APR, APY, and Mortgage Math: A Real World Example

I have lots of readers here in the central Iowa area, so it came as no surprise to me that when I began hearing an ad frequently on local radio advertising a particular mortgage product in terms that were a bit on the confusing side, I received an email about it. Jim writes in:

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

APR vs. APY Breakdown

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

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

The trick here is to understand that we’re talking about two separate and somewhat different things. An example will illustrate this difference clearly.

An Example: Quarterly Interest

Let’s say you have a loan from a bank that has 3.99% with interest that is compounded quarterly. That means that every three months, your loan is charged 1/4 of the interest for the year, which would be 3.99% divided by 4, or 0.9975% interest.

Let’s say your loan has a balance of $100,000 at the start of the year, to make the math more clear.

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

At the second quarter, your loan has a balance of $100,997.50 and that balance will be charged 0.9975% interest, or $1,007.45. This gives your loan a new balance of $102,004.95.

At the third quarter, your loan has a balance of $102,004.95 and that balance will be charged 0.9975% interest, or $1,017.50. This gives your loan a new balance of $103,022.45.

At the fourth quarter, your loan has a balance of $103,022.45 and that balance will be charged 0.9975% interest, or $1,027.65. This gives your loan a new balance of $104,050.10.

Over the course of a year, your $100,000 loan turned into $104,050.10, earning $4,050.10 in interest. That’s 4.05% of the balance of the loan, which is your APY.

Thus, this loan has a 3.99% interest rate, but a 4.05% APY.

In the United States, APY is legally defined as being the rate achieved when using daily compounding. In this case, that would give you an APY of 4.07%. So, where does the rest of that 4.22% come from?

The Other Parts of a Mortgage

What the radio ad isn’t telling you is that in order to get that 3.99% interest rate, you’ll have to pay some fees and possibly a discount point or two. These are up-front costs that add to the balance of the loan.

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

These fees will be rolled into the true APR that the lender has to give you (not that nominal rate given on the radio that doesn’t include these fees), and it’s that APR that you should be paying attention to if you’re intending to live in the house for a long time.

Another point worth considering is the fact that banks are allowed to advertise interest rates as much as 0.125% lower than what they’ll actually give you. In theory, this is done to allow for market fluctuation between the time you hear the ad and the time you sign on the dotted line, but lenders often push this so that they can advertise with seemingly incredible low rates.

What’s the moral of the story? Two things.

First, shop around. Getting a mortgage is a major financial decision, one that will have an impact on you for a long time. You owe it to your finances to shop around.

Second, get the APR on paper. Remember that APR takes into account most loan costs (points, most loan fees, mortgage insurance), but doesn’t account for some other charges, like application fees, title insurance, title examination, appraisals, document prep, and so on. You’ll likely have to come up with some additional cash for those when you move forward with the loan.

No matter what, never take out a mortgage based on an advertisement. This is far too important of a decision to do it based on a radio ad. Spend the time doing your homework and shopping around first, even if your favorite radio host is recommending a particular product.

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  1. Molly says:

    These kinds of concrete number examples are very helpful. Thanks.

  2. Jonathan says:

    I’ve always wondered something about APY, so now seems a good time to ask it. I understand APY when speaking in terms of a savings account. When talking about a loan, however, the term APY does not seem like an accurate term. The same concept applies, but it is not a yield for me in this case, it is what I’m paying in interest. I suppose you could say that the customer pays a 3.99 APR on the mortgage, and the lender receives a 4.22% APY, but that makes it sound like the bank is somehow getting more than the customer is paying them.

    Sorry for the ramble. Basically I’m just trying to say that for loans there should be a separate term roughly equivalent to APY, but that more accurately reflects that it is the amount being paid, not the yield. Hope that makes sense.

  3. Ruth says:

    Another thing to look out for is that lending agencies advertise their BEST rate – and to get that rate you have to meet certain criteria, like a 730 credit score, for example. You may be offered a different best rate based on your credit score, current debts, income, etc.

  4. Molly says:

    @Jonathan, it is the yield to the lender. The term APY seems to be consistently used across the industry like that – so if you have a savings account, you’re the lender, and the APY applies to you. The opposite is true when you have a loan or a credit card balance.

  5. valleycat1 says:

    Yes, Ruth (comment 3), and the criteria are completely invisible to the consumer & explanations from the lender as to why they can’t give you the best rate are inscrutable at best.

  6. Ryan Loos says:

    I love how banks and other financial institutions can get away with this type of advertising without telling you all of the facts. Like in comment #3 about the credit score. This is just like in the auto industry when they advertise 0% interest loans but they know that is just a teaser rate to get someone on the dealership lot. About 65% of people who come in for the 0% do not qualify and end up with a higher interest rate.

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