Mortgage Rates: APR and APY – Mortgage Math Made Easy

I have a lot of readers here in the central Iowa area, so I was not surprised that when I started listening to an ad on the local radio a lot promoting a particular mortgage product in somewhat confusing terms, I emailed it about it. Jim writes in:

I just heard an ad on the radio offering a 3.99% mortgage. That makes sense to me. I’m confused if the ad immediately mentions an APY of 4.22%. What does that mean? What interest rate will I actually be charged?

First, let’s break down the terms.

APR or Annual Percentage Rate, defines the interest rate that is charged to the loan amount. You will be charged a total of 3.99% interest for this loan over the course of a year.

APY, or Annual Percentage Yield, describes the percentage of the principal of the loan that you will have to pay over the course of the year.

The trick here is to understand that we are talking about two different and slightly different things. An example should clearly illustrate this difference.

An example: quarterly interest
Let’s say you have a loan from a bank at 3.99% with interest accruing quarterly. This means that every three months your loan will be charged 1/4 of the annual interest, which would be 3.99% divided by 4 or 0.9975% interest.

Let’s say your loan had a balance of $ 100,000 at the beginning of the year, to make the calculation clearer.

In the first quarter, your loan of $ 100,000 will be charged 0.9975% interest, or $ 997.50. This will give your loan a new balance of $ 100,997.50.

In the second quarter, your loan has a balance of $ 100,997.50 and that balance is calculated at 0.9975% interest, or $ 1,007.45. This will give your loan a new balance of $ 102,004.95.

In the third quarter, your loan has a balance of $ 102,004.95 and that balance is calculated at 0.9975% interest, or $ 1,017.50. This will give your loan a new balance of $ 103,022.45.

In the fourth quarter, your loan has a balance of $ 103,022.45 and that balance is calculated at 0.9975% interest, or $ 1,027.65. This will give your loan a new balance of $ 104,050.10.

Over the course of one year, your $ 100,000 loan became $ 104,050.10 with $ 4,050.10 in interest. That’s 4.05% of the loan balance, that’s your APY.

So this loan has an interest rate of 3.99% but an APY of 4.05%.

In the United States, APY is defined by law as the rate that accrues on a daily basis. In that case, you would get an APY of 4.07%. Where does the rest of that 4.22% come from?

The other parts of a mortgage
What the radio commercial doesn’t tell you is that you will have to pay some fees and possibly a discount point or two to get that 3.99% interest rate. These are up-front costs that are added to the balance of the loan.

In this particular case, the fees and points will add enough to the loan balance to increase the APY from 4.07% to 4.22%. In other words, the sum of the fees and points will be about $ 165 on a $ 100,000 loan or about $ 817 on a $ 500,000 loan.

These fees are factored into the actual APR the lender is required to give you (not the nominal rate posted on the radio that doesn’t include these fees), and this is the APR to watch out for if you intend to live in the home for a long time.

Another point worth mentioning is the fact that banks are allowed to offer up to 0.125% lower interest rates than they actually give you. In theory, this is done to account for market fluctuations between the time you hear the ad and the time you sign the dotted line, but lenders often push this so they can advertise what appear to be incredibly low rates.

What is the moral of the story? Two things.

First you poke around. Taking out a mortgage is an important financial decision that will influence you for a long time to come. You owe it to your finances to poke around.

Second, you get the APR on paper. Keep in mind that the APR accounts for most of the borrowing costs (points, most loan fees, mortgage insurance) but not some other fees like application fees, title insurance, title review, reviews, document preparation, etc. You will likely have to put some extra cash on these if you can proceed with the loan.

Under no circumstances should you take out a mortgage based on an advertisement. This is far too important a decision to be made on the basis of a radio commercial. Spend the time doing your homework and shopping first, even if your favorite radio host recommends a specific product.

related posts
How to calculate APR and APY in a spreadsheet – and why you would want it
An Introduction to Compound Interest Using Tables, Part 2: Monthly Compound Interest, APRs, and APYs
The Simple Dollar Morning Roundup: V8 Revenge Edition
Explain simple interest, compound interest, APR and APY
Building a Better Blog For 2007: Don’t Forget the Basics Foundation

Add / view comments on this post.


The Christian Science Monitor has assembled a diverse group of the best business-related bloggers. Our guest bloggers are not employed or directed by the Monitor, and the views expressed are the bloggers’ own opinions, as are the responsibility for the content of their blogs. To contact us about a blogger, click here. To add or view a comment on a guest blog, please go to the blogger’s own website by clicking the link above.

Comments are closed.