Question

1. A 30-year mortgage for $220,000 has monthly payments at a 6% nominal annual rate. If a borrower’s loan origination fee is 3% and is added to the initial balance, what is the true effective cost of the loan? (8 pts)
2. If the house is sold after six years and the loan is paid off, what is the effective interest rate? (4 pts)

Graph the effective interest rate as the time to sell the house and pay off the loan varies from one to 15 year

i found the answers in chegg i couldnt get can u please include a solution with clarity and please include the graph in the solution also.

Answer 1

1. True Effective Cost of Loan = Total Interest Cost + Origination Fee

= $ 17,985 + $ 6,600 = $ 24,585

2. Effective Interest Rate at year 6

= Interest Upto year 6 / Cost of Loan

= $ 6268 / $ 226,000

= 2.77 %

Effective Interest rate is defined as the total interest cost incurred over the period of loan tenure.

In the given question, since origination fee has been added to the initial balance of the loan, the interest is also to be paid on the fee amount. Therefore, the total cost of loan will include the total interest paid as well as the additional fees paid on the loan.

In part 2, effective interest rate has been calculated upto the year in which the loan has been paid off through the proceeds from tha sale of the house.

The effective interest rate is lower than the actual interest rate of 6% because the loan has been pre-maturely paid.

The graph represents the effective interest rates from Year 1 to 15 as calculated in Column H( highlighted in Pink in the screenshots)

For any query or clarification, please leave a comment.