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Posted on Sep 02, 2024

1. (12 marks Fred, (30) buys a 5 year endowment policy with a face amount of $200,000. The insurer has priced the policy assuming mortality

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1. (12 marks Fred, (30) buys a 5 year endowment policy with a face amount of $200,000. The insurer has priced the policy assuming mortality according to Appendix D, ultimate rates and an effective rate of 5%. Claims are paid at the end of the year and premiums are paid at the beginning of the year. The company pays a commission of 10% each year and incurs a per policy expense of $85 plus a claims cost of $250. a) calculate the net annual premium for this policy b) calculate the gross annual premium for this policy Appender D. Tables Table D.1 Standard Select and Ultimate Survival Model. * +1 +2 +2 +1 +2 +2 100000.00 20 60 96568.13 9628748 95940.6062 99975.04 21 61 96232.34 95920 27 95534.43 63 20 99995.08 99973.75 99949.71 22 62 95858.91 95511.80 9508253 64 21 99970.04 99948.40 99923.98 23 63 95443.51 95057.36 94579.7365 22 99944.63 99922.65 99897.79 24 64 94981.34 94551.7294020.3366 23 99918,81 99896.43 99871.08 25 65 94467.11 93989.16 993980567 24 99892.52 99869.70 99843.80 26 66 93895.00 93363.38 92706,06 68 25 99865.69 99842.38 99815.86 27 67 93258.63 92667.50 91936.88 69 26 99838.28 9981441 99787.20 28 68 92551,02 91894.03 91082.43 70 27 99810.20 99785.70 99757.71 29 69 91764.58 91034.84 90133.96 71 28 99781.36 99756.17 99727.29 30 70 90891.07 90081.15 89082.09 72 29 99751.69 99725.70 99695.83 31 71 89921.62 89023.56 87916.84 73 30 99721.06 99694.18 99663.20 32 72 88846.72 87852.03 86627.64 74 31 99689.36 99661 48 99629.26 33 73 87656.25 86555.99 85203.46 75 32 99656.47 99627.47 99593.83 34 74 86339.55 85124.37 83632.8976 33 99622.23 99591.96 99556.75 35 75 84885.49 83545.75 81904.34 77 34 99586.47 99554.78 99517.80 36 76 83282.61 81808.54 80006.23 78 35 99549,01 99515.73 99476.75 37 77 81519.30 79901.17 77927.35 79 36 99509.64 99474.56 99433.34 38 78 79584.04 77812.44 75657.16 80 37 99468.12 99431.0299387.29 39 79 77465.70 75531.88 73186,3181 38 99424.18 99384.82 99338.26 40 80 75153.97 73050.22 70507.1982 39 99377.52 99335.62 99285.88 41 67614.60 83 40 99327.82 99283.06 99229.76 42 64506.50 84 41 99274.69 99226.72 99169.41 43 61184.88 85 42 99217.72 99166.14 991043344 57656.68 86 43 99156.42 99100.80 99033.94 45 53934.73 87 44 99090.27 99030.10 98957.57 46 50038.65 88 45 99018.67 98953.40 98874.50 45995.64 89 46 98940.96 98869.96 98783.91 48 41841.05 90 47 98856,38 98778.94 98684.88 37618.56 91 48 98764.09 98679.44 98576.37 33379.88 92 49 98663.15 98570.40 98457.24 51 29183.78 93 50 98552.51 98450.6798326.1952 250943394 51 98430.98 98318.95 98181.77 53 21178.30 95 52 98297.24 98173.79 98022.38 17501.76 96 53 98149.81 98013.56 97846.20 55 14125.8997 54 97987.03 97836.44 97651.21 56 11102.5398 55 97807.07 97640.40 97435.17 57 8469.73 99 56 97607.84 97423.18 97195.56 58 6248.17 100 57 97387.05 97182.2596929.5959 58 97142.13 96914.80 96634.14 60 1. (12 marks Fred, (30) buys a 5 year endowment policy with a face amount of $200,000. The insurer has priced the policy assuming mortality according to Appendix D, ultimate rates and an effective rate of 5%. Claims are paid at the end of the year and premiums are paid at the beginning of the year. The company pays a commission of 10% each year and incurs a per policy expense of $85 plus a claims cost of $250. a) calculate the net annual premium for this policy b) calculate the gross annual premium for this policy Appender D. Tables Table D.1 Standard Select and Ultimate Survival Model. * +1 +2 +2 +1 +2 +2 100000.00 20 60 96568.13 9628748 95940.6062 99975.04 21 61 96232.34 95920 27 95534.43 63 20 99995.08 99973.75 99949.71 22 62 95858.91 95511.80 9508253 64 21 99970.04 99948.40 99923.98 23 63 95443.51 95057.36 94579.7365 22 99944.63 99922.65 99897.79 24 64 94981.34 94551.7294020.3366 23 99918,81 99896.43 99871.08 25 65 94467.11 93989.16 993980567 24 99892.52 99869.70 99843.80 26 66 93895.00 93363.38 92706,06 68 25 99865.69 99842.38 99815.86 27 67 93258.63 92667.50 91936.88 69 26 99838.28 9981441 99787.20 28 68 92551,02 91894.03 91082.43 70 27 99810.20 99785.70 99757.71 29 69 91764.58 91034.84 90133.96 71 28 99781.36 99756.17 99727.29 30 70 90891.07 90081.15 89082.09 72 29 99751.69 99725.70 99695.83 31 71 89921.62 89023.56 87916.84 73 30 99721.06 99694.18 99663.20 32 72 88846.72 87852.03 86627.64 74 31 99689.36 99661 48 99629.26 33 73 87656.25 86555.99 85203.46 75 32 99656.47 99627.47 99593.83 34 74 86339.55 85124.37 83632.8976 33 99622.23 99591.96 99556.75 35 75 84885.49 83545.75 81904.34 77 34 99586.47 99554.78 99517.80 36 76 83282.61 81808.54 80006.23 78 35 99549,01 99515.73 99476.75 37 77 81519.30 79901.17 77927.35 79 36 99509.64 99474.56 99433.34 38 78 79584.04 77812.44 75657.16 80 37 99468.12 99431.0299387.29 39 79 77465.70 75531.88 73186,3181 38 99424.18 99384.82 99338.26 40 80 75153.97 73050.22 70507.1982 39 99377.52 99335.62 99285.88 41 67614.60 83 40 99327.82 99283.06 99229.76 42 64506.50 84 41 99274.69 99226.72 99169.41 43 61184.88 85 42 99217.72 99166.14 991043344 57656.68 86 43 99156.42 99100.80 99033.94 45 53934.73 87 44 99090.27 99030.10 98957.57 46 50038.65 88 45 99018.67 98953.40 98874.50 45995.64 89 46 98940.96 98869.96 98783.91 48 41841.05 90 47 98856,38 98778.94 98684.88 37618.56 91 48 98764.09 98679.44 98576.37 33379.88 92 49 98663.15 98570.40 98457.24 51 29183.78 93 50 98552.51 98450.6798326.1952 250943394 51 98430.98 98318.95 98181.77 53 21178.30 95 52 98297.24 98173.79 98022.38 17501.76 96 53 98149.81 98013.56 97846.20 55 14125.8997 54 97987.03 97836.44 97651.21 56 11102.5398 55 97807.07 97640.40 97435.17 57 8469.73 99 56 97607.84 97423.18 97195.56 58 6248.17 100 57 97387.05 97182.2596929.5959 58 97142.13 96914.80 96634.14 60