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Paul obtained an adjustable rate mortgage (ARM) loan of $50 million for 20 years from a bank to purchase an apartment at West Kowloon two years ago. The mortgage interest rate was HIBOR + 2%. However, in the first two years, Paul was only required to make monthly interest-only payment. Since the loan origination, the HIBOR did not change and remained at 1.5% in the last two years. However, payments after two years will be adjusted to fully amortize the loan at maturity. a) Calculate the monthly payment for the first two years. (3 marks) b) Calculate loan balance at the end of Year 2. (3 marks) c) If the HIBOR increased to 2.5% at the end of Year 2, the interest rate would be reset at the start of Year 3, Calculate Sam's new monthly payment and the percentage rise in his monthly payment. (4 marks) d) Suggest two reasons for Paul's choice of using an ARM instead of a fixed-rate mortgage. (4 marks) e) Briefly explain why banks may prefer a HIBOR mortgage to a fixed-rate mortgage. (6 marks)