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Posted on Jul 12, 2024

answer is approximately 193 5. Consider the following portfolio of ammities-due currently being paid by a pension plan. Nuomber of Annuitants. 65 70 75 4

answer is approximately 193

5. Consider the following portfolio of ammities-due currently being paid by a pension plan. Nuomber of Annuitants. 65 70 75 4 85 : 2 Each anmuity has an annual payment of 1 as long as the annuitant surrines. Assine an earned interest rate of 6% and mortality given in the Illustrative Life Table. Calculate the variance of the present value of these obligations. XXS 88998 82239 88 $$$$ 88888888888888 ILT: Illustrative Life Table for Exam MLC questions (not Exam LTAM) (Exam MLC': predecessor of Exam LTAM) Illustrative Life Table: Basic Functions and Single Benefit Premiums at i=0.06 X 10000 1000A 1000/AJ 49.00 10,000,000 9,740,503 9,705,588 9,663,731 9,617,802 20.42 0.98 0.85 0.01 1.03 5 16.8010 17.0379 16.9119 18.7384 18 5133 1000, 290 89 305.00 305 24 303.96 301 3 2502 8.45 9.37 11 33 14 30 35.50 42.72 52.65 85.28 D 5 10 15 20 1000,E, 1000, E. 728 54 54195 743.89 553.48 744.04 553 34 74371 562.60 743 18 551.64 743 01 551.30 742.88 551.00 742.68 550.73 74240 550 30 74229 549.07 21 22 23 24 22 23 9,607,898 9,597,695 9.587,160 8,570,288 9,566,017 1.00 1.10 1.13 1.18 1.22 10.4511 16.4081 16.3484 16 2878 18.2242 15 06 15.87 16.76 17.71 18.75 68.24 7135 74.62 78.05 81.55 301.40 300 82 300,19 209.49 208.73 297.00 297.00 298.01 29492 293 74 1.27 1.39 9,552,319 9,541,153 0.528,475 9,515 235 9,501,381 18.1574 16.0873 18.0139 15.0368 85 41 89.40 93.50 97.82 102.48 549.53 54905 548.53 547 98 547.33 742.08 741.81 741.54 741 24 740.91 1.30 1.46 1.53 20 30 19.87 21.07 22 38 23.70 25.31 2005 2.72 30.53 15.6561 31 32 33 1.01 1.70 1.70 1.00 2.01 15.7716 15.8831 15 5905 15.4938 15.3920 546.65 545.90 545.07 544.17 543.18 202.45 201.04 289.50 287.82 206.00 35 34.80 107 27 112.26 117.51 122.99 128.72 134.70 140.94 147.46 154.25 181.32 740.55 740.16 739.72 739.25 738.73 738.10 737 54 735.88 738.11 735 29 9,488,854 9,471,501 2,455,522 9.436,571 9.420 657 9,401.688 9,881,500 9,350.184 9,337,427 9,313,165 8,287,264 9,250,571 9,229,025 8,198 149 9,164,051 38 38 2.14 220 2.43 2.50 2.78 15 2870 15. 1767 15.0816 14.9410 14.8106 37.29 30.81 42.55 45.48 48.63 542.11 540 92 539.63 538.22 538.67 284.00 251.84 270.48 276.92 274.14 41 9 3 23 89 88 % 3% 84 83 = = = = = = = = = = = = = = = = = = = = = 3882 8aaa a . 2.98 3.20 3.44 3.71 146864 14.5510 14.4102 142639 14.1121 43 52.01 55.62 59.48 83 81 188.69 176.35 154.33 102.01 201.20 734.40 733.42 732,34 731.17 729 88 534.99 533.14 531.12 528 12 525 52 271, 12 287.05 264.31 260.48 256 34 45 4.31 4.06 6, 127,425 098,040 9,045,679 9,000,057 4,950,001 13.9548 13.7014 13.0224 13.4475 13.2008 210.12 219.36 22892 238.82 249.05 5.04 72.72 77.73 83.00 88.73 94.76 729.47 720.93 725 24 723.39 721.37 251.88 247.08 241.93 238.39 230.47 523 89 521.00 $17.91 514,51 510.81 45 47 48 49 50 5.46 5.92 6.42 6.97 7.58 8.24 8.95 13.0803 12.8870 12.6896 124856 12 2758 259.61 270.50 281.72 293.27 305.14 101.15 107.92 115.09 122.67 130 67 719.17 718 76 714.12 711.24 708.10 508.78 502.40 497.64 492.47 488 86 224.15 217.42 210 27 202.70 194.72 51 52 53 54 55 8,897,913 8,840,770 8.779,128 8.712,621 8,840,861 8,563,435 8,479,908 8,389,826 8,292,713 8,188,074 9.75 10.62 1158 12.62 13.78 12.0604 11.8395 11.6133 11,3818 11.1454 317.33 329.84 342.65 355.75 389.13 139 11 147.99 157.33 167,13 177 41 704.67 700.93 590,85 892.41 687.56 480.79 474.22 467.12 459.46 451.20 185.32 177.53 168,37 158.87 149.06 51 682 29 8,075,403 7,954,179 7,823,879 15.01 16.38 17.68 19.52 21.32 10.9041 10.6584 10.4084 10.1544 9.8969 382.79 398.70 410.85 425.22 439.80 188.17 199.41 211.13 223.34 236.03 676.56 870.33 663.56 656.23 442.31 432.77 422.54 411.61 399 94 139.00 128.75 118.38 107.97 97 80 7,533,964 DM wnik mot ebolo vw har : Max) Illustrative Life Table: Basic Functions and Single Benefit Premiums at i = 0.06 10000EX 1000, 1000A, 1000/AJ 66 67 68 69 70 23 29 25.44 27.79 30.37 33.18 9.6362 9.3726 9.1066 B.8387 8.5893 454.58 469 47 484.53 499.70 514.95 249.20 262.83 276.92 291.46 306.42 1000, 1000, 848.27 387.53 639.68 374.36 630.35 380.44 620.30 345.77 509.48 330.37 87.37 77.38 67.74 58.54 49.88 88 67 68 69 70 71 72 73 74 75 7.373,338 7,201,635 7,018,432 6,823,367 6,616,155 6,396,809 6,184,683 5,920,394 5,884,051 5,396,081 5,117,152 4,828,182 4,530,360 4,225,163 3,914,365 38.26 39.62 43.30 47 31 51.69 8.2988 8.0278 7.7588 7.4884 7.2170 530.28 545.60 560.83 576.24 591.49 321.78 337.54 353 84 370.08 388.81 597.79 585 25 571.81 557.43 542 07 31427 297.51 280.17 282.31 244.03 41.86 34 53 27.98 22.19 17 22 71 72 73 74 75 76 77 78 79 80 58.47 61.68 67.37 73.56 80.30 6.9403 6.6836 8.4207 6.1610 5.9050 608.65 821.68 635.56 651.26 865.75 403.80 421.02 438.42 455.95 473.59 525.71 S08.35 480.97 470 57 450.19 225.46 208.71 187.94 169.31 151 00 13.04 9.81 6.89 4.77 3.19 78 77 78 79 BO 81 82 83 84 85 3,600,038 3,284,542 2.970,496 2,080,734 2,358,246 87.84 95.61 104.28 113.60 123 89 5.6533 5.4083 5.1645 4.0282 4.6980 680.00 693.98 70767 721.04 734.07 491.27 508.96 526.60 544.15 561.57 428.86 408.62 383.57 359.79 335.40 133.19 116.08 99 81 84.59 70.58 2.05 1.27 0.75 0.42 0.22 81 82 83 84 85 B6 87 88 89 90 2,000,000 1,787 299 1,524,750 1,281,683 1,058,491 134.94 148.89 159.81 172.75 188.77 4.4742 4.2571 4.0470 3.8442 3.6488 746.74 759.03 770.92 782.41 793.40 578 80 595.79 612.51 628.92 844.06 310.56 285.44 260.21 235.11 210.36 57.83 48.50 36.61 28.17 21.13 0.11 0.05 0.02 0.01 0.00 BG 87 88 89 90 91 92 93 858,670 882,707 530,950 403,072 297,981 204.93 222.27 240.86 260.73 281.91 3.4611 3.2812 3.1091 2.9450 2.7888 804.09 814.27 824.01 833 30 842.14 680.61 875.83 690.59 704.80 718.61 186.21 162.90 140.89 119.79 100.43 15.41 10.91 7.47 4.93 3.13 0.00 0.00 0.00 0.00 0.00 91 92 93 95 95 98 97 98 90 100 213,977 148,832 99,965 84.617 40,049 304.45 328.34 353.60 380 20 408.12 2.8408 2.5002 2.3678 22428 2.1252 850.53 858.48 265.99 873 08 879.70 731.83 744.50 758.60 768.13 779.08 82.78 66.97 53.09 41.14 31.12 1.90 1.10 0.80 0.31 0.15 0.00 0.00 0.00 0.00 0.00 96 97 98 99 100 101 102 103 104 105 23,705 13,330 7,101 3,558 1.658 437.28 467.51 498.99 531.28 564 29 20152 1.9123 1.8164 1.7273 1.6447 885.93 891.78 897.19 902.23 908.90 789,44 799.21 808.41 817.02 825.06 22.91 16.37 11.33 7.58 4.86 0.07 0.03 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 101 102 103 104 105 108 107 109 109 110 727 292 108 36 11 59783 831.84 665.45 698.97 731.87 1.5685 1.4984 1.4341 1,3755 1.3223 911.22 915.19 918.82 922.14 925.15 832.53 839.46 845.84 851.89 857.04 2.99 1.76 0.98 0.52 0.26 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 106 107 108 109 110 5. Consider the following portfolio of ammities-due currently being paid by a pension plan. Nuomber of Annuitants. 65 70 75 4 85 : 2 Each anmuity has an annual payment of 1 as long as the annuitant surrines. Assine an earned interest rate of 6% and mortality given in the Illustrative Life Table. Calculate the variance of the present value of these obligations. XXS 88998 82239 88 $$$$ 88888888888888 ILT: Illustrative Life Table for Exam MLC questions (not Exam LTAM) (Exam MLC': predecessor of Exam LTAM) Illustrative Life Table: Basic Functions and Single Benefit Premiums at i=0.06 X 10000 1000A 1000/AJ 49.00 10,000,000 9,740,503 9,705,588 9,663,731 9,617,802 20.42 0.98 0.85 0.01 1.03 5 16.8010 17.0379 16.9119 18.7384 18 5133 1000, 290 89 305.00 305 24 303.96 301 3 2502 8.45 9.37 11 33 14 30 35.50 42.72 52.65 85.28 D 5 10 15 20 1000,E, 1000, E. 728 54 54195 743.89 553.48 744.04 553 34 74371 562.60 743 18 551.64 743 01 551.30 742.88 551.00 742.68 550.73 74240 550 30 74229 549.07 21 22 23 24 22 23 9,607,898 9,597,695 9.587,160 8,570,288 9,566,017 1.00 1.10 1.13 1.18 1.22 10.4511 16.4081 16.3484 16 2878 18.2242 15 06 15.87 16.76 17.71 18.75 68.24 7135 74.62 78.05 81.55 301.40 300 82 300,19 209.49 208.73 297.00 297.00 298.01 29492 293 74 1.27 1.39 9,552,319 9,541,153 0.528,475 9,515 235 9,501,381 18.1574 16.0873 18.0139 15.0368 85 41 89.40 93.50 97.82 102.48 549.53 54905 548.53 547 98 547.33 742.08 741.81 741.54 741 24 740.91 1.30 1.46 1.53 20 30 19.87 21.07 22 38 23.70 25.31 2005 2.72 30.53 15.6561 31 32 33 1.01 1.70 1.70 1.00 2.01 15.7716 15.8831 15 5905 15.4938 15.3920 546.65 545.90 545.07 544.17 543.18 202.45 201.04 289.50 287.82 206.00 35 34.80 107 27 112.26 117.51 122.99 128.72 134.70 140.94 147.46 154.25 181.32 740.55 740.16 739.72 739.25 738.73 738.10 737 54 735.88 738.11 735 29 9,488,854 9,471,501 2,455,522 9.436,571 9.420 657 9,401.688 9,881,500 9,350.184 9,337,427 9,313,165 8,287,264 9,250,571 9,229,025 8,198 149 9,164,051 38 38 2.14 220 2.43 2.50 2.78 15 2870 15. 1767 15.0816 14.9410 14.8106 37.29 30.81 42.55 45.48 48.63 542.11 540 92 539.63 538.22 538.67 284.00 251.84 270.48 276.92 274.14 41 9 3 23 89 88 % 3% 84 83 = = = = = = = = = = = = = = = = = = = = = 3882 8aaa a . 2.98 3.20 3.44 3.71 146864 14.5510 14.4102 142639 14.1121 43 52.01 55.62 59.48 83 81 188.69 176.35 154.33 102.01 201.20 734.40 733.42 732,34 731.17 729 88 534.99 533.14 531.12 528 12 525 52 271, 12 287.05 264.31 260.48 256 34 45 4.31 4.06 6, 127,425 098,040 9,045,679 9,000,057 4,950,001 13.9548 13.7014 13.0224 13.4475 13.2008 210.12 219.36 22892 238.82 249.05 5.04 72.72 77.73 83.00 88.73 94.76 729.47 720.93 725 24 723.39 721.37 251.88 247.08 241.93 238.39 230.47 523 89 521.00 $17.91 514,51 510.81 45 47 48 49 50 5.46 5.92 6.42 6.97 7.58 8.24 8.95 13.0803 12.8870 12.6896 124856 12 2758 259.61 270.50 281.72 293.27 305.14 101.15 107.92 115.09 122.67 130 67 719.17 718 76 714.12 711.24 708.10 508.78 502.40 497.64 492.47 488 86 224.15 217.42 210 27 202.70 194.72 51 52 53 54 55 8,897,913 8,840,770 8.779,128 8.712,621 8,840,861 8,563,435 8,479,908 8,389,826 8,292,713 8,188,074 9.75 10.62 1158 12.62 13.78 12.0604 11.8395 11.6133 11,3818 11.1454 317.33 329.84 342.65 355.75 389.13 139 11 147.99 157.33 167,13 177 41 704.67 700.93 590,85 892.41 687.56 480.79 474.22 467.12 459.46 451.20 185.32 177.53 168,37 158.87 149.06 51 682 29 8,075,403 7,954,179 7,823,879 15.01 16.38 17.68 19.52 21.32 10.9041 10.6584 10.4084 10.1544 9.8969 382.79 398.70 410.85 425.22 439.80 188.17 199.41 211.13 223.34 236.03 676.56 870.33 663.56 656.23 442.31 432.77 422.54 411.61 399 94 139.00 128.75 118.38 107.97 97 80 7,533,964 DM wnik mot ebolo vw har : Max) Illustrative Life Table: Basic Functions and Single Benefit Premiums at i = 0.06 10000EX 1000, 1000A, 1000/AJ 66 67 68 69 70 23 29 25.44 27.79 30.37 33.18 9.6362 9.3726 9.1066 B.8387 8.5893 454.58 469 47 484.53 499.70 514.95 249.20 262.83 276.92 291.46 306.42 1000, 1000, 848.27 387.53 639.68 374.36 630.35 380.44 620.30 345.77 509.48 330.37 87.37 77.38 67.74 58.54 49.88 88 67 68 69 70 71 72 73 74 75 7.373,338 7,201,635 7,018,432 6,823,367 6,616,155 6,396,809 6,184,683 5,920,394 5,884,051 5,396,081 5,117,152 4,828,182 4,530,360 4,225,163 3,914,365 38.26 39.62 43.30 47 31 51.69 8.2988 8.0278 7.7588 7.4884 7.2170 530.28 545.60 560.83 576.24 591.49 321.78 337.54 353 84 370.08 388.81 597.79 585 25 571.81 557.43 542 07 31427 297.51 280.17 282.31 244.03 41.86 34 53 27.98 22.19 17 22 71 72 73 74 75 76 77 78 79 80 58.47 61.68 67.37 73.56 80.30 6.9403 6.6836 8.4207 6.1610 5.9050 608.65 821.68 635.56 651.26 865.75 403.80 421.02 438.42 455.95 473.59 525.71 S08.35 480.97 470 57 450.19 225.46 208.71 187.94 169.31 151 00 13.04 9.81 6.89 4.77 3.19 78 77 78 79 BO 81 82 83 84 85 3,600,038 3,284,542 2.970,496 2,080,734 2,358,246 87.84 95.61 104.28 113.60 123 89 5.6533 5.4083 5.1645 4.0282 4.6980 680.00 693.98 70767 721.04 734.07 491.27 508.96 526.60 544.15 561.57 428.86 408.62 383.57 359.79 335.40 133.19 116.08 99 81 84.59 70.58 2.05 1.27 0.75 0.42 0.22 81 82 83 84 85 B6 87 88 89 90 2,000,000 1,787 299 1,524,750 1,281,683 1,058,491 134.94 148.89 159.81 172.75 188.77 4.4742 4.2571 4.0470 3.8442 3.6488 746.74 759.03 770.92 782.41 793.40 578 80 595.79 612.51 628.92 844.06 310.56 285.44 260.21 235.11 210.36 57.83 48.50 36.61 28.17 21.13 0.11 0.05 0.02 0.01 0.00 BG 87 88 89 90 91 92 93 858,670 882,707 530,950 403,072 297,981 204.93 222.27 240.86 260.73 281.91 3.4611 3.2812 3.1091 2.9450 2.7888 804.09 814.27 824.01 833 30 842.14 680.61 875.83 690.59 704.80 718.61 186.21 162.90 140.89 119.79 100.43 15.41 10.91 7.47 4.93 3.13 0.00 0.00 0.00 0.00 0.00 91 92 93 95 95 98 97 98 90 100 213,977 148,832 99,965 84.617 40,049 304.45 328.34 353.60 380 20 408.12 2.8408 2.5002 2.3678 22428 2.1252 850.53 858.48 265.99 873 08 879.70 731.83 744.50 758.60 768.13 779.08 82.78 66.97 53.09 41.14 31.12 1.90 1.10 0.80 0.31 0.15 0.00 0.00 0.00 0.00 0.00 96 97 98 99 100 101 102 103 104 105 23,705 13,330 7,101 3,558 1.658 437.28 467.51 498.99 531.28 564 29 20152 1.9123 1.8164 1.7273 1.6447 885.93 891.78 897.19 902.23 908.90 789,44 799.21 808.41 817.02 825.06 22.91 16.37 11.33 7.58 4.86 0.07 0.03 0.01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 101 102 103 104 105 108 107 109 109 110 727 292 108 36 11 59783 831.84 665.45 698.97 731.87 1.5685 1.4984 1.4341 1,3755 1.3223 911.22 915.19 918.82 922.14 925.15 832.53 839.46 845.84 851.89 857.04 2.99 1.76 0.98 0.52 0.26 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 106 107 108 109 110