3. You are considering buying a 9 million apartment so that your child can go to an elite public school. You can take a 30-year mortgage to finance 70% of the price with an interest rate of 5.145% (APR). You also have the option to report a fake transaction price of 11 million to the bank and finance 70% of the 11 million (and you still only pay 9 million to the seller). (1) What are your monthly payments for the two cases (borrow 70% of 9 and 11 million)? (2pts) (2) Other than the down payment, now you need to pay a total 0.7 million now for all the fees associated with the transaction (taxes, commission, etc.) if you borrow 70% of 9 million. You need to pay 1 million fees now if you want to borrow 70% of 11 million. Suppose your opportunity cost of capital is 7.2% (that is, you can invest your cash elsewhere and make 7.2% per year in term of APR, monthly compounding), which choice should you take? Hint: calculate the PV of the costs of these two purchasing method. (4pts) (3) You plan to sell the apartment after 3 years. In the meantime, you do not plan to live in this apartment, and you can rent it out for 8000 per month. After 3 years, you expect to sell the apartment for 11.5 million, and pre-pay the outstanding balance of your mortgage. What is the NPV of this investment, assuming you borrow 70% of 11 million? Remember you need to pay 0.7 million fees right now. Use the discount rate of 7.2% (APR, monthly compounding) as in part (2). (4pts)