My personal answer:

(1) First choice: 0.0344million; Second choice: 0.0421million

(2) First choice: PMT=0.0344 million, r=0.6%, n=360, so PV=5.0679 million, NPV=8.4679 million

Second choice: PMT=0.0421 million, r=0.6%, n=360, so PV=6.2022 million, NPV=8.5022 million

(3) Down payment=11-7.7=3.3 million

PMT=0.0421 million, r=0.6%, n=36, so PV of year 1-36=1.36 million

PMT=0.0421 million, r=0.43%, n=324, so PV of year 37-360=5.93 million

FV=11.5 million, r=0.6%, n=36, so PV of selling=9.27 million

PMT=0.008 million, r=0.6%, n=324, so PV of rent=0.92 million

NPV=9.27+0.92-1.36-5.93-3.3=-0.4 million

If there's something wrong with my answer, please point it out. Thanks!

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)