Please help with the attached question:
Illustrative Life Table: Basic Functions and Single Benefit Premiums at / = 0.06 1000qx Six 1000A, 1000AJ 1000,Ex 100010Ex 100020Ex X 10,000,000 20.42 16.8010 49.00 25.92 728.54 541.95 299 89 9,749,503 0.98 17.0379 35,59 8.45 743 89 553.48 305.90 9,705,588 0.85 16.9119 42.72 9.37 744.04 553.34 305.24 9,653,731 0.91 16.7384 52.65 11.33 743.71 552 69 303.96 15 16 5133 65 28 14.30 743 16 20 9,617,802 1.03 551.64 301.93 9,607.896 1.05 16.4611 68.24 15.06 743.01 551.36 301.40 21 300.82 9,597.695 1.10 16.4061 71.35 15.87 742.86 551.06 9,587,169 1.13 16.3484 74.62 16.76 742.68 550.73 300.19 9,576,268 1.18 16.2878 78.05 17.71 742.49 550 36 299.49 24 9,565,017 1.22 81.65 18.75 549.97 298.73 25 16.2242 742 29 16.1574 85.43 19.87 742.06 549 53 297.90 26 26 9,553,319 1.27 27 9,541,153 1.33 16.0873 89.40 21.07 741.81 549.05 297.00 27 93.56 22.38 741.54 548.53 296.01 28 28 9,528,475 1 39 16.0139 29 9,515,235 1.46 15,9368 97.92 23.79 741.24 547.96 294.92 29 30 9.501,381 1.53 15 8561 102.48 25.31 740.91 547.33 293 74 30 9,486,854 15.7716 107.27 26.95 740.65 546.65 292.45 31 1.61 31 32 9,471,591 1.70 15,6831 112 28 28.72 740.16 545.90 291.04 32 9,455,522 1.79 15.5906 117.51 30.63 739.72 545.07 289.50 33 33 34 9.438,571 1.90 15.4938 122.99 32.68 739.25 544.17 287.82 34 286.00 35 35 9.420,657 2.01 15.3926 128.72 34.88 738.73 543.18 9,401,688 15.2870 134.70 37.26 738. 16 542.11 284.00 36 36 2.14 37 9,391,566 2 28 15.1767 140.94 39.81 737.54 540.92 281.84 37 38 9,360,184 2.43 15,0616 147.46 42.55 736.86 539.63 279.48 38 2.60 154.25 45.48 736.11 538.22 276.92 39 39 9,337,427 14.9416 40 40 2.78 14.8166 161.32 48.63 735.29 536.67 274.14 9,313, 166 534.99 271.12 41 41 9,287,264 2.98 14.6864 168.69 52.01 734.40 42 9,259,571 3.20 14 5510 176.36 55.62 733 42 533.14 267 85 42 43 9,229,925 3.44 14.4102 184.33 59.48 732 34 531.12 264.31 43 44 44 9, 198,149 3.71 14.2639 192.61 63 61 731.17 528,92 260.48 256.34 45 45 9, 164,051 4.00 14.1121 201 20 68.02 729.88 526.52 46 46 9, 127,426 4.31 13.9546 210.12 72.72 728.47 523.89 251.88 47 9,083 049 4.66 13.7914 219.36 77.73 726.93 521.03 247.08 47 48 9,045,679 5,04 13.6224 228.92 83.06 725.24 517.91 241.93 48 9,000,057 5.40 13.4475 238 82 AB. 73 723.39 514.51 235.39 49 49 5.97 13.2668 249.05 94.76 721.37 510 81 230.47 50 8,950,901 6.42 719.17 506.78 51 8,897,913 13.0803 259.61 101.15 224.15 51 52 8,840,770 6.97 12.8879 270.50 107.92 716.76 502.40 217.42 52 53 8,779,128 7.58 12.6896 281.72 115,09 714.12 497-64 210 27 53 8,712 621 8.24 12 4856 293.27 122.67 711.24 202.70 54 54 492 47 55 8,640,861 8,96 12.2758 305. 14 130 67 708.10 486.86 194.72 55 56 B,563,435 9.75 12.0604 317.33 139 11 704.67 480.79 186.32 56 57 8,479,909 10.62 11.8395 329.84 147.99 700.93 174 22 177.53 57 58 8,389,826 11.58 11.6133 342.65 157.33 696.85 467-12 158.37 58 59 B,292,713 12.62 11,3818 355 75 167.13 692.41 459.46 158.87 69 8,188,074 13.76 11.1454 369.13 177.41 687.56 451.20 149.06 60 60 61 8,075, 403 15.01 10.9041 382.79 188.17 682 29 442.31 139.00 61 7,954,179 16.38 10.6594 306.70 199.41 676 56 432 77 128.75 62 62 7,823,879 17 88 10.4084 410.85 211.13 670.33 422.54 118 38 63 63 64 7,683,979 19.52 10. 1544 425.22 223.34 663.56 411.61 107.97 64 236.03 656.23 399 94 97.60 65 65 7,533,964 21.32 9 8969 439.80Illustrative Life Table: Basic Functions and Single Benefit Premiums at / = 0.06 Lives are independent. X 1000Abx 1000( Axd 1000Ax= =10 1000(Asia) X 16.1345 86.73 50.89 16.2844 78.24 34.71 16.6432 57.93 16.51 16.4093 71.17 19.17 5 10 16.4080 67.95 18.13 16.1541 85.62 22.70 10 15 16.2187 81.96 21.67 15.8187 104.60 28.49 15 20 15,9005 99.87 27.00 15.3934 128.67 37.00 20 21 15.8272 104.12 28.33 15.2962 134.18 39.11 21 15.7502 108.48 29.77 15.1945 139.94 41.39 23 15.6696 113.04 31.33 15.0883 145.95 43.83 24 15.5851 117.82 33.01 14.9774 152.22 46.46 24 25 15,4967 122 83 34.82 14.8617 158.77 49.28 25 26 15.4041 128.07 36,77 14.7411 165.60 52.31 26 27 15.3073 133.55 38.87 14.6154 172.71 55.56 27 28 15.2062 139.27 41.12 14.4845 180. 12 59.03 28 29 15.1005 145.26 43 55 14.3484 187.83 62.75 29 30 14,9901 151.50 46.16 14.2068 195.84 66.72 37 14.8750 158,02 48.96 14.0590 204.16 70.97 31 14.7549 164.82 51.96 13.9071 212.80 75.50 14.6298 171.90 55.18 13.7488 221.76 80.34 14.4995 179.27 58,63 13.5848 231.05 85.48 34 35 14.3640 186.94 62.32 13.4150 240.66 90.96 35 14.2230 194.92 66.26 13.2393 250.60 96.78 35 14.0766 203.21 70.48 13.0579 280.88 102.96 37 13.9246 211.81 74.98 12.8705 271.48 109.52 38 $8898 13,7870 220.74 79.77 12 6774 282.41 1 16.46 39 13 6036 229.99 84.89 12.4784 293.68 123.80 40 41 13,4344 239.56 90.32 12.2737 305.26 131.56 41 42 13.2594 249.47 96.11 120633 317.17 139.75 42 43 13.0785 259.70 102.25 11.8474 329.39 148,38 43 44 12.8919 270.27 108.76 11.6260 341.92 157.46 44 45 12.6994 281.16 115.66 11.3994 354.75 166.99 45 46 12.5011 292.39 122.95 11.1677 367.87 177.00 46 47 12.2971 303.94 130.67 10.9310 381.26 187.48 47 48 12.0873 315.81 130.80 10.6898 394.92 198.44 48 49 11.8720 328.00 147.38 10.4441 408. 82 209.88 49 50 11.6513 340.49 156.41 10.1944 422.96 221.81 50 51 1 1.4252 353.29 165,89 9.9409 437.31 234.22 51 52 11.1941 366.37 175.85 9.6840 451.85 247.10 52 53 10.9580 379.74 186.28 9.4240 466.57 260.46 53 54 10.7172 393.37 197.18 9.1614 481.43 274.27 54 65 10.4720 407-24 208,57 9.8966 496,42 288.54 55 56 10.2227 421.35 220.44 8.6301 511.50 303.24 56 57 9.9896 435.68 232.79 8.3623 526.66 318.35 57 58 9.7131 450.20 245.62 0.0938 541.86 333.85 58 59 9.4535 464.90 258.93 7.8249 557.08 349.73 59 60 9. 1911 479.75 272.69 7.5563 572.28 365.94 60 61 8.9266 494.72 286.91 7 2085 587.44 382.46 61 62 8.6602 509.80 301.56 7.0221 602 53 399.26 62 63 8 3926 524.95 316.62 6.7574 617.50 416.30 63 64 8. 1241 540,15 332.09 6.4952 632.34 433.53 64 65 7.8552 555.36 347.92 6.2360 647 02 450.93 654) Derive a recursion relationship for IA , _ in terms of IA, _ and A _ and use it to find 44:6 45:5 45-51 IA. 44.6
