Question

Kevin in California has owned his home for 2 years and expects to live in it for at least 7 years. He originally borrowed $700,000 at 4% interest rate for 15 years to buy the home. He still owes $629,000 on the loan. Interest rate have since fallen to 1.99%, and Kevin is considering refinancing the loan for 13 years to finish the loan as the original planned time. He would have to pay 1 point on the new loan with no prepayment penalty on the current loan. Suppose that the account savings can be invested monthly at 2% interest rate. The possible prepayment penalty and the closing cost can be investment at the beginning of the new loan at 2%, monthly compounding.

a) What is Kevin's current monthly payment?
b) Calculate the monthly payment on the new loan.
c) Advise Kevin on whether he should refinance his mortgage using the Run the Numbers worksheet, "When you Should Refinance Your Mortgage" on page 285

Answer 1

a) Kevin's current monthly payment is $4,640.99. b) The monthly payment on the new loan is $4,212.05. c) Kevin should consider refinancing if the total cost of the new loan is lower than the total cost of the current loan.

Step-by-step explanation:

a) To calculate Kevin's current monthly payment, we need to use the formula for calculating the monthly payment on a loan. The formula is:

Monthly Payment = loan amount * (monthly interest rate / (1 - (1 + monthly interest rate)^(-number of months)))
Using this formula, we can plug in the values provided: loan amount = $629,000, interest rate = 4%, and number of months = 15 years * 12 months/year = 180 months. After calculating, Kevin's current monthly payment is $4,640.99.

b) To calculate the monthly payment on the new loan, we need to follow the same formula as above, but with the new loan amount and interest rate. The new loan amount is $629,000 (remaining balance on the current loan), and the interest rate is 1.99%. The number of months for the new loan is 13 years * 12 months/year = 156 months. After calculations, the monthly payment on the new loan is $4,212.05.

c) To advise Kevin on whether he should refinance his mortgage, we need to compare the total cost of the current loan to the total cost of the new loan. We can do this using the Run the Numbers worksheet on page 285, which takes into account the prepayment penalty and closing costs. Knowing the closing cost and prepayment penalty would be helpful in providing more accurate advice to Kevin. However, based on the provided information, Kevin should consider refinancing if the total cost of the new loan is lower than the total cost of the current loan.