Question 3 (25 marks) Today is your 50th birthday, and you anticipate that you will continue working until your 65th birthday. You currently have $50,000 in a bank account and $200,000 in shares. You plan to add to these savings by the following annual increments: i. depositing $2,000 a year for 10 years, and then $4,000 per year, into your bank account, the first deposit to be made today, and the last on your 65th birthday; ii. adding $6000 to your share portfolio today, and increasing this amount by 4% per annum with the last addition on your 65th birthday. The bank account is expected to earn 5% per annum, and the share portfolio 12% per annum. On your retirement aged 65, you intend to deposit all your savings into an investment account that will earn 10% per annum. 2 In answering the following questions, students should use the annuity functions. a. b. Draw a timeline of the above cash flows (8 marks) What is the value of your savings on your 65th birthday (after you have made your annual deposit)? (15 marks) c. If you expect to live for 20 years after you retire, how much can you withdraw each year after retirement (20 equal withdrawals beginning one year after you retire) to end up with a zero balance on your anticipated demise? (7 marks) Question 4 (20 marks)