How the Annual Percentage Rate (APR) is Calculated

The Annual Percentage Rate (APR) is required by law to be disclosed for consumer credit, including mortgage loans. It is helpful to understand what the APR means and does not mean to the borrower.

To start with, consider two lenders who charge 8 percent in interest on a $100,000 loan. Lender A also charges 3 points but does not charge the borrower any fees for taking the application, doing an appraisal, etc. Lender B charges only 2 points, but charges the borrower $1000 to cover the application fee, credit report, appraisal, etc.

In this example, the borrower's expenses are identical with the two lenders: 3 points, or $3000 up front, and 8 percent interest over time. However, lender B would be allowed to quote a lower APR, based on 8 percent plus only two points. Lender B's fees can be separated out and not included in the APR.

To calculate the APR for a loan with points, go through the following steps:

1. Add the points to the loan amount to get an Adjusted Balance.
2. Find the monthly payment on the Adjusted Balance.
3. Return to the original loan amount, and find the interest rate that would result in the monthly payment found in step 2. This is the APR.

One point is one percent of the actual loan balance. In our example, the actual loan balance is $100,000 and lender A's 3 points amount to $3000, for an Adjusted Balance of $103,000. Next, calculate the monthly payment using the loan's interest rate and the Adjusted Balance. Using the mortgage payment calculator, the monthly payment on a loan of $103,000 at a rate of 8 percent is $755.78.

Now, the APR is the interest rate that would amortize the original balance of $100,000 using the monthly payment we just calculated, of $755.78. We solve for the APR the way we solve any high-order polynomial: by repeated guessing. If we plug in 8.3 percent and a balance of $100,000 into the mortgage payment calculator, the monthly payment comes out below $755.78. If we try 8.4 percent, it comes out high. If we use 8.31 percent, it comes out at $755.49, which is as close as we can get without taking the APR out to three decimal places.

The APR calculation pretends that we amortize points over the life of the mortgage. Because of this, it is unwise to compare APR's on mortgages with different terms, for example a 30-year term compared with a 15-year term. If both loans charge the same number of points and the same interest rate, the 15-year loan will have the higher APR (in our example, it would be 8.51 percent).

Other regulatory points of note:

• The APR must be disclosed within three days after the borrower's application has been received.
• The APR can change by as much as 1/8 of one percent before settlement without requiring disclosure by the lender.
• The APR is considered accurate if it is not more than 1/8 of one percent above or below the rate that would be calculated in accordance with the official method.
• Mortgage insurance premiums (PMI) must be included in the calculation of APR.

Based on the foregoing, never choose a loan based on APR aloneYou need to know:

• The interest rate
• Points
• Fees
• PMI payments

Then, use the mortgage analysis worksheet to see how the loan would work and to compare it with other loans.