25 0 426KB
Lic. Sabino Oscar Ramos
Matemática Actuariales [Teoría /Problemas]
Lic. Sabino Oscar Ramos
x 51 52 53 54 55 56 57 58 59 60 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 94 95 96 97 98 99
lx 8.689.404,0 8.610.244,0 8.524.486,0 8.431.654,0 8.331.317,0 8.223.010,0 8.106.161,0 7.980.191,0 7.884.528,0 7.698.698,0 7.542.106,0 7.374.370,0 7.195.099,0 7.003.925,0 6.800.351,0 6.584.614,0 6.355.865,0 6.114.088,0 5.859.253,0 5.592.012,0 5.313.586,0 5.025.855,0 4.731.089,0 4.431.800,0 4.129.906,0 3.826.895,0 3.523.881,0 3.221.884,0 2.922.055,0 2.626.372,0 2.337.524,0 2.058.541,0 1.792.639,0 1.542.781,0 1.311.348,0 1.100.037,0 909.929,0 741.474,0 594.477,0 468.174,0 361.365,0 272.552,0 200.072,0 142.191,0 97.165,0 63.037,0 37.787,0 19.331,0 6.415,0
dx 79.160,0 85.758,0 92.832,0 100.337,0 108.307,0 116.849,0 125.970,0 95.663,0 185.830,0 156.592,0 167.736,0 179.271,0 191.174,0 203.574,0 215.737,0 228.749,0 241.777,0 254.835,0 267.241,0 278.426,0 287.731,0 294.766,0 299.289,0 301.894,0 303.011,0 303.014,0 301.997,0 299.829,0 295.683,0 288.848,0 278.983,0 265.902,0 249.858,0 231.433,0 211.311,0 190.108,0 168.455,0 146.997,0 126.303,0 106.809,0 88.813,0 72.480,0 57.881,0 45.026,0 34.128,0 25.250,0 18.456,0 12.916,0 6.415,0
Matemática Actuariales [Teoría /Problemas]
v^ x 0,221463 0,215013 0,208750 0,202670 0,196767 0,191036 0,185472 0,180070 0,174825 0,169733 0,164789 0,159990 0,155330 0,150806 0,146413 0,142149 0,138009 0,133989 0,130086 0,126297 0,122619 0,119047 0,115580 0,112214 0,108945 0,105772 0,102691 0,099700 0,096796 0,093977 0,091240 0,088582 0,086002 0,083497 0,081065 0,078704 0,076412 0,074186 0,072026 0,069928 0,067891 0,065914 0,063994 0,062130 0,060320 0,058563 0,056858 0,055202 0,053594
qx 0,009110 0,009960 0,010890 0,011900 0,013000 0,014210 0,015540 0,011988 0,023569 0,020340 0,022240 0,024310 0,026570 0,029066 0,031724 0,034740 0,038040 0,041680 0,045610 0,049790 0,054150 0,058650 0,063260 0,068120 0,073370 0,079180 0,085700 0,093060 0,101190 0,109980 0,119350 0,129170 0,139380 0,150010 0,161140 0,172820 0,185130 0,198250 0,212461 0,228140 0,245771 0,265931 0,289301 0,316659 0,351238 0,400558 0,488422 0,668150 1,000000
px 0,990890 0,990040 0,989110 0,988100 0,987000 0,985790 0,984460 0,988012 0,976431 0,979660 0,977760 0,975690 0,973430 0,970934 0,968276 0,965260 0,961960 0,958320 0,954390 0,950210 0,945850 0,941350 0,936740 0,931880 0,926630 0,920820 0,914300 0,906940 0,898810 0,890020 0,880650 0,870830 0,860620 0,849990 0,838860 0,827180 0,814870 0,801750 0,787539 0,771860 0,754229 0,734069 0,710699 0,683341 0,648762 0,599442 0,511578 0,331850 0,000000
Dx 1.924.383,079178 1.851.312,673313 1.779.488,937464 1.708.844,883886 1.639.329,675185 1.570.891,663317 1.503.465,327623 1.436.991,678222 1.378.413,259784 1.306.723,800643 1.242.859,181176 1.179.823,364148 1.117.613,444386 1.056.231,476760 995.661,521304 935.994,917504 877.163,615315 819.219,733810 762.208,427644 706.256,349545 651.545,515481 598.314,841566 546.819,148758 497.308,090868 449.933,483453 404.778,530011 361.871,959219 321.222,807196 282.844,432432 246.818,815218 213.275,455157 182.350,557512 154.171,177721 128.818,253416 106.305,040747 86.577,684864 69.529,476119 55.007,277774 42.817,574091 32.738,371160 24.533,450770 17.964,895710 12.803,373531 8.834,317149 5.861,024111 3.691,662285 2.148,481494 1.067,102899 343,804388
Nx 31.303.173,615308 29.378.790,536130 27.527.477,862817 25.747.988,925353 24.039.144,041467 22.399.814,366282 20.828.922,702965 19.325.457,375342 17.888.465,697120 16.510.052,437336 15.203.328,636693 13.960.469,455517 12.780.646,091369 11.663.032,646982 10.606.801,170222 9.611.139,648917 8.675.144,731413 7.797.981,116099 6.978.761,382289 6.216.552,954645 5.510.296,605101 4.858.751,089619 4.260.436,248053 3.713.617,099295 3.216.309,008426 2.766.375,524974 2.361.596,994962 1.999.725,035743 1.678.502,228548 1.395.657,796116 1.148.838,980898 935.563,525741 753.212,968230 599.041,790509 470.223,537093 363.918,496346 277.340,811482 207.811,335363 152.804,057589 109.986,483498 77.248,112337 52.714,661567 34.749,765857 21.946,392326 13.112,075177 7.251,051066 3.559,388780 1.410,907287 343,804388
Lic. Sabino Oscar Ramos
Matemática Actuariales [Teoría /Problemas]
TABLAS C.S.O-1958 –Al 3% x 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 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50
Sx 6.979.643.889,091730 6.690.680.872,292680 6.411.717.855,493620 6.142.394.838,694560 5.882.414.573,332970 5.631.491.152,910680 5.389.347.948,078180 5.155.717.290,208270 4.930.340.084,074650 4.712.965.520,550730 4.503.350.723,494630 4.301.260.413,546080 4.106.466.591,794800 3.918.748.167,638640 3.737.890.612,012560 3.563.685.701,069080 3.395.931.142,682990 3.234.430.357,576230 3.078.992.332,462790 2.929.431.417,138740 2.785.567.189,820120 2.647.224.380,567330 2.514.232.844,156690 2.386.427.418,669940 2.263.647.838,320510 2.145.738.643,406830 2.032.549.041,082240 1.923.932.815,840470 1.819.748.192,981520 1.719.857.663,766430 1.624.127.861,352690 1.532.429.399,453690 1.444.636.719,526150 1.360.627.983,989720 1.280.284.935,305170 1.203.492.798,233820 1.130.140.150,084530 1.060.118.797,317300 993.323.593,988390 929.652.305,526392 869.005.451,814352 811.286.104,262241 756.399.758,529627 704.254.190,779768 654.759.354,351648 607.827.311,869686 563.372.147,560910 521.309.888,094142 481.558.408,083056 444.037.323,916487 408.667.900,456910
Cx 68.737,864078 16.471,863512 13.787,524240 12.837,749355 11.934,192532 11.156,965268 10.417,328443 9.789,463915 9.266,744711 8.839,091615 8.571,528447 8.449,523417 8.392,725265 8.525,775224 8.704,931731 8.864,549710 9.064,961408 9.243,828940 9.346,987979 9.327,221755 9.299,602473 9.214,012103 9.075,862598 8.936,960188 8.751,644451 8.569,542258 8.432,941393 8.296,153852 8.200,069105 8.140,858368 8.076,940422 8.045,566673 8.007,660454 7.998,081059 8.014,251004 8.117,922897 8.269,053799 8.492,305291 8.838,257506 9.237,170726 9.709,220641 10.218,176080 10.731,608929 11.271,289102 11.831,248466 12.429,128790 13.079,355175 13.772,151762 14.518,518355 15.306,897482 16.145,109059
Mx 1.583.267,661787 1.514.529,797709 1.498.057,934197 1.484.270,409957 1.471.432,660602 1.459.498,468070 1.448.341,502803 1.437.924,174359 1.428.134,710445 1.418.867,965734 1.410.028,874119 1.401.457,345672 1.393.007,822255 1.384.615,096990 1.376.089,321766 1.367.384,390035 1.358.519,840325 1.349.454,878917 1.340.211,049977 1.330.864,061997 1.321.536,840242 1.312.237,237769 1.303.023,225666 1.293.947,363068 1.285.010,402880 1.276.258,758429 1.267.689,216171 1.259.256,274779 1.250.960,120927 1.242.760,051821 1.234.619,193453 1.226.542,253031 1.218.496,686358 1.210.489,025904 1.202.490,944844 1.194.476,693840 1.186.358,770943 1.178.089,717145 1.169.597,411854 1.160.759,154348 1.151.521,983622 1.141.812,762981 1.131.594,586901 1.120.862,977972 1.109.591,688870 1.097.760,440404 1.085.331,311614 1.072.251,956439 1.058.479,804677 1.043.961,286322 1.028.654,388840
Rx 85.639.039,020883 84.055.771,359096 82.541.241,561386 81.043.183,627189 79.558.913,217231 78.087.480,556629 76.627.982,088559 75.179.640,585757 73.741.716,411397 72.313.581,700953 70.894.713,735219 69.484.684,861100 68.083.227,515428 66.690.219,693173 65.305.604,596183 63.929.515,274417 62.562.130,884382 61.203.611,044057 59.854.156,165140 58.513.945,115163 57.183.081,053166 55.861.544,212924 54.549.306,975154 53.246.283,749488 51.952.336,386420 50.667.325,983540 49.391.067,225111 48.123.378,008940 46.864.121,734162 45.613.161,613235 44.370.401,561413 43.135.782,367960 41.909.240,114929 40.690.743,428571 39.480.254,402667 38.277.763,457823 37.083.286,763983 35.896.927,993039 34.718.838,275894 33.549.240,864040 32.388.481,709692 31.236.959,726071 30.095.146,963089 28.963.552,376188 27.842.689,398216 26.733.097,709346 25.635.337,268942 24.550.005,957328 23.477.754,000889 22.419.274,196212 21.375.312,909890
Lic. Sabino Oscar Ramos
Matemática Actuariales [Teoría /Problemas]
TABLAS C.S.O-1958 –Al 3% x 51 52 53 54 55 56 57 58 59 60 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 94 95 96 97 98 99
Sx 375.372.949,456641 344.076.742,490256 314.704.918,603049 287.184.407,389155 261.443.385,112725 237.411.207,720182 215.018.360,002824 194.196.403,948782 174.877.913,222364 156.996.414,174167 140.486.335,382445 125.282.980,391367 111.322.484,581465 98.541.812,135710 86.878.753,134342 76.271.925,609734 66.660.785,960817 57.985.641,229404 50.187.660,113305 43.208.898,731016 36.992.345,776371 31.482.049,171270 26.623.298,081651 22.362.861,833598 18.649.244,734303 15.432.935,725877 12.666.560,200903 10.304.963,205941 8.305.238,170198 6.626.735,941650 5.231.078,145534 4.082.239,164636 3.146.675,638895 2.393.462,670665 1.794.420,880156 1.324.197,343064 960.278,846717 682.938,035236 475.126,699873 322.322,642284 212.336,158786 135.088,046449 82.373,384881 47.623,619024 25.677,226698 12.565,151520 5.314,100455 1.754,711674 343,804388
Cx 17.020,413268 17.902,007499 18.814,278700 19.743,027617 20.690,545601 21.672,209578 22.683,397140 23.717,295197 24.752,176517 25.804,702944 26.836,035052 27.846,132456 28.830,119731 29.779,577475 30.692,340447 31.569,314301 32.395,426690 33.150,537220 33.751,832634 34.140,260776 34.253,620066 34.069,046937 33.584,286567 32.889,905740 32.050,094700 31.116,904870 30.109,192046 29.022,370671 27.787,429861 26.354,462530 24.712,991185 22.868,198504 20.862,501653 18.761,224706 16.631,092560 14.526,528604 12.497,067972 10.587,549962 8.832,089122 7.251,375599 5.853,988533 4.638,272789 3.596,142589 2.715,982830 1.998,652386 1.435,656647 1.018,801464 692,217844
Mx 1.012.509,279781 995.488,866513 977.586,859013 958.772,580313 939.029,552696 918.339,007095 896.666,797517 873.983,400377 850.266,105180 825.513,928663 799.709,225720 772.873,190667 745.027,058211 716.196,938480 686.417,361005 655.725,020557 624.155,706256 591.760,279566 558.609,742346 524.857,909713 490.717,648937 456.464,028871 422.394,981934 388.810,695367 355.920,789627 323.870,694927 292.753,790057 262.644,598011 233.622,227340 205.834,797479 179.480,334949 154.767,343764 131.899,145260 111.036,643607 92.275,418902 75.644,326342 61.117,797738 48.620,729766 38.033,179804 29.201,090682 21.949,715083 16.095,726550 11.457,453761 7.861,311171 5.145,328342 3.146,675955 1.711,019308 692,217844
Rx 20.346.658,521050 19.334.149,241269 18.338.660,374757 17.361.073,515743 16.402.300,935430 15.463.271,382734 14.544.932,375639 13.648.265,578122 12.774.282,177745 11.924.016,072565 11.098.502,143901 10.298.792,918182 9.525.919,727514 8.780.892,669303 8.064.695,730823 7.378.278,369818 6.722.553,349260 6.098.397,643004 5.506.637,363438 4.948.027,621091 4.423.169,711379 3.932.452,062442 3.475.988,033571 3.053.593,051637 2.664.782,356270 2.308.861,566643 1.984.990,871716 1.692.237,081659 1.429.592,483648 1.195.970,256307 990.135,458829 810.655,123880 655.887,780116 523.988,634856 412.951,991249 320.676,572347 245.032,246005 183.914,448267 135.293,718501 97.260,538697 68.059,448015 46.109,732931 30.014,006382 18.556,552621 10.695,241450 5.549,913108 2.403,237153 692,217844