A borrower takes out a 30-year mortgage loan for $100,000 with an interest rate of 6% plus 4 points.What is the effective annual interest rate on the loan if the loan is carried for all 30 years?

Question

Quizplus · Accepted Answer

The borrower pays 4 points, or 4% of the loan amount, upfront as a closing cost. Therefore, the actual amount received by the borrower is $100,000 - $4,000 = $96,000. The annual interest on the loan is 6%. However, because of the points, the effective annual interest rate is higher. To calculate the effective annual interest rate over the 30-year period, we can use the following formula:

Effective Annual Interest Rate = (1 + (Annual Interest Rate - Points)) ^ (Number of Years in Loan) - 1

Plugging in the values:

Effective Annual Interest Rate = (1 + (0.06 - 0.04))^30 - 1 = 0.064, or 6.4%

Therefore, the best choice is C, with an effective annual interest rate of 6.4%.

A Borrower Takes Out a 30-Year Mortgage Loan for $100,000