Steve, (45), was hit by a truck belonging to XYZ. Steve suffered permanent injuries and, as the result of a lawsuit, was awarded a non-reviewable structured settlement. The structured settlement will provide Steve with the following payments: . A death benefit of 100,000 payable at the moment of death if Steve dies before age 65. A survival benefit of 200,000 payable on Steve's 65th birthday. A monthly life annuity-due of 4,000 per month. . SULT XYZ decides to purchase the structured settlement from the JAB Insurance Company. JAB uses the following assumptions to calculate the present value of the benefits: i. Steve's force of mortality at age x 2 45 is 4x = uur + 0.02, where SULT is the force of mortality of the Standard Ultimate Life Table. ii. 8 = 0.045 iii. The two-term Woolhouse formula is used to calculate monthly and continuous annuity values, and to calculate insurance functions from the annuity values. You are given that, based on the assumptions above, including the extra mortality, 445 = 14.4893 345:207 = 11.4411 a) Show that the actuarial present value of the survival benefit is 52,050 to the nearest 10. You should calculate the value to the nearest 0.1. (5 marks) b) Calculate the actuarial present value of the monthly annuity due. (5 marks) c) Calculate the actuarial present value of the death benefit. (5 marks) d) Determine the reserve that JAB should hold at the end of 20 years, assuming that Steve is alive at that time. (5 marks) Steve, (45), was hit by a truck belonging to XYZ. Steve suffered permanent injuries and, as the result of a lawsuit, was awarded a non-reviewable structured settlement. The structured settlement will provide Steve with the following payments: . A death benefit of 100,000 payable at the moment of death if Steve dies before age 65. A survival benefit of 200,000 payable on Steve's 65th birthday. A monthly life annuity-due of 4,000 per month. . SULT XYZ decides to purchase the structured settlement from the JAB Insurance Company. JAB uses the following assumptions to calculate the present value of the benefits: i. Steve's force of mortality at age x 2 45 is 4x = uur + 0.02, where SULT is the force of mortality of the Standard Ultimate Life Table. ii. 8 = 0.045 iii. The two-term Woolhouse formula is used to calculate monthly and continuous annuity values, and to calculate insurance functions from the annuity values. You are given that, based on the assumptions above, including the extra mortality, 445 = 14.4893 345:207 = 11.4411 a) Show that the actuarial present value of the survival benefit is 52,050 to the nearest 10. You should calculate the value to the nearest 0.1. (5 marks) b) Calculate the actuarial present value of the monthly annuity due. (5 marks) c) Calculate the actuarial present value of the death benefit. (5 marks) d) Determine the reserve that JAB should hold at the end of 20 years, assuming that Steve is alive at that time
