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)