You want to buy a car which will cost you $10,000. You do not have sufficient funds to purchase the car. You do not expect the price of the car to change in the foreseeable future. You can either save money or borrow money to buy the car.

• Plan 2: You decide to borrow $13,000 from the bank and purchase the car now, as well as cover some other expenses. The bank offers two options for the structure of the repayments.

- Option 1: The first repayment will not start until you graduate from university. Therefore, no month-end-instalments will be made for the first 36 months. Then, commencing at the end of the 37^th month, a total of 30 month-end-instalments of $X will be made over the life of the loan. The nominal interest rate is 6% per annum compounded monthly.

d) Calculate X. (2 mark)

e) Your parents agree to help you repay the loan by contributing a lump sum of $1,800 when you successfully graduate from university. Calculate the new value of X. (1 mark)

- Option 2: For the first 36 months (while you are still studying), you will be making month-end-instalments of $Y. Then, commencing at the end of the 37^th month (when you graduate from university), you will double the amount of monthly repayment for the remaining 30 month-end-instalments. The nominal interest rate is 6% per annum compounded monthly.

f) Calculate the value of Y. (3 marks)