Mary plans to buy a flat in Tuen Mun, and the selling price is $6,000,000. Mary is offered two mortgage loans: one from Hang Seng Bank (HSB) and another from the developer Sino Group (Sino).

(i) a 25-year loan at "Prime rate (P) - 2.8%" from HSB, based on a loan-to-value ratio (LTV) of 60%

(ii) a 25-year loan at "Prime rate (P) + 1%" from Sino, based on an LTV of 80%, but Mary can pay interest only in the first three years Both loans require monthly payments and are fully amortizing.

(a) Suppose the prime rate is 5% and is expected to remain constant for a long period of time, calculate the (i) down payments, (ii) monthly payments, and (iii) also the loan balances at the end of Year 3, of the two loans mentioned above. (6 marks)

(b) Calculate the total interest expenses of the two loans. How much do they differ? (5 marks)

(c) Suppose Mary takes up the loan offered by Hang Seng Bank finally. If the housing price is expected to rise by 7% per year, and Mary would like to hold the property for four full years before selling it. Calculate Mary's expected appreciation on housing price and expected return on equity. (5 marks)

(d) If the housing price grows at the rate expected by Mary, what is her realized return from this investment when she sells the property at the end of Year 4? (4 marks)