Using AM92 and an interest rate of 6% p.a., evaluate or approximate the following, showing all working. Assume ultimate mortality unless directed otherwise. Round your answers to 5.d.p or to the nearest cent for dollar values. a) The probability that a life aged 50 dies between age 60 and 65 . (2 marks) b) The probability that a life aged 30.3 who was select at age 30 dies in the next 1.5 years, assuming a constant force of mortality. (4 marks) c) The expected present value and standard deviation of the present value of a whole life annuity of $100 payable annually in arrears to a select life aged 37. (5 marks) d) The expected present value of a $100,000, ten-year endowment insurance payable immediately on death to a life aged 55. (4 marks) e) The expected present value of a whole of life annuity of $5000 per annum payable monthly in arrears to a life aged 65. (4 marks)