Problem 3 (Required, 30 marks) Peter borrows an amount of $80,000 today and agrees to make quarterly interest payments to the lender. The loan charges compound interest at an annual effective interest rate 10.209%. At the same time, he makes the quarterly deposit into a sinking fund that earns compound interest at an annual effect interest rate 7.228%. The amount of kth deposit is k times the amount of interest payment made at kth payment date. Suppose that the borrower will repay the loan principal immediately once the account balance exceeds the loan principal at some repayment date, calculate (a) The number of payments made over the entire loan. (b) The total amount paid by the borrower over the entire loan. (*Note: In this problem, we assume that the first repayment/ deposit is made 3 months after today)