How to Calculate APR and EAR on a Mortgage Loan?

What is the APR and EAR on a mortgage loan for a new warehouse?

Given a 30-year mortgage loan for 80% of a $2,400,000 purchase price with a $13,000 monthly payment, what are the APR and EAR on this loan?

Answer:

The Annual Percentage Rate (APR) on this loan is 243.75%, and the Effective Annual Rate (EAR) is approximately 20.73%.

To calculate the Annual Percentage Rate (APR) and the Effective Annual Rate (EAR) on a loan, we need to consider the loan amount, monthly payment, and loan term.

In this case, the loan amount is 80% of $2,400,000, which is $1,920,000. The monthly payment is $13,000, and the loan term is 30 years.

To calculate the APR, we can use the following formula:

APR = ((Monthly payment * Loan term) / Loan amount) * 12 * 100

APR = (($13,000 * 30) / $1,920,000) * 12 * 100

APR = (390,000 / 1,920,000) * 12 * 100

APR = 0.203125 * 12 * 100

APR = 2.4375 * 100

APR = 243.75%

To calculate the EAR, we need to consider the compounding frequency. Assuming monthly compounding, we use the formula:

EAR = (1 + (APR / n))^n - 1

Since the compounding is monthly, n = 12

EAR = (1 + (0.203125 / 12))^12 - 1

EAR = (1 + 0.01692708)^12 - 1

EAR = (1.01692708)^12 - 1

EAR = 1.207314 - 1

EAR = 0.207314 or 20.73%