You are buying a car at a cost of $42,000 by taking a loan. The nominal interest rate is 9% per annum compounded monthly. The bank offers 2 options for the structure of the repayments.

• Option 1: The loan will be repaid over 10 years by equal month-end-instalments.

a) Calulate the monthly installment. (1 mark)

b) Calculate the interest component for the 20^th repayment. (2 marks)

c) Calculate the loan outstanding immediately after 8 years (immediately after the payment on that date). (2 marks)

d) Hence or otherwise, calculate the cumulative principal repayments during the 9^th year. (2 marks)

• Option 2: Month-end-instalments of $X will be made for the first 3.5 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 3.5 years by month-end-instalments of $2X.

e) Calculate X. (3 marks)