Please answer the following using ACTUARIAL NOTATION . Thanks! I DO NOT WANT SOLUTIONS! PLEASE WORK OUT EACH PROBLEM SEPERATELY! Thank you so much! I have included the Illustrative Table at 6%.
Illustrative Life Table: Basic Functions and Single Benefit Premiums at i = 0.06 I. 1000q 10004, 1000/AJ 1000,E, 1000,Ex 1000, Ex X 10,000,000 20.42 16.8010 49.00 25.92 720 54 541 95 298 89 9,740,503 0.98 17.0379 35.59 8.45 743.89 553.48 305.90 9,705,588 0.85 16.0119 42.72 9.37 744.04 553 34 305 74 10 9,663,731 0.91 18 7:384 52.55 11.93 743.71 552.69 303.96 15 9,617,802 1.03 16 5133 65.28 14.30 743.16 651.64 301.93 20 9,607,895 1.00 16.4611 68.24 15.06 743.01 551.36 301.40 9,597,695 1.10 16.4061 71.35 15.87 747 86 551.00 300.82 22 9,587,169 1.13 16.3484 74.62 16.76 742 68 550.73 300.10 23 9,576,288 1.18 16.2878 78.05 17.71 742 49 550 36 799.49 74 9,565,017 25 1.22 16 7242 A1 65 18.75 742 29 549.97 298.73 26 9,553,319 1.27 16.1674 85.43 19.87 742.06 549 51 297 90 20 27 9,511,153 1.33 16 0073 89.40 21.07 741.81 549.05 297.00 27 28 9 528, 475 1.39 16.0139 93.56 22 38 741.54 548.53 296.01 28 29 9.515.235 1.46 15.9368 97 97 23 79 741 24 547.90 294.92 29 30 9,501,301 1.53 15.8581 102.48 25.31 740.91 517.33 203 74 30 31 9, 186,854 1.61 15.7716 107 27 26.95 740.55 546.65 292.45 31 32 9,471,591 1.70 15.6831 112 28 28.72 740.16 545.90 201.04 32 23 33 9,455,522 1.79 15.6906 117.51 30.63 739.72 545 07 289.50 34 9.438,671 1 90 15.4938 122.99 32.68 739.25 544.17 287.82 31 35 9,420,057 2.01 15.3926 128.72 34.88 738.73 643.18 286.00 35 36 9.401,688 2.14 15.2870 134.70 37.28 738.16 542.11 284.00 36 37 9.381,500 2.28 15.1787 140.91 30.81 737.54 640.02 281.84 37 38 9,360, 184 243 15.0616 14/.46 42 55 736.86 5:19.63 279.4A 38 39 9,337,427 2 60 14.9410 154.25 45.48 730.11 538.22 276.92 39 40 9,313,160 2.78 14.8166 161.32 48.63 735.29 536.67 274.14 40 41 9.28/,264 2 98 14.6864 168.89 52.01 734.40 534.90 271.12 41 47 9,259,571 3.20 14.5510 176.36 55.62 733.42 533.14 267 85 42 43 9,229,825 3.44 14.4102 184.33 59 40 732 34 531.12 264.31 43 44 9, 198, 149 3.71 14 2639 192.61 83.61 731.17 528.92 260.48 44 45 9, 164,051 1.00 14.1121 201.20 68.02 729.88 526 52 756 34 45 46 9, 177,420 4.31 13.9546 210.12 72.72 728.47 523.89 251.88 46 47 9,088,049 4.66 13.7914 219.26 14.13 /26 93 521.03 247.08 47 9,045,679 5.04 13.6274 728 92 83.00 725.24 517.91 241.93 48 49 9,000,057 5.40 13.4475 238.82 88.73 723.39 514.51 236.30 40 50 8,950,901 5.02 13.2668 249.05 94 76 /21.3/ 510 81 230 47 51 8,897,913 6.42 13.0803 259.61 101.15 719 17 506.78 224.15 8, 8-40,770 6.97 12.8879 270.50 107.92 716. 76 502 40 217.42 52 8.770,128 7 58 12.G89G 281.72 115.09 714.12 497.64 210 27 53 64 8 712,621 8.24 12. 1856 293.27 122 67 711.24 402.47 202.70 54 8,640,861 194.72 55 55 8.93 12 2758 305 14 130 67 708 10 486.80 56 8,563,435 9.75 12.0604 317.33 139 11 704.67 480 79 180 32 50 57 8,479,908 10.62 11.8395 329.84 147.99 700.93 474 22 177.53 57 58 A 309, 820 11.58 11.6133 3-12.65 157.33 696.85 467.12 168.37 58 59 8,292,713 12.62 11.3818 355.75 167.13 692.41 459 4R 158 87 60 8.188.074 13.76 11 1454 309.13 177 41 687.56 451.20 149.06 51 8,075,403 15.01 10.9041 312 79 188.17 082 29 442 31 139 00 61 67 7,954 179 16.38 10.6584 306.70 190.41 676.56 432 77 128.75 62 63 7.823,879 17.88 10.4084 410 85 211.13 670 33 422 54 118 38 /,683 979 19.52 10.1544 425.22 223.34 863.56 411.61 107.97 64 65 7,533,964 21.32 9 8969 439.80 236.03 656 23 309 94 97 60 65Illustrative Life Table: Basic Functions and Single Benefit Premiums at / = 0.06 X 1000q. 1000A 1000(4) 1000Ex 1000,Ex 1000,Ex X 7,373,338 23.29 9.6362 15-4.56 240 20 648.27 387.53 87.37 66 7,201,635 25.44 9.3726 469 47 267.83 639 06 374.30 77_38 07 7,018,432 27.79 9.1086 484.53 276.92 630.35 360.41 67.71 30.37 /BER F 791.46 620 30 345.77 58 54 69 6,823,367 70 6,010 155 33.18 8.5693 514.95 306.42 809 46 330.37 49.88 TO 71 6,396,609 36 26 A.2988 530.20 321.78 597.79 314.27 41.86 71 72 6, 184,683 39.62 8.0278 515.60 337.54 585.25 207.61 34.53 72 73 6,920,394 43.30 7.7568 560 93 353 64 571.81 280.17 27.96 73 74 5,604,051 47.31 7.4864 576.24 370.08 557.43 262.31 22 19 74 75 5.396,081 51.69 7.21/0 591.49 386 81 542 07 244 0a 17 72 75 76 5,117,152 56.17 6.0493 606.65 403.80 525.71 225.46 13.04 76 77 4,828,182 61.68 6.6836 621 68 421 02 508 35 208 71 9 61 77 7A 4,520,360 67.37 8.4207 838.58 438.42 489.97 187.94 6.88 78 79 4.225, 163 73.56 6.1610 651.26 455.95 470.57 169.31 4.77 79 80 3,914,365 80 30 5 9050 605 75 473.59 450 19 151 00 3.19 3,600,038 87.64 5.6533 880.00 491.2/ 428.86 133.19 205 81 3,284,542 95 61 5.4063 893.98 508.90 406.62 116.06 1.27 82 2,970,496 104.28 5.1645 107.67 526.60 383.57 89.81 0.75 84 2,660,734 113.69 4.9282 721.04 544.15 359.79 84.59 0.42 84 2,350 246 123.89 4.6980 734.07 581.57 335.40 70.58 0.22 85 2,086 090 134 94 4 4742 746.74 578.80 :310.56 57.83 0.11 87 1,787,299 146.89 4.2571 759.03 595.79 285.44 46.50 0.05 1,524,758 159.81 4.0470 770.92 612.51 260.21 36.61 0.02 89 1.281,093 1/3.75 3.8442 782.41 628. 92 235.11 28.17 0.01 1,058 491 188.77 3.6488 793.48 844.98 210.36 21.13 0.00 90 91 858.676 204.93 3.4611 104.09 660 61 106 21 15.41 0.00 92 682 707 222.27 3.2812 814.27 875.83 162 90 10.91 0.00 93 530 959 210.86 3.1091 824.01 600.50 140.69 7.47 0.00 94 403,0/2 260.73 2.9450 704 AG 119 79 4 93 0.00 94 95 95 297,981 281.91 2 7888 842. 14 718.61 100.43 3.1 0.00 213,977 304 45 2.6406 850.53 731.83 A2 7A 1.90 0.on 97 148,832 328.34 2.5002 858.48 744.50 66.97 1.10 0.00 98 99,965 353.60 23676 865.99 756 60 63.09 0.60 0.00 66 64,617 380 20 2 2420 873 08 768.13 41.14 0.31 100 40,049 408. 12 2. 1252 879.70 779.08 31.12 0.15 0.00 100 101 23,705 437.28 2.0152 885.93 789.44 22 91 0.07 0.00 101 102 13,339 467.61 1.9123 891.76 790.21 16.37 0.03 0.00 102 103 7,101 498.99 1.0164 197.19 800 41 11 33 0.01 0.00 103 104 3.558 531.28 1.7273 902.23 817.02 7.58 0.00 0.00 104 105 1.668 564.20 1.6447 906.90 825.06 4.86 0.00 0.00 105 108 727 597.83 1.5685 911 22 832.53 299 0.00 0.00 106 107 292 631.64 1.4984 915 19 839.46 1.76 0.00 0.00 107 10A 108 685.45 1.4341 918.82 845.84 0.98 0.00 0.00 108 109 36 698.97 1.3765 922 14 851.69 0.52 0.00 0.00 109 110 11 731 87 1 3223 925 15 857.04 0.26 1401. Using the Illustrative Table at 6%, find the level annual benefit premium for a 25-year endowment insurance issued to (40) with death benefit 1000 and endowment benefit 2000 in each of the following cases. (a) fully discrete , (b) fully continuous (assumed UDD) , (c) semi-continuous (assume UDD)
