You have just purchased a new warehouse. To finance the purchase, you’ve arranged for a 35-year mortgage loan for 85 percent of the $3,350,000 purchase price. The monthly payment on this loan will be $16,800. What is the APR on this loan? What is the EAR on this loan?

APR = 2.43%

EAR = 2.46%

Explanation:

(a) What is the APR on this loan?

Annual percentage rate (APR) is the yearly interest rate that a borrower pays or an investor earns. It is expressed in percentage term without taking compounding into consideration.

This can be calculated using the Annual Percentage Rate (APR) formula as follows:

APR = {[(Fees + Interest amount) / Principal / n] * 365} * 100 ……………… (1)

Where;

APR = ?

Fees = 0

Interest amount = Interest rate * Purchase price = 85% * $3,350,000 = $2,847,500

Principal = Purchase price = $3,350,000

n = Number of days in the mortgage term = 365 days * 35 years = 12,775 days

Substituting the values into equation (1), we have:

APR = {[(0 + 2,847,500) / 3,350,000 / 12,775] * 365} * 100

APR = 2.43%

(b) What is the EAR on this loan?

The Effective Annual Rate (EAR) refers to the interest rate earned by an investor in a year after the compounding has been adjusted for over a specified period.

This can be calculated using the Effective Annual Rate (EAR) formula as follows:

EAR = (1 + i/n)^n – 1 (2)

Substituting the values into equation (2), we have:

i = Stated annual interest rate = APR = 2.43%, or 0.0243

n = Number of compounding periods = 12

EAR = (1 + 0.0243/12)^12 – 1

EAR =  0.0246, or 2.46%

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