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(ii) u biti (iii) 4 40+1 341 40+1 3P40 = 0.98462. For a fully discrete three year term insurance of 100,000 on Anne, age 40, you are given: (i) Anne's future mortality follows a double decrement model, where: Decrement 1 is death from Disease 1. Decrement 2 is death from any cause except Disease 1. , = A+ Bc40+ for all t20, where A = 0.0001, B=1.075.10-4, c= 1.12. (2) or all t 20. (iv) i = 0.05. (a) Show that per = 0.995 to the nearest 0.001. You should calculate the value to the nearest 0.0001. You are also given that , p. m = 0.99027, and spoo (b) (i) Show that the expected present value at issue of Anne's death benefits is 1400 to the nearest 100. You should calculate the value to the nearest 1. (ii) Show that the net annual premium for Anne's insurance is 490 to the nearest 10. You should calculate the premium to the nearest 0.1. Anne purchases a policy rider that pays an additional 50,000 at the end of the year of death, if death is due to Disease 1. (c) (i) Write down an integral expression for al), in terms of the dependent survival probabilities, pelo, and the force of mortality from Disease 1, u bts. (ii) Using your expression from part (C)(i), prove that , ! 1 (7) 940 4 (iii) Show that the net premium for the Disease 1 rider is 60 to the nearest 10. You should calculate the premium to the nearest 0.1. (d) Calculate the net premium reserve at time 1 for the policy, including the Disease 1 rider. == (ii) u biti (iii) 4 40+1 341 40+1 3P40 = 0.98462. For a fully discrete three year term insurance of 100,000 on Anne, age 40, you are given: (i) Anne's future mortality follows a double decrement model, where: Decrement 1 is death from Disease 1. Decrement 2 is death from any cause except Disease 1. , = A+ Bc40+ for all t20, where A = 0.0001, B=1.075.10-4, c= 1.12. (2) or all t 20. (iv) i = 0.05. (a) Show that per = 0.995 to the nearest 0.001. You should calculate the value to the nearest 0.0001. You are also given that , p. m = 0.99027, and spoo (b) (i) Show that the expected present value at issue of Anne's death benefits is 1400 to the nearest 100. You should calculate the value to the nearest 1. (ii) Show that the net annual premium for Anne's insurance is 490 to the nearest 10. You should calculate the premium to the nearest 0.1. Anne purchases a policy rider that pays an additional 50,000 at the end of the year of death, if death is due to Disease 1. (c) (i) Write down an integral expression for al), in terms of the dependent survival probabilities, pelo, and the force of mortality from Disease 1, u bts. (ii) Using your expression from part (C)(i), prove that , ! 1 (7) 940 4 (iii) Show that the net premium for the Disease 1 rider is 60 to the nearest 10. You should calculate the premium to the nearest 0.1. (d) Calculate the net premium reserve at time 1 for the policy, including the Disease 1 rider. ==