Please, be neat and detailed. Explanations would be great. I need to understand it. Thank you.

1. [5 points total] Drs. Bhattacharya and Malinowski are expecting their third child and therefore are in the market for a new, larger, home. They are looking at a traditional colonial style home with a swimming pool on Nottingham Terrace that will cost $999,000 to purchase. They are now comparing lending options and have identified two potential options. They have asked for your expert opinion to help them make an informed decision. Option A: A 30-year adjustable rate mortgage (ARM) in which the initial interest rate of 4.25% APR for the first three years of the loan. After this initial fixed rate period the interest rate will change as described below. This option will require a 22% down payment, which will be paid from their savings. The $12,800 in closing costs and fees can be included in the financed amount (i.e. the loan). Payments will made on a monthly basis. N (years) i (APR) 1-3 4.25% 4-6 4.75% 7-9 4.95% 10-30 5.05% Option B: Conventional 30-year mortgage with an interest rate of 4.75% APR with monthly payments. If they choose this option, they would need to make a 20% down payment and would owe an additional $12250 in closing costs and fees. They will make the down payment from their savings, however the lender will allow them to include the closing costs and fees in the loan finance amount (i.e. the amount borrowed). a) [2 point) Find the monthly payment for all years in both cases. b) [1 points) Consider the 89th payment specifically. How much with the couple's payment will be applied toward principal and how much toward interest? Compute interest and principle paid at payment 89 and the remaining balance after payment 89. c) [2 points) If they choose the conventional 30-year mortgage (i.e. Option B) then the couple will consider refinancing their loan once they have made 120 payments. Assume that the refinance option would be a conventional loan for an additional 15 years with an interest rate of 4.125% APR with no additional refinancing or closing costs. Payments will once again be made monthly. What will be the total interest paid in this scenario (consider both the original and refinanced loan)