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Illustrative Life Table

Ark Life would like to provide 10 year term insurance and annuity contract to individuals with age range between (25) and (40) with the following benefit. On death before age 55, a benefit of 250,000 is paid immediately. No benefit is payable on the death after age 55. On attaining age 55, the life receives an annuity of 10,000 per annum payable monthly in arrears. Level premiums are payable monthly in advance for 10 years. Mortality follows the constructed life tables and interest rate is 5% pa. Calculate the level monthly premium the insurance company shall charge individuals for each age between (25) to (40).

2. Ark Life would like to provide 10 year term insurance and annuity contract to individuals with age range between (25) and (40) with the following benefit. On death before age 55, a benefit of 250,000 is paid immediately. No benefit is payable on the death after age 55. On attaining age 55, the life receives an annuity of 10,000 per annum payable monthly in arrears. Level premiums are payable monthly in advance for 10 years. Mortality follows the constructed life tables and interest rate is 5% pa. Calculate the level monthly premium the insurance company shall charge individuals for each age between (25) to (40). 1 4 5 Nm 0 0 6 7 9 10 11 12 13 14 15 16 17 18 Age 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Illustrative Life Table Japan at i=0.05 my 10009x , 100042 Ax 1000 EX 100010E, 1000 20EX 0.001861 100000 1.859269413 20.5084270123.40823748 0.023408237781.5213417612.1122234375 2490713 0.000299 99814.07306 0.298955304 20.5220043 22.76170007 0.0227617 782.9042936 613.2211498 375.8322858 0.000164 99784.23311 0.163986553 20.50423436 23.60788747 0.023607887783.0843823 613.3536199 375.8153738 0.000132 99767.869840.131991288 20.48280499 24.62833401 0.024628334 783.149381 613.4094376 375.7342064 0.000106 99754.70135 0.105994382 20.45964573 25.73115571 0.025731156 783.202637 613.4327476 375.6545592 0.000093 99744.12791 0.092995676 20.43479399 26.91457191 0.026914572 783.231616 613.4358148 375.5685442 0.000069 99734.85214 0.06899762 20.40843159 28.16992451 0.028169925 783.2645124613.4045303 375.4848017 0.000081 99727.97067 0.08099672 20.38025935 29.51145933 0.029511459783.2535468 613.3542332 375.3841853 0.000064 99719.89303 0.063997952 20.35092068 30.90853907 0.030908539783.2598129 613.2720493 375.2790924 0.000069 99713.51116 0.06899762 20.31976714 32.3920411 0.032392041 783.2363154613.1665756 375.17628 0.000051 99706.63117 0.0509987 20.28715526 33.94498766 0.033944988 783.2112523613.0396632375.0536174 0.000083 99701.54626 0.082996556 20.25254588 35.59305354 0.035593054 783.138417 612.8821323 374.9081249 0.000073 99693.27138 0.072997336 20.2168511 37.29280483 0.037292805783.0851654612.7221909374.7825517 0.000094 99685.99403 0.093995582 20.17916668 39.08730101 0.039087301 782.9739752612.5341141 374.6427839 0.000101 99676.62399 0.1009949 20.14001809 40.95151974 0.04095152 782.8628008612 3809997 374.5004466 0.000144 99666.557160.143989632 20.09904889 42.90243375 0.042902434782.7258118 612.2377193 374.3514251 0.000151 99652.20621 0.1509886 20.0568893244.91003239 0.044910032 782.5974553612.1324234 374.2054565 0.000215 99637.15986 0.214976889 20.01275548 47.01164363 0.047011644782.4464285 612.0185774 374.0498194 0.000236 99615.740170.235972154 19.9676858549.15781672 0.049157817782.3173355 611.9292292 373.9084553 0.000276 99592.23363 0.275961916 19.92077089 51.39186245 0.051391862 782.2328498 611.8668156373.7592956 0. 0308 99564.74997 0.30795257319.8722934353.70031289 0.053700313 782.1866994 611.793396 373.5997345 0.000344 99534.08875 0.343940839 19.82201234 56.09465046 0.05609465 782.180442 611.7132563 373.4253041 0.00038 99499.85491 0.379927809 19.76991264 58.57558868 0.058575589 782.1859173611.6679912 373.24461 0.000344 99462.05215 0.343940839 19.7158988961.14767201 0.061147672782.2007789611.6276225373.0595266 0.000335 99427.84309 0.334943894 19.65845518 63.883086770.063883087782.2054721 611.548116 372.8279285 0.000316 99394.54034 0.315950077 19.5979421566.76465963 0.06676466 782.1577591 611.4478304 372.559589 0.000337 99363.13663 0.336943222 19.53401103 69.80899869 0.069808999782.0615596 611.3145493 372.2326253 0.000361 99329.656890.360934847 19.46727094 72.98709791 0.072987098 781.9982152611.1739631 371.8791722 0.000338 99293.80536 0.337942884 19.39763577 76.30305839 0.076303058 781.9317481 611.0321872 371.4666153 0.000396 99260.24972 0.395921602 19.32404799 79.80723872 0.079807239 781.8254126 610.8507376 370.9899583 19 20 21 22 23 24 25 26 27 28 29 30 31 32 2 00000 12000 1 12 1217166 non2121717 791 740000 (10662 27047710 3 4 5 6 7 8 9 0 -1 -2 3 4 -5 -6 -7 8 -9 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 0.000439 99220.95044 0.438903654 19.24787103 83.43471266 0.083434713 781.7448888 610.6632352 370.4757519 0.000418 99177.40201 0.41791265 19.16867779 87.20581959 0.08720582 781.6706265 610.4580868 369.9204548 0.000446 99135.95452 0.445900557 19.08508758 91.18630583 0.091186306781.5541663 610.2078503 369.2670133 0.000474 99091.74974 0.47388768 18.99781309 95.34223372 0.095342234 781.4392863 609.9455173368.6047735 0.000499 99044.79138 0.49887552 18.90666338 | 99.68269613 0.099682696781.3134847 609.6461076 367.849172 0.000534 98995.38036 0.533857447 18.81138109 | 104.2199482 0.104219948 781.154113 609.3072385 366.9835395 0.000567 98942.53094 0.566839286 18.71193965 108.9552547 0.108955255 780.9658775 608.9052284 366.1100589 0.000593 98886.44642 0.59282421 18.60808443 113.9007416 0.113900742 780.762072 608.4669745365.1123066 0.000635 98827.82414 0.63479843 18.49945557 119.0735441 0.119073544 780.5411476 607.9329749364.0109667 0.000703 98765.0884 0.702752953 18.38609982 124.4714372 0.124471437780.2836115 607.3332411 362.799375 0.000775 98695.68094 0.774699765 18.26824287 130.08367280.130083673 780.009 606.6776753 361.4848007 0.000828 98619.22142 0.827657303 18.14571249 135.9184527 0.135918453 779.6822447605.9719133360.0655131 0.000876 98537.5985 0.875616424 18.01791077 142.0042488 0.142004249 779.3244527 605.1495619 358.5058563 0.000965 98451.31736 0.964534537 17.88446625 148.3587502 0.14835875 778.8608926 604.3240963 356.8526657 0.001055 98356.35766 1.054443683 17.745806 154.961619 0.154961619 778.349349 603.3814823 355.0277643 0.001194 98252.64642 1.193287466 | 17.60165626 161.8258926 0.161825893 777.7829169 602.2963725 353.020806 0.001287 98135.40277 1.286172171 17.452565 168.9254764 0.168925476777.2036844 601.2595094 350.9170938 0.001471 98009.18375 1.46991861 17.29744073 176.3123461 0.176312346776.5052923 600.0527916 348.5222229 0.001622 97865.11822 1.620685269 17.1375035 183.9284046 0.183928405 775.9076134 598.7682553 345.9993843 0.001783 97706.50967 1.7814114 16.97188476 191.8150113 0.191815011 775.2065098 597.3645941 343.2293888 0.001939 97532.45418 1.937121354 16.80040744 199.9805982 0.199980598774.3759337 595.8432549 340.1378565 0.002186 97343.52198 2.183612442 16.62262786 208.44629250.208446292 773.6189643 594.1950529 336.7857581 0.002241 97130.96145 2.238490834 16.43965709 217.1591862 0.217159186 772.7607236 592.4252101 333.1990288 0.002526 96913.53469 2.522812347 16.24801097 226.285192 0.226285192 771.7004512 590.49882 329.2531789 0.002855 96669.04002 2.850928363 16.05090494 235.6711934 0.235671193 770.5876905 588.3968512 325.220364 0.002917 96393.44352 2.912749689 15.8486335 245.3031665 0.245303166 769.4496031 586.124742 320.615952 0.003296 96112.67354 3.290574155 15.63661071 255.3994899 0.25539949 768.0719842583.6366633315.5426943 0.003614 95796.407663.607477362 15.4191792 265.7533714 0.265753371766.6347317 580.8192676 310.1285831 0.003969 95450.82429 3.96113393 15.19495361 276.4307804 0.27643078 765.1917516 577.8519172 304.2275666 0.004333 95072.73079 4.323626099 14.9639756 287.4297332 0.287429733 763.5689727 574.5727018 297.71927 0.004709 94661.671854.697930042 14.72584342 298.7693607 0.298769361 761.7454602 570.8512326 290.6477334 0 -1 -2 3 mt no No No 2 3 66 67 68 69 70 71 72 73 74 75 76 77 78 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 0.005169 94216.95794 5.155663708 14.48016239 310.4684578 0.310468458 759.8723496 566.7932718 282.8427234 0.005498 93731.20699 5.482913659 14.22752283 322.4989129 0.322498913 757.6219073 562.4322246 274.035866 0.006092 93217.28688 6.073481392 13.96547044 334.9775982 0.334977598 755.172695 557.5848211 264.2976673 0.006724 92651.13342 6.701444495 13.69693202 347.7651418 0.347765142 752.48304 552.7228151 253.8008732 0.007171 92030.23699 7.145349729 13.42172356 360.8703067 0.360870307 749.3989297547.0097558 242.1111687 0.008135 91372.64876 8.102000432 13.13667588374.4440057 0.374444006 745.905904 540.6491987 229.683436 0.008736 90632.34752 8.697952028 12.84760094 388.2094789 0.388209479 742.3653134533.9502326 216.1029675 0.00966 89844.03171 9.613492076 12.54913274 402.4222503 0.40242225 738.3540544 526.4801543201.3375788 0.010831 88980.31682 10.77255591 12.24429986 416.9381018 0.416938102734.5319239518.1577006 185.9121026 0.011843 88021.77139 11.7731477 11.93508624 431.6625601 0.43166256 729.9313277 509.1479475 169.689958 0.012893 86985.47807 12.81024133 11.61862838 446.731982 0.446731982 724.8222542 499.0227257 152.966508 0.014154 85871.1731 14.05430307 11.29424176462.1789638 0.462178964 719.2553625 487.2335794 136.0261295 0.01485 84664.31361 14.74028252 10.96303162 477.9508754 0.477950875 713.0456604 474.0044156 119.2229173 0.017114 83416.33771 16.96838736 10.61769096494.3956685 0.494395668 705.4257055459.1829145 102.6738024 0.018867 82000.89698 18.69013222 10.27288988 510.8147674 0.510814767 697.5285593442.6085023 86.91468415 0.020603 80468.28937 20.39220832 9.921977449 527.52488340.527524883688.4759993 424.8289585 72.20129598 0.022825 78827.36325 22.56648033 9.563088821 544.614818 0.544614818 677.4138989 404.7249244 58.80571215 0.025594 77048.50711 25.26925003 9.198828443 561.9605503 0.56196055 664.7602558 382.421971846.86522811 0.028372 75101.54912 27.9732944 8.83194653 579.4311176 0.579431118 650.9302269 358.7944412 36.3823947 0.03193 73000.71138 31.42562009 8.460203624 597.1331608 0.597133161 634.5381796333.2822196 | 27.58209956 0.036801 70706.6187536.132074028.087364241 614.8874171 0.614887417617.0570346 306.532148 20.27525132 0.041681 68151.84197 40.82429117 7.720697258 632.3477496 0.63234775 597.4558908 279.1805311 14.59910164 0.046618 65369.59133 45.5480714 7.357079684 649.6628722 0.649662872 575.2780322 251.5227989 10.1824637 0.053877 62392.13252 52.45135218 6.99347287 666.9774824 0.666977482 551.2026118 223.6010947 6.93456964 0.059866 59119.5808 58.10926151 6.641502289 683.7379863 0.683737986 525.2358806 196.3692154.476103867 0.069082 55684.1856266.74984957 6.289028187 700.52246730.700522467 496.7646924169.9538003 2.862092485 0.079508 51967.27461 76.42936863 5.950687062 716.6339494 0.716633949 467.2822469 145.2979755 1.79142608 0.089369 47995.44862 85.49194217 5.628396182731.9811342 0.731981134437.2195441 122.5484715 1.125316124 0.102132 43892.2245 97.08964037 5.314131406 746.9461235 0.746946124 405.6604413 101.4017792 0.694682756 0.115597 39630.74421 109.1658429 5.016929895 761.0985764 0.761098576 373.8686222 82.75898904 0.413993915 0.130265 35304.42062 122.1372335 4.734637033 774.5410937 0.774541094 342.1213361 66.14396387 0 0.146006 30992.43635 135.8474817 4.466949772 787.2881061 0.787288106 310.9426401 52.29269243 0 0.164288 26782.19192 151.5023806 4.212563388 799.4017434 0.799401743 280.29047 40.48326332 0 96