Answer each question, showing your work. If you use a financial calculator, please still show your work, writing down how the problem gets solved (being as specific as possible). A house is to be sold for $400,000. The current mortgage interest rate is 3.5%. a. What are the monthly payments, assuming zero down, and a thirty year mortgage? b. What are the total principal and interest payments on this loan? c. Redo (a) with biweekly payments. d. Suppose the term of the loan is 15 years. Redo (a). e. Suppose that one second after the loan is signed, the rate rises to 4%. Evaluate the value of the 30 year loan to the lender. f. Evaluate the new value of the 15 year loan to the lender. Why is this number larger than the answer to (e) ? g. Suppose, in the thirty year mortgage, the borrower retires (prepays) the mortgage after ten years. What is the remaining principal? h. Now assume the lender charges one point. What is the new effective interest rate being charged the borrower (without prepayment)? i. What is the effective interest rate with one point, and prepayment after 10 years?