Question 6 (a) Answer the following questions relating to time value of money: (i) Jenny invests $77,500 today in an account that earns interest at the rate of 7% per annum. What will be the value of Jenny's investment in eight years' time? (3 marks) (b) (ii) June has just been awarded a scholarship that will pay her $18,000 per year for the next four years as she pursues her post-graduate studies overseas. Using a discount rate of 3% per annum, what is the value of these payments today? (3 marks) (iii) Joseph will be retiring today. The company is offering Joseph a gratuity in recognition of his long service with the company. Joseph has been given the following payout options: Option 1: Receive a lump sum payment of $555,000 in ten years' time. Option 2: Receive $33,000 payment per year for the next fifteen years. Option 3: Receive $260,000 today. Given that the interest rate is at 9 percent per year, which alternative would provide Joseph with the highest payout? (Provide the computation for all the options.) (8 marks) (iv) Kenny borrowed $640,000 to purchase a new apartment. He agreed to pay the bank in 30 equal annual installment payments. The interest charged is fixed at 2% per annum compounded annually. How much will these equal annual payments be? (4 marks) Explain the term 'annuity'. (2 marks)