Question 3 (10 marks) (a) A family makes fixed payments at regular intervals (an annuity) to save for the future cost of their newly born child going to university. The family will make payments of $100 at the start of every month for 18 years into an investment policy with a guaranteed rate of return of 6% p.a. with monthly compounding. Assuming that there is no tax on the returns, how much will the investment be worth at the end of the 18th year? (5 marks) Answer: (b) Mr. Gates sold his successful IT business today in return for a fixed stream of payments to be received over a period of 5 years. Each payment is $100,000. The first payment will be received 6 months after today and the payments will continue semi-annually until the end of the 5th year. Mr Gates approaches his bank to borrow some money which will be secured by the present value of the future income stream. (i) What is the Present Value of the future income stream using a annual compounding interest rate of 4.00%? (3 marks) Answer: (ii) What is the Present Value of the future income stream using the same information as for part (i) except that each payment is made at the start of each 6 month period? (2 marks) Answer: