You are buying a property costing of $750,000 by taking a mortgage to cover the entire purchase price. The nominal interest rate is 6% per annum compounded monthly. The bank offers 3 options for the structure of the repayments.

• Option 1: The mortgage will be repaid over 25 years by equal month-end-instalments.

a) Calculate the monthly instalment. (1 mark)

b) Calculate the size of the interest component for the 36th repayment. (2 marks)

c) Calculate the mortgage outstanding balance immediately after the first 298 payments. (1 mark)

• Option 2: No month-end-instalments will be made for the first 18 months. Then, commencing at the end of the 19thmonth, a total of 282 month-end-instalments of $X will be made over the life of the mortgage. Further, a residual payment of $25,000 will be made at the end of the 300thmonth at the same time as the last instalment of $X.

d) Calculate X. (3 marks)

• Option 3: Month-end-instalments of $Y will be made for the first 5 years. Then the bank offers you a payment free period (i.e., no repayments required) of 5 years. After that, the remaining balance will be repaid over 15 years by month-end-instalments of $Y.

e) Calculate Y. (3 marks)