Last updated 1996 Sep 29

Life and Commutation Tables


Male Individual Annuity, 1983
8% interest

Summary of Actuarial Methods | ACCT 503 Syllabus



l[x] = lives at age x
v = 1 / (1 + interest rate)
D[x] = l[x] v^(x)
N[x] = Sum [from x=1 to omega-1] D[x]
omega = last surviving age
        
    
                    8.0% = interest rate    0.925926 = v
       MIA 1983                                      NSP life annuity
    dec rate     x = age lives=l[x]     D[x]     N[x]at max(65, x)
             NA       0          NA
             NA       1          NA       NA       NA       NA
             NA       2          NA       NA       NA       NA
             NA       3          NA       NA       NA       NA
             NA       4          NA       NA       NA       NA
      0.000419        5  1,000,000 680583.2  9082607  0.07810
      0.000389        6    999,581 629905.6  8402024  0.08438
      0.000370        7    999,192   583019  7772119  0.09117
      0.000391        8    998,822 539632.7  7189100  0.09850
      0.000409        9    998,432 499464.5  6649467  0.10642
      0.000424       10    998,024   462278  6150002  0.11498
      0.000438       11    997,600 427853.7  5687724  0.12423
      0.000450       12    997,163 395987.3  5259871  0.13423
      0.000461       13    996,715 366489.9  4863883  0.14504
      0.000472       14    996,255 339186.1  4497393  0.15671
      0.000483       15    995,785   313913  4158207  0.16933
      0.000495       16    995,304 290519.8  3844294  0.18296
      0.000508       17    994,811 268866.6  3553774  0.19770
      0.000523       18    994,306 248824.1  3284908  0.21362
      0.000540       19    993,786 230272.2  3036084  0.23083
      0.000559       20    993,249 213099.9  2805812  0.24943
      0.000581       21    992,694 197204.4  2592712  0.26954
      0.000605       22    992,117 182490.6  2395507  0.29127
      0.000632       23    991,517 168870.5  2213017  0.31476
      0.000661       24    990,890 156262.8  2044146  0.34016
      0.000692       25    990,236 144592.1  1887883  0.36761
      0.000724       26    989,550 133788.9  1743291  0.39730
      0.000756       27    988,834   123789  1609502  0.42939
      0.000788       28    988,086 114532.8  1485713  0.46409
      0.000819       29    987,308 105965.3  1371181  0.50162
      0.000850       30    986,499 98035.64  1265215  0.54219
      0.000881       31    985,661 90696.59  1167180  0.58606
      0.000913       32    984,792 83904.34  1076483  0.63351
      0.000945       33    983,893 77618.27 992578.8  0.68481
      0.000980       34    982,963 71800.85 914960.5  0.74030
      0.001023       35    982,000 66417.12 843159.7  0.80030
      0.001077       36    980,995 61434.42 776742.6  0.86521
      0.001146       37    979,939 56822.46 715308.1  0.93544
      0.001232       38    978,816 52553.09 658485.7  1.01143
      0.001341       39    977,610 48600.32 605932.6  1.09369
      0.001476       40    976,299 44939.95 557332.3  1.18278
      0.001641       41    974,858 41549.65 512392.3  1.27929
      0.001842       42    973,258 38408.77 470842.7  1.38390
      0.002079       43    971,465 35498.16 432433.9  1.49737
      0.002352       44    969,446 32800.34 396935.7  1.62053
      0.002657       45    967,166 30299.25 364135.4  1.75430
      0.002988       46    964,596 27980.32 333836.1  1.89969
      0.003343       47    961,714 25830.29 305855.8  2.05781
      0.003718       48    958,499 23836.98 280025.5  2.22989
      0.004110       49    954,935 21989.22 256188.6  2.41727
      0.004518       50    951,010 20276.71 234199.3  2.62143
      0.004938       51    946,714  18689.9 213922.6  2.84399
      0.005370       52    942,039 17220.01 195232.7  3.08675
      0.005811       53    936,980 15858.83 178012.7  3.35169
      0.006260       54    931,535 14598.78 162153.9  3.64098
      0.006718       55    925,704 13432.77 147555.1  3.95703
      0.007184       56    919,485 12354.19 134122.3  4.30250
      0.007658       57    912,879 11356.89 121768.2  4.68033
      0.008146       58    905,888 10435.11 110411.3  5.09376
      0.008671       59    898,509 9583.428 99976.16  5.54644
      0.009266       60    890,718 8796.602 90392.74  6.04255
      0.009961       61    882,465  8069.53 81596.13  6.58699
      0.010787       62    873,674 7397.361  73526.6  7.18553
      0.011769       63    864,250 6775.524 66129.24  7.84499
      0.012920       64    854,079 6199.799 59353.72  8.57349
      0.014248       65    843,044 5666.386 53153.92  9.38057
      0.015761       66    831,032   5171.9 47487.53  9.18184
      0.017467       67    817,934  4713.32 42315.64  8.97788
      0.019373       68    803,648 4287.956 37602.32  8.76929
      0.021486       69    788,079 3893.412 33314.36  8.55660
      0.023810       70    771,146 3527.554 29420.95  8.34033
      0.026353       71    752,785 3188.484 25893.39  8.12091
      0.029120       72    732,947 2874.498 22704.91  7.89874
      0.032123       73    711,603 2584.067 19830.41  7.67411
      0.035398       74    688,745 2315.796 17246.34  7.44726
      0.038986       75    664,364 2068.353 14930.55  7.21857
      0.042930       76    638,463 1840.478  12862.2  6.98851
      0.047272       77    611,054 1630.987 11021.72  6.75770
      0.052054       78    582,168 1438.784  9390.73  6.52685
      0.057325       79    551,864 1262.861 7951.945  6.29677
      0.063132       80    520,229 1102.285 6689.084  6.06838
      0.069523       81    487,386 956.1994   5586.8  5.84271
      0.076547       82    453,501 823.8162   4630.6  5.62091
      0.084229       83    418,787 704.4033 3806.784  5.40427
      0.092498       84    383,513  597.289 3102.381  5.19410
      0.101261       85    348,039 501.8898 2505.092  4.99132
      0.110424       86    312,796 417.6555 2003.202  4.79630
      0.119894       87    278,256 344.0151 1585.546  4.60894
      0.129609       88    244,895 280.3424 1241.531  4.42863
      0.139643       89    213,154 225.9328 961.1888  4.25431
      0.150099       90    183,389 179.9842  735.256  4.08511
      0.161082       91    155,862 141.6377 555.2718  3.92037
      0.172699       92    130,756 110.0208 413.6341  3.75960
      0.185049       93    108,174 84.27804 303.6134  3.60252
      0.198219       94     88,157 63.59488 219.3353  3.44895
      0.212291       95     70,682 47.21219 155.7404  3.29873
      0.227346       96     55,677 34.43469 108.5282  3.15171
      0.243467       97     43,019 24.63528 74.09354  3.00762
      0.260903       98     32,545 17.25686 49.45826  2.86601
      0.279903       99     24,054 11.80971  32.2014  2.72669
      0.300716      100     17,321 7.874203 20.39169  2.58968
      0.323592      101     12,113  5.09843 12.51749  2.45517
      0.348780      102      8,193 3.193165 7.419057  2.32342
      0.376529      103      5,335  1.92542 4.225892  2.19479
      0.407088      104      3,327 1.111522 2.300473  2.06966
      0.440707      105      1,972 0.610217 1.188951  1.94841
      0.477634      106      1,103 0.316009 0.578734  1.83138
      0.518120      107        576 0.152845 0.262725  1.71890
      0.562412      108        278 0.068197  0.10988  1.61121
      0.610761      109        122 0.027632 0.041683  1.50850
      0.663417      110         47 0.009959 0.014051  1.41091
      0.720626      111         16 0.003104 0.004092  1.31851
      0.782640      112          4 0.000803 0.000989  1.23129
      0.849708      113          1 0.000162 0.000186  1.14920
      0.922077      114          0 2.25E-05 2.41E-05  1.07215
      1.000000      115          0 1.62E-06 1.62E-06  1.00000


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