn't seem like a lot, but you get excited about saving 50 cents on cereal with the knowledge of coupons in the paper. It took you just as long to read this post as it would to clip a coupon, and this post could save you a heck of a lot more money.

You're welcome.