You are buying a car at a cost of $38,000 by taking a loan. The nominal interest rate is 12% per annum compounded monthly. The bank offers 2 options for the structure of the repayments. Option 1: The loan will be repaid over 8 years by equal month-end-instalments. a) Calulate the monthly installment. (1 mark) b) Calculate the interest component for the 25th repayment. (2 mark) c) Calculate the loan outstanding immediately after 5 years (immediately after the payment on that date). (2 marks) d) Hence or otherwise, calculate the cumulative principal repayments during the 6th year. (2 marks) Option 2: Month-end-instalments of $X will be made for the first 4 years. Then the bank offers you a payment free period (i.e., no repayments required) of 1 year. After that, the remaining balance will be repaid over 3 years by month-end-instalments of $2X. e) Calculate X. (3 marks)