Suppose that you have just celebrated your 18^th birthday today. You decide to start saving money to purchase your first home in 12 years, which will cost $650,000. You aim to save sufficient money to pay the 15% initial deposit, and will take a mortgage to cover the 85% of property cost. The nominal interest rate for the savings account is 13% per annum compounded fortnightly. The nominal interest rate charged by the mortgage provider is 6% per annum compounded monthly.

a) Calculate the required size of fortnight-end-saving instalments, so that you will have sufficient funds to pay the initial deposit for the property. (1 mark)

b) To help you, your parents will deposit $300 into your savings account at the end of every 2 years. If you also make the regular fortnightly deposit found in part (a), calculate the future value of your savings immediately after the last deposit. (2 marks)

Suppose that you have just celebrated your 30^th birthday today. The bank offers 2 options for the structure of the mortgage repayments.

• Option 1: The mortgage will be repaid over 20 years by equal fortnight-end-instalments.

c) Calculate the fortnightly repayment. (1 marks)

d) Calculate the interest component for the 24^th repayment. (1 marks)

e) Calculate the mortgage outstanding balance immediately after the first 200 payments. (1 mark)

• Option 2: No month-end-instalments will be made for the first 12 months. Commencing at the end of the 13^th month, a total of 150 month-end-instalments of $X will be made. Then the bank offers you a payment free period (i.e., no repayments required) of 2 years. After that, you will continue to make the month-end-instalments of $X for the remaining life of the loan. Further, a residual payment of $10,000 will be made at the end of the 240^th month at the same time as the last instalment of $X.

f) Calculate the value of X. (4 marks)