You are considering a 30-year mortgage that charges 0.4% interest each month to pay off a $250,000 mortgage.

a. Determine the monthly payment p that allows the loan to be paid off at 360 months.

b. Now assume that you have been paying the mortgage for 8 years and now have an opportunity to refinance the loan. You have a choice between a 20-year loan at 4% per year with interest charged monthly and a 15-year loan at 3.8% per year with interest charged monthly. Each of the loans charges a closing cost of $2500. Determine the monthly payment p for both the 20-year loan and the 15-year loan. Do you think renaming is the right thing to do? If so, do you prefer the 20-year or the 15-year option?