Question 5 [15 marks]. Thomas Brown plans to retire at age 67 with a pension of 30,000 per year, paid annually in advance during his remaining lifetime. Assume an effective annual interest rate of 4% and the mortality given by table AMCOO select values. You can find the table in the appendix. (a) Show that the expected present value of the pension at retirement is approximately 369,659. (b) In order to cover the cost of the pension, Thomas wants to make monthly payments in arrears starting at age 30 until retirement. What are the monthly premiums assuming he survives until retirement? (c) How does the expected present value in (a) change when he switches to a pension of 2,500 paid monthly in advance during his remaining lifetime? Give reasons. [6] [5] [4] Question 5 [15 marks]. Thomas Brown plans to retire at age 67 with a pension of 30,000 per year, paid annually in advance during his remaining lifetime. Assume an effective annual interest rate of 4% and the mortality given by table AMCOO select values. You can find the table in the appendix. (a) Show that the expected present value of the pension at retirement is approximately 369,659. (b) In order to cover the cost of the pension, Thomas wants to make monthly payments in arrears starting at age 30 until retirement. What are the monthly premiums assuming he survives until retirement? (c) How does the expected present value in (a) change when he switches to a pension of 2,500 paid monthly in advance during his remaining lifetime? Give reasons. [6] [5] [4]