Question

1 Approved Answer

Posted on Jul 22, 2024

5. An insurer issues a 15-year annual premium endowment insurance with sum insured $100,000 to a select life aged 35. The insurer incurs initial expense

image text in transcribed

5. An insurer issues a 15-year annual premium endowment insurance with sum insured $100,000 to a select life aged 35. The insurer incurs initial expense of $2,000 plus 40% of the first premium, and renewal expenses of 2.5% of each subsequent premium. The death benefit is payable immediately on death. Calculate the gross premium using the Standard Select and Ultimate Survival Model with Uniform Distribution of Death over Fractional Ages and 5% per year interest. Appendix D. Tables 583 Table D.1 Standard Select and Ultimate Survival Model. 10x1 1(x)+1 1x +2 x+2) 11 1+1 1x+2 x + 2 100000.00 20 60 96568.13 96287.48 95940.60 62 99975.04 21 61 96232.34 95920.27 95534.43 63 20 99995.08 99973.75 99949.71 22 62 95858,91 95511.80 95082.53 64 21 99970.04 99948.40 99923.98 23 63 95443.51 95057.36 94579.73 65 22 99944.63 99922.65 99897.79 24 64 94981.34 94551.72 94020.33 66 23 99918.81 99896.43 99871.08 25 65 94467.11 93989.16 93398.05 67 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 99814.41 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 83632.89 76 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 73186.31 81 38 99424.18 99384.82 99338.26 40 80 75153.97 73050.22 70507.19 82 39 99377.52 99335.62 99285.88 67614.60 83 40 99327.82 99283.06 99229.76 42 64506.50 84 41 99274.69 99226.7299169.41 43 61184.88 85 42 99217.72 99166.14 99104.33 44 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 49 37618.56 91 48 98764.09 98679.44 98576.37 50 33379.88 49 98663.15 98570.40 98457.24 51 29183.78 93 50 98552.51 98450.67 98326.19 52 25094.33 94 51 98430.98 98318.95 98181.77 53 21178.30 95 52 98297.24 98173.79 98022.38 54 17501.76 96 53 98149.81 98013.56 97846.20 55 14125.89 97 54 97987.03 97836.44 97651.21 56 11102.53 98 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 97182.25 96929.59 59 58 97142.13 96914.80 96634.14 60 59 96870.22 96617.70 96305.75 61 92 5. An insurer issues a 15-year annual premium endowment insurance with sum insured $100,000 to a select life aged 35. The insurer incurs initial expense of $2,000 plus 40% of the first premium, and renewal expenses of 2.5% of each subsequent premium. The death benefit is payable immediately on death. Calculate the gross premium using the Standard Select and Ultimate Survival Model with Uniform Distribution of Death over Fractional Ages and 5% per year interest. Appendix D. Tables 583 Table D.1 Standard Select and Ultimate Survival Model. 10x1 1(x)+1 1x +2 x+2) 11 1+1 1x+2 x + 2 100000.00 20 60 96568.13 96287.48 95940.60 62 99975.04 21 61 96232.34 95920.27 95534.43 63 20 99995.08 99973.75 99949.71 22 62 95858,91 95511.80 95082.53 64 21 99970.04 99948.40 99923.98 23 63 95443.51 95057.36 94579.73 65 22 99944.63 99922.65 99897.79 24 64 94981.34 94551.72 94020.33 66 23 99918.81 99896.43 99871.08 25 65 94467.11 93989.16 93398.05 67 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 99814.41 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 83632.89 76 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 73186.31 81 38 99424.18 99384.82 99338.26 40 80 75153.97 73050.22 70507.19 82 39 99377.52 99335.62 99285.88 67614.60 83 40 99327.82 99283.06 99229.76 42 64506.50 84 41 99274.69 99226.7299169.41 43 61184.88 85 42 99217.72 99166.14 99104.33 44 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 49 37618.56 91 48 98764.09 98679.44 98576.37 50 33379.88 49 98663.15 98570.40 98457.24 51 29183.78 93 50 98552.51 98450.67 98326.19 52 25094.33 94 51 98430.98 98318.95 98181.77 53 21178.30 95 52 98297.24 98173.79 98022.38 54 17501.76 96 53 98149.81 98013.56 97846.20 55 14125.89 97 54 97987.03 97836.44 97651.21 56 11102.53 98 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 97182.25 96929.59 59 58 97142.13 96914.80 96634.14 60 59 96870.22 96617.70 96305.75 61 92