Problem #4 (20 points) Two years ago, you signed a loan contract with a re-payment schedule of 10-year fixed-rate, at 5.50 percent interest. You have paid all your monthly payments during the past two years and now have an outstanding balance of $65,000. The current market rates are at 4.0% but you are obliged to continue paying your mortgage based on initial rate of 5.50%. Question 1. If you could re-finance with the new rate of 4%, how much in total (in terms of present value) would have you gained? Question 2. Suppose your lending officer approaches you with a new proposal: if you pay a $5,000 lump-sum pre-payment penalty you can switch to a new contract with the current 4.00 percent repayment schedule for the remaining part of the loan. Will you accept this proposal? Why? What is the maximum penalty that still convinces you to accept the deal?