Gracelyn was just born and her parents regularly put aside some money to set up a trust fund for her university tuition fee payments when she turns 18. The trust fund earns 5% per year, and the interest is compounded and paid semi-annually. Gracelyn expects to pay $18,000 at the beginning of each half-year for three years. The first payment is to be made when she turns 18 and starts her degree at the university. a) How much money should the trust fund have when Gracelyn turns 18 so that she can withdraw $18,000 at the beginning of each half-year for three years with no money left in the trust after the last withdrawal? (3 marks) b) Assume Gracelyn's parents would like to deposit the same amount of money semi-annually in the trust fund for 18 years, with the first amount deposited half a year after she was born. How much should they deposit so that the trust fund would accumulate enough balance for her university tuition payments at her 18 years old, i.e. your answer to part a)? (3 marks) c) If Gracelyn's parents deposit the money at the beginning of each half-year, without calculation, explain whether this semi-annual deposit would be higher or lower than your answer to part b). (3 marks) d) What is the effective annual rate that the trust fund earns? (3 marks) e) If Gracelyn's grandparents deposited a lump sum of $2000 in the trust fund when she was just born as a gift, given your answer to parts a) and b), what is the remaining trust fund balance after she just completes her three-year study at the university at 21 (3 marks) years old