9. actuarial LTAM question

1,300 lives, all age 50 are issued a: 3-year term insurance, paying $10,000 at end of year of death. Each insured pays a single premium based on 5% interest and mortality which follows the law l; = 100 - r. All premiums are deposited into a fund out of which all benefits are paid. Over the 3-year period, the fund earns interest of 5%% per annum and mortality follows (, = 102 - r. Find the amount remaining in the fund immediately after third year claims are paid (ignoring expenses) Select one: a. $20,000 but less than $30,000 b. $0 but less than $10,000 c. $10,000 but less than $20,000 d. less than $0 e. $30,000 or more Illustrative Life Table: Basic Functions and Single Benefit Premiums at 1-0.06 1000, 1000A, 1000(A) 1000E, ToddjpE, 26. 4. 10,000,000 00) pAAA 9,003,731 17,02 15. Ed. 17037 A 1.7354 10,514 45.00 $6.5 n 255 $ 19 A 19. 14.04. 0.99 S 061 1.0g 1000+E, 1. 5349 + 10 30$ O 11 1 14,30 6. 5A 1.0 1.10 11. 72 BE 1. 11 1 10 11 +ML HEA 1 11 .14 11 ? TB. 1. 1.06 1 168 1 . 15 5 . 51. AA 0 3 Ap 301,40 100.62 5 . 4 27B. 16. 29 . ,07,500 4, , ,387,1 76,27 6,017 ,, 1. 2 . $ ,501,501 w 1.a 10.7. 72. . 297,90 %E 11 1 15 AO 1, a n: t 1 31 54. 14 5 s 7b6 A 14 24 2 1 E A + s 17 AA A71, 43,71 5,420,007 + * 16.683 $ $ 6. 3 1 12 11 t 2246 CA 2 . 4.07. 4 te TIM2 = A 1 201 12 4. E 4,401A 0 31 14 1. 4. 5.1 16 177 16 - 64 e 14 274 z 36,67 1. 16 4.4. 14 14 11.2 * 27B 14. L 0 31 1 4B ) 15 14 1A z 14 *HM 1A 149 6 . 42 HR 120 44 l 4 14. 04 . . A A2 17, + 4. 14 i2 16 2AJ A 2013 2. 11 20, s 11. 116, 4,47 7M 5 D/ D DOBR 049 be 90,067 11.) 3 4.08 1: 40 174 14 14 131008 15 AL 05 m . M2 AT 1041 2 * 42 7 1 4. t 13.003 2 AM L 246 .60 11 6 /12 7 12 a 201 41 1o7 5 0 117 076 712 12 704 10 2 40 41. 4 . 15 . 2 ip ar E 30 4 30/ 194, 7 I . E in 1 436 = * 123 Lo4 12.004 1005 MU U16 454 1 54 2 it te7. 474 40712 1 . 4520 A/ A 140 L TK 1 41 4 . 16 : 14. LA 1 -4 .41 1 ) 4 7 . Li A 970 7 14 11 1 ) L 13 Illustrative Life Table: Basic Functions and Single Benefit Premiums at /= 0.06 100040EX 1000,EX 10002 1000A, 1000A 7,373,338 7,201,635 7,018,432 8.823 367 6,616, 155 1000g 23.29 25 44 27.79 30.37 33.18 9.6362 9.3726 9.1068 8.8387 8.5893 454,55 469 47 484.53 499 70 249.20 202 83 276.92 291,46 308.42 648.27 639.66 630.35 020.30 809 48 397.53 374.35 360.44 345.77 330 37 87,37 77.38 67.74 58,54 49.88 70 514.96 70 530 25 41.86 34 53 8.390.609 0.154.663 5,920,394 5.664,051 5.306.081 36.26 39.62 43.30 47.31 51.00 - 27.06 8.2988 8.0278 7.7568 7.4884 7.2170 545 60 560.03 576.24 591.49 321.78 337.54 353.64 370.08 388.81 597.79 585 25 571,81 557.43 542.07 314 27 297.51 280.17 202.31 244.03 22.19 1722 75 78 5.117.152 4.828 182 4,530,360 4,225,153 -3.914, 365 58.47 61.88 67.37 73.56 80.30 6.9493 6.8835 6.4207 6.1610 608.65 621.88 125.58 651.28 606.75 403,80 421.02 438.42 455.95 .473.59 525.71 508.35 489,97 470.57 450,19 225.46 206.71 107.94 189.31 151.00 13.04 9161 6.88 -4.77 79 3.19.260 - 5. 0050 133.19 2.05 5.6533 680.00 693.98 3,600,035 3,284,542 2070.498 2,880,734 2.358 245 87.64 95.61 104.28 113,60 123.80 428.86 406.82 383.57 350.79 335.40 401.27 508.95 528.50 544.15 561.57 5.1645 4.9282 4 6080 1.27 0.75 0.42 118,06 99,81 84.59 70.56 721.04 734.07 0.22 310.56 B6 134.04 146.89 4.4742 4.2571 4.0470 3.8442 2,066,000 1.787,299 1,524,758 1,281,083 1,058.491 578.80 595.70 012.51- 743.74 750.03 7 70.82 782.41 793 46 08 57.83 48.50 3861 28.17 21.13 88 0.11 0.05 0.02 0.01 0.00 285,44 280.21 235.11 210.36 188.77 0486 544,96 0.00 204.93 3.4611 04.09 222.27 3.2812 8 14.27 240.86131091824.01 280.73 2.540 833.30 281.91 27888 B42.14 858,676 682.707 530 950 403 072 297,881 RAD 1 675.83 690.59 704. 718.61 188.21 162.90 140.69 119.79 100.43 15.41 10.91 7.47 4.93 3.13 0.00 - 0.00 850.53 731.83 213.977 148,832 190 1.10 304.45 328.34 353.60 380.20 408.12 2.8408 2 5002 23878 2.2425 2.1252 0.60 82.78 56.97 52.09 41.14 31.12 885.99 87305 879.70 09 756.60 769.13 779,00 0.00 0.00 0.00 0.31 0.15 100 100 101 437.28 23.705 13.339 457.51 885.93 891.78 0.07 0.03 22.91 18.37 11.33 0.00 20152 1.9123 1.8164 1.2273 1.6447 780.44 799.21 808.41 817.02 825.06 499,99 53128 584.29 0.01 105 90223 900.00 0.00 0.00 0.00 0.00 4.86 105 2.90 0.00 292 597 B3 631.64 665,45 698.97 731.87 1.78 1.5685 1,4984 1.4341 1.3755 1.3223 911 22 915,10 018,82 022.14 925.15 822.63 830.48 845 84 251.69 857.04 0.00 0.00 0.00 0.00 110 0.00 100 0.00 0.00110 0.28 0.00 Page 246