How do you use APR to calculate loan costs?

Lately it seems that many people are receiving offers to refinance their mortgages. Should you refinance? What does that offer tell you about expenses? It does say something about expenses. Here’s how you may determine what they’re saying those expenses are.

Online there is a lot of discussion about the APR, but not a lot of help using it to calculate what it is supposed to tell you – how much in fees may you pay for this loan?

You can use the difference between the stated loan interest rate and the Annual Percentage Rate (APR) to estimate the costs of borrowing. The fundamental calculation is basically the same for any time of loan, be it for a car, a home, etc.

  • Interest rate refers to the annual cost of a loan to a borrower and is expressed as a percentage. I’ll call it the note rate.
  • APR is the annual cost of a loan to a borrower — including fees. Like an interest rate, the APR is expressed as a percentage. Unlike an interest rate, however, it includes other charges or fees such as mortgage insurance, most closing costs, discount points and loan origination fees. This is done by amortizing the fees out over the life of the loan as if they were additional payments, and then calculating a new rate. The APR is typically higher than the note rate because it includes additional expenses.

Note that it is NOT the numerical values of interest rates today, or in the future (in other words, interest rates are low today); rather, it is the relative DIFFERENCE between the note and APR rates that informs you.

The APR is intended to give you more information about what you’re really paying. There are some caveats to using it though.

First, if you don’t intend to stay long term in the house you’re borrowing for, then it may be more beneficial to pay closing costs up front in cash rather than put them into the loan. Secondly, if you’re comparing loans from more than one lender, be sure to have them explicitly explain what costs are included in the loan, and what costs are not, because different lenders include costs differently. This is especially important for those quotes where the APR and note rate are the same – what costs are you paying that are not included in the amount borrowed directly?

Let’s use the handy online calculator that solves for any missing loan input to go through an example.

The fees are added to the original loan amount ($200,000 + $3,000) to create a new loan amount ($203,000) … or the amount you are really borrowing. This total borrowed amount, along with the note rate (5.00%), is used to calculate a monthly payment ($1,089.75) based on a 30 year note amortized monthly (excludes property taxes and insurance; and the calculator can do other loan terms too).  The APR is then calculated by working backwards to figure out what the rate would have to be for a loan with the that monthly payment ($1,089.75) and the original loan amount ($200,000).  This is your APR (5.13%).

First an example to get used to the calculator:

Using the calculator for the above example, assuming you’re receiving offers from lenders on a Truth in Lending form:

  • First, from the Truth in Lending form, you would enter
    • The amount of the loan = the total amount borrowed including expenses or $203,000.
    • The interest rate charged for the NOTE rate, or 5%.
    • Number of months (for a 30 year mortgage (12 x 30), or 360.
    • Number of payments per year, or 12.
    • Finally, press the “Compute” button for the amount of the payment.
  • Then, working backwards as explained in the example, you would enter
    • The amount of the loan now = the total amount borrowed without fees, or $200,000.
    • Number of months (for a 30 year mortgage (12 x 30), or 360.
    • Number of payments per year, or 12.
    • The amount of the payment, or $1089.75.
    • Finally, press the “Compute” button for the interest rate charged for the APR rate, or 5.131%.

Now, how do you use the offer?

But, when you get an offer to refinance, all you have is the interest rate and APR, payment, and a total loan amount. What are the total fees they’re including in that loan offer? They have not yet provided a Truth in Lending form (so you can check things via the first example above). You may still do the process above using the information typically provided in those refinance offers: Loan amount, note rate, APR, and monthly payment … but, now you’re interested in how much you’ll actually receive AFTER fees.

Using the calculator, you would enter:

  • The APR rate stated, or 5.13%.
  • Number of months (for a 30 year mortgage (12 x 30), or 360.
  • Number of payments per year, or 12.
  • The amount of the payment, or $1089.75.
  • Finally, press the “Compute” button for the total amount you’ll actually receive after fees, or $200,029.49.
  • The difference between the “total amount borrowed” of $203,000 and $200,029.49 would represent the fees paid to obtain the loan proposed ($2970.51).

To see how the greater the spread between the APR and note rate affects the net proceeds you’ll receive with a higher APR, use the same inputs at above except change the interest rate to represent an APR offer of 5.5% and “Compute” the amount of the loan: $191,928.69. In this case the fees would equal $203,000 minus $191,928.69, or $11,071.31 in fees. You can see that the higher the APR relative to the note’s interest rate, the greater the fees.

Other loans may use the same process to calculate the fees buried in the offer.

The Consumer Financial Protection Bureau has a short discussion online about APR and a more detailed discussion may be found here.

Will you live long enough in the home to recover those fees in the above example? Divide the difference between monthly payments, what you’re paying now and the new payments after getting the loan, into the fees paid to see how many months it will take to breakeven.

There’s a lot more to consider than the basic calculation above to get an idea of fees paid (such as affordability based on your income), which are beyond the scope of this post’s objective of showing you how to calculate what the dollar amount of fees may be paid in the offer you’re receiving. Here you get the basic idea how to determine the fees they’re considering when providing you a loan.

Photo By N. Hurd, engraver [Public domain], via Wikimedia Commons

2 Responses to How do you use APR to calculate loan costs?

  1. Larry Frank, Sr. October 25, 2018 at 9:12 am #

    Here’s a possible way to evaluate many mortgage offers without triggering a loan application (and that effect on your credit score)

  2. Larry Frank, Sr. August 21, 2019 at 8:42 am #

    When it comes to making an informed decision about the right home loan, there are two standardized documents you’ll receive in the process to help you to understand the loan that you are applying for: the Loan Estimate and the Closing Disclosure.

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