You are a bank officer designing a mortgage for a young couple. The current mortgage rate for 30-year fixed-rate mortgages is 3.5%, compounded monthly. The couple is buying a $300,000 house and has a down payment of $60,000. They wish to take out a fixed-rate mortgage on the remainder. a. What would be their monthly payment? b. Suppose the couple takes the mortgage. After 5 years, what would be the remaining principal amount owed on the mortgage? c. Suppose that after 5 years, fixed-rate mortgage rates drop to 2.25%. If the couple refinanced the loan (at no cost for now), how much could they reduce their monthly payment such that they still pay off the loan at the same time (25 years from when they refinance, for a total of 30 years)?d. Alternatively, the couple could decide to refinance at 2.25%, continue to make the same mortgage payment, and reduce how long it takes to repay their mortgage. If they kept their same payment, how much earlier would they pay off the mortgage? e. Suppose that there were title and escrow fees associated with refinancing the mortgage, paid at the time of the refinancing. What is the most these fees could be in order for it to be worthwhile for the couple to refinance?