Question 5 [15 marks). Thomas Brown plans to retire at age 67 with a pension of 30,000 per year, paid annually in advance during his remaining lifetime. Assume an effective annual interest rate of 4% and the mortality given by table AMCOO select values. You can find the table in the appendix. (a) Show that the expected present value of the pension at retirement is approximately 369,659. (b) In order to cover the cost of the pension, Thomas wants to make monthly payments in arrears starting at age 30 until retirement. What are the monthly premiums assuming he survives until retirement? (c) How does the expected present value in (a) change when he switches to a pension of 2,500 paid monthly in advance during his remaining lifetime? Give reasons. [6] [5] AMCOO Male Life Table 1-1+1 Age x 17 18 19 Agex 17 9997.5094 10000.0000 18 9992.9305 9994.6901 9995.4200 19 9988.3337 9990.1025 9990.8321 20 9983.6991 9985.4871 9986.2163 21 9979.0567 9980.8438 9981.5827 22 9974.3666 9976.1827 9976.9213 23 9969.6487 9971.4740 9972.2222 24 9964.8832 9966.7276 9967.4854 25 9960.0701 9961.9336 9962.7010 26 9955.1996 9957.0921 9957.8691 27 9950.2618 9952.1832 9952.9698 28 9945.2469 9947.1972 9947.9933 29 9940.1847 9942. 1340 9942.9398 30 9935.0655 9936.9939 9937.7794 31 9929.8794 9931.7671 9932.5024 32 9924.5767 9926.4238 9927.0892 33 9919.1182 9920.9344 9921.5201 34 9913.4841 9915.2596 9915.7755 35 9907.6152 9909.3799 9909.8162 36 9901.4922 9903.2460 9903.6126 37 9895.0760 9896.8385 9897.1357 38 9888.3275 9890.1087 9890.3363 39 9881.1880 9882.9977 9883.1559 40 9873.5893 9875.4570 9875.5558 41 9865.4534 9867.4085 9867.4578 42 9856.7223 9858.7745 9858.7942 43 9847.3090 9849.4875 9849.4875 44 9837.1169 9839.4312 9839.4312 45 9826.0499 9828.5291 9828.5291 46 9813.9735 9816.6562 9816.6562 47 9800.7439 9803.6786 9803.6786 48 9786.2090 9789.4437 9789.4437 49 9770.1885 9773.7708 9773.7708 50 9752.4550 9756.4712 9756.4712 51 9732.8031 9737.3192 9737.3192 52 9710.9228 9716.0627 9716.0627 53 9686.5083 9692.4138 9692.4332 54 9659.2100 9666.0213 9666.1182 55 9628.6170 9636.5205 9636.7719 56 9594.3554 9603.4960 9604.0069 57 9555.9547 9566.5317 9567.3964 58 9512.9284 9525.1558 9526.4767 = = = = = = = = = = = = = = = = = = = = = = = = G T = + = = = = = = = = = = = = Ages 59 9464.7096 9478.8531 9480.7305 60 9410.6849 9427.0212 9429.5820 61 9350.1805 9369.0144 9372.4010 62 9282.4873 9304.1589 9308.5187 63 9206.8320 9231.7028 9237.1968 64 9122.3956 9150.8360 9157.6369 65 9028.3257 9060.7100 9069.0001 66 8923.7129 8960.4327 8970.3747 67 8807.6361 8849.0571 8860.8106 68 8679.1539 8725.6105 8739.3111 69 8537.3365 8589.1250 8604.8568 70 8381.2654 8438.6022 8456.4058 71 8210.1056 8273.0800 8292.9181 72 8023.0608 8091.6666 8113.3848 73 7819.4936 7893.5124 7916.8461 74 7598.8879 7677.9138 7702.4263 75 7360.9680 7444.3113 7469.3894 76 7105.6585 7192.3651 7217.1705 77 6833.2053 6921.9772 6945.4296 78 6543.2750 6633.3614 6654.1244 79 6234.6920 6326.2215 6343.5631 80 5905.8869 6000.3050 6014.4463 81 5557.1270 5655.4241 5667.9541 82 5191.0860 5293.5691 5305.7888 83 4811.5773 4917.5469 4930-2080 84 4422.4381 4531.0383 4544.0494 85 4027.2597 4137.4915 4150.7347 86 3630.1730 3740.8772 3754.2191 87 3235.7358 3345.6473 3358.9374 88 2848.8406 2956.5986 2969.6769 89 2474.5254 2578.7306 2591.4291 90 2117.7709 2217.0436 2229.1940 91 1876.3069 1887.7528 92 1571.4202 93 1283.8047 94 1027.5920 95 804.3661 96 614.5164 97 457.2229 98 330.5502 99 231.6268 100 156.9026 Agex 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 99 100 AMCOO Male Life Functions (4%) Del+1 D. D--]+1 D. Agex 17 18 19 20 22 23 24 25 26 12 3 Age x D. 17 5132.45 5133.73 15 4932.79 4933.6 4934.02 19 4740.89 4741.73 4742.07 20 4556.43 4557,54557.58 21 4379.154379.93 4380.25 22 4208.74 4209.50 4209.82 23 4044.95 4045.9 4045.9 24 3887.51 3888.23 3888.53 25 3736.19 3736.89 3737.18 26 3590.73 3591.42 3591.70 27 3450.92 3451.58 3451.85 3316.52 3317.17 3317.43 3187.33 3187.96 3188.22 300 3063.173063.76 3064.00 31 2943.81 2944.37 294.59 32 2829.08 2829.61 2829.80 33 2718.77 2719.27 2719.43 34 2612.72 2613.19 2613.32 2510.74 | 2511.19 2511.30 2412.68 | 2413.11 241320 7 2318.39 23 18.80 2313.87 38 2227.70 2228.10 2228.15 2140.47 2140.86 2140.90 40 2056.56 2056.95 2056.97 41 1975.83 1976.22 1976.23 42 1898.16 1898.55 1898.56 43 1823.41 1823.81 1823.81 44 1751.46 1751.87 1751.87 45 16582.20 1682.63 1682.63 46 1615.52 1615.96 1615.96 47 1551.29 1551.75 1551.75 48 1489.41 1489.90 1489.90 49 1429.78 1430.30 1430.30 500 1372.29 1372.86 1372.86 51 1316.85 1317.47 1317.47 52 1263.36 | 1264.03 1264.05 53 1211.71 1212.45 1212.46 4 1161.83 1162.65 1162.66 5 1113.60 1114.52 1114.55 56 1066.96 1067.98 1068.05 57 102 1.82 1022.95 1023.04 58 978.049 97935 979.49 Agex D. Agex 30 935.71 937.11 937.29 59 60 94.58 896.14 896.38 60 61 854.65 856.37856.68 61 62 15.83 ALTI 818.11 62 67 778.05 780.16 780.62 63 64 741.27 743.58 74.13 64 65 105.41 07.94 708.59 65 6 670.42 673.18 673.92 66 67 636.25 639.24 640.00 67 68 602.85 606.08 07.03 68 69 570.19 573.65 574.70 69 0 538.24 541.92 543.07 0 1 1506.97 510.86 512.08 71 72 476.36 480.44 48173 72 73 46.42 450.65 451.98 73 74 417.14 421.48 422.82 74 75 388.54 392.94 394.26 75 76 360.64 365.0M 366.30 76 333.47 37.80 33895 TT 78 307.04 311.27 31224 78 79 28131 285.44 286.22 79 80 256.11 260.32 260.93 800 81 231.82 255.92 236.44 8L A2 208.22 212.33 212.82 82 83 185.58 189.66 190.15 83 84 164.01 168.03 168.52 84 85 143.6L 14754 148.0L 85 56 124.47 128.26 128.72 6 87 106.68 I10.30 I10.74 87 88 90.31 93.73 4.14 88 89 75.43 78.60 78.99 89 90 62.07 64.95 65.34 90 91 52.88 53.20 91 97 42.58 92 93 13.45 93 4 15.74 94 95 19.38 95 96 14.23 6 7 10.18 97 98 7.108 98 99 4.77 9 100 3. II 1000 42 43 44 45 52 53 4 55 516 57 58 AMC00 Male Life Functions (4%) Mis lll M-1|- 12 | Agex M. M. Agex 17 478.10 479.31 17 18 475.89 476.71 477.05 18 19 473.75 474.54 474.88 19 20 471.68 472.45 472.77 20 21 469.68 470.42 470.74 21 467.74 468.47 468.7 17 23 465.87 466.57 466.86 23 24 464.005 464.73 465.02 24 25 462.28 462.94 463.22 15 26 46056 61.21 461.48 26 27 458.89 459.52 459.78 27 28 457.25 457.86 458.12 28 29 455.66 456.25 456.50 29 30 454.11 454.07 454.91 30 31 452.60 453.13 453.34 31 32 45L12 451.62 451.800 32 33 449.65 450.12 450.27 33 4 448.18 448.63 448.76 4 35 446.72 47.14 47.15 35 36 445.24 45.65 445.74 36 37 43.76 444.15 444.22 7 38 42.25 42.4 442.69 38 9 440.72 41.10 41.13 400 439.16 439.53 439.5 40 41 437.54 43792 437.93 41 42 435.88 436.26 436.26 42 43 434.15 434.54 434.4 43 4 432.35 432.75 432.75 45 430.47 430.88 430.88 45 46 428.50 428.92 428.92 46 47 426.42 426.87 426.87 47 48 424.23 424.70 424.70 48 49 42191 422.41 422.41 30 419.43 419.98 419.98 50 51 416.80 417.39 417.39 51 52 413.98 414.62 414.62 52 53 410.95 411.66 411.66 53 407.70 408.49 408.50 4 55 404.20 05.08 405.10 55 56 400.43 401.41 401.46 57 396.37 7.46 97.55 57 92.01 393.21 393.34 58 Agex M M, M Agex 50 387300 388.64 388.82 9 60 382.24383.72 383.95 60 61 376.79 378.43 378.73 61 62 370.93 372.74 373.11 62 63 34.6M 36.64 367.09 63 64 357.89 360.00 360.62 64 65 350.67 353.07 153.70 65 66 4295 45.57 46.29 67 34.71 337.55 33837 67 68 325.95 329.02 329.93 69 316.66 31994 120.95 69 70 306.83 310.32 11.42 70 1 106.46 300.15 301.32 1 72 285.56 289.42 290.66 T2 73 274.15 28.16 279.44 73 74 262.26 26.38 267.67 14 75 249.92 254.10 255.37 76 137.17 241.36 24257 76 77 224.18 228.21 2011 78 210.67 21470 215.64 73 79 196.93 20NO.83 201.63 79 80 182.84 186.76 18735 80 81 168.47 129 1290 AL 82 153.96 157.90 15837 A. 83 19.50 143.41 143.88 83 84 125.24 129.10 12956 84 85 111.32 115.0% 115.4 85 86 97.87 101.50 101.94 36 87 85.02 88.49 35.91 87 88 72.90 76.17 76.57 33 89 61.63 4.67 65.04 89 51.30 4.08 4.42 90 91 4.49 4.30 91 92 36.23 92 93 28.74 93 94 22.32 94 95 16.94 95 96 1254 96 97 9.0M 97 98 6.33 98 99 4.29 99 100 281 100 4 58 AMC00 Male Life Functions (4%) Mis lll M-1|- 12 | Agex M. M. Agex 17 478.10 479.31 17 18 475.89 476.71 477.05 18 19 473.75 474.54 474.88 19 20 471.68 472.45 472.77 20 21 469.68 470.42 470.74 21 467.74 468.47 468.7 17 23 465.87 466.57 466.86 23 24 464.005 464.73 465.02 24 25 462.28 462.94 463.22 15 26 46056 61.21 461.48 26 27 458.89 459.52 459.78 27 28 457.25 457.86 458.12 28 29 455.66 456.25 456.50 29 30 454.11 454.07 454.91 30 31 452.60 453.13 453.34 31 32 45L12 451.62 451.800 32 33 449.65 450.12 450.27 33 4 448.18 448.63 448.76 4 35 446.72 47.14 47.15 35 36 445.24 45.65 445.74 36 37 43.76 444.15 444.22 7 38 42.25 42.4 442.69 38 9 440.72 41.10 41.13 400 439.16 439.53 439.5 40 41 437.54 43792 437.93 41 42 435.88 436.26 436.26 42 43 434.15 434.54 434.4 43 4 432.35 432.75 432.75 45 430.47 430.88 430.88 45 46 428.50 428.92 428.92 46 47 426.42 426.87 426.87 47 48 424.23 424.70 424.70 48 49 42191 422.41 422.41 30 419.43 419.98 419.98 50 51 416.80 417.39 417.39 51 52 413.98 414.62 414.62 52 53 410.95 411.66 411.66 53 407.70 408.49 408.50 4 55 404.20 05.08 405.10 55 56 400.43 401.41 401.46 57 396.37 7.46 97.55 57 92.01 393.21 393.34 58 Agex M M, M Agex 50 387300 388.64 388.82 9 60 382.24383.72 383.95 60 61 376.79 378.43 378.73 61 62 370.93 372.74 373.11 62 63 34.6M 36.64 367.09 63 64 357.89 360.00 360.62 64 65 350.67 353.07 153.70 65 66 4295 45.57 46.29 67 34.71 337.55 33837 67 68 325.95 329.02 329.93 69 316.66 31994 120.95 69 70 306.83 310.32 11.42 70 1 106.46 300.15 301.32 1 72 285.56 289.42 290.66 T2 73 274.15 28.16 279.44 73 74 262.26 26.38 267.67 14 75 249.92 254.10 255.37 76 137.17 241.36 24257 76 77 224.18 228.21 2011 78 210.67 21470 215.64 73 79 196.93 20NO.83 201.63 79 80 182.84 186.76 18735 80 81 168.47 129 1290 AL 82 153.96 157.90 15837 A. 83 19.50 143.41 143.88 83 84 125.24 129.10 12956 84 85 111.32 115.0% 115.4 85 86 97.87 101.50 101.94 36 87 85.02 88.49 35.91 87 88 72.90 76.17 76.57 33 89 61.63 4.67 65.04 89 51.30 4.08 4.42 90 91 4.49 4.30 91 92 36.23 92 93 28.74 93 94 22.32 94 95 16.94 95 96 1254 96 97 9.0M 97 98 6.33 98 99 4.29 99 100 281 100 4 58 AMCOO Male Life Functions (4%) Agex A, 17 0.09315 0.09337 23.578 23.572 18 0.09647 0.09669 23.492 23.486 19 0.09993 0.10014 23.402 23.396 20 0.10352 0.10373 23.309 23.303 21 0.10725 0.10747 23.211 23.206 22 0.11114 0.11135 23.110 23.105 23 0.11517 0.11539 23.005 23.000 24 0.11937 0.11959 22.896 22.891 25 0.12373 0.12395 22.783 22.777 26 0.12826 0.12848 22.665 22.659 27 0.13297 0.13320 22.543 22.537 28 0.13787 0.13809 22.415 22.410 29 0.14296 0.14318 22.283 22.277 30 0.14825 0.14847 22.146 22.140 31 0.15375 0.15396 22.003 21.997 32 0.15946 0.15966 21.854 21.849 33 0.16539 0.16558 21.700 21.695 34 0.17154 0.17172 21.540 21.535 35 0.17792 0.17809 21.374 21.370 36 0.18454 0.18471 21.202 21.198 37 0.19141 0.19157 21.023 21.019 38 0.19853 0.19868 20.838 20.834 39 0.20590 0.20605 20.647 20.643 40 0.21354 0.21369 20.448 20.444 41 0.22145 0.22160 20.242 20.238 42 0.22963 0.22978 20.030 20.026 43 0.23810 0.23826 19.809 19.805 44 0.24685 0.24702 19.582 19.578 45 0.25590 0.25608 19.347 19.342 46 0.26524 0.26543 19.104 19.099 47 0.27488 0.27509 18.853 18.848 48 0.28483 0.28506 18.594 18.589 49 0.29508 0.29533 18.328 18.321 50 0.30564 0.30591 18.053 18.046 51 0.31651 0.31681 17.771 17.763 52 0.32768 0.32801 17.480 17.472 53 0.33915 0.33953 17.182 17.172 54 0.35091 0.35135 16.876 16.865 55 0.36297 0.36347 16.563 16.550 56 0.37530 0.37589 16.242 16.227 57 0.38791 0.38859 15.914 15.897 58 0.40079 0.40158 15.580 15.559 Agex 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 51 52 53 54 55 56 57 Agex A A, 59 0.41391 0.41483 15.238 15.214 60 0.42728 0.42834 14.891 14.863 61 0.44087 0.44209 14.537 14.506 62 0.45467 0.45607 14.179 14.142 63 0.46866 0.47025 13.815 13.774 64 0.48281 0.48462 13.447 13.400 65 0.49711 0.49916 13.075 13.022 66 0.51154 0.51384 12.700 12.640 67 0.52608 0.52863 12.322 12.256 68 0.54069 0.54352 11.942 11.869 69 0.55536 0.55847 11.561 11.480 70 0.57005 0.57345 11.179 11.090 71 0.58476 0.58843 10.796 10.701 72 0.59945 0.60338 10.414 10.312 73 0.61411 0.61827 10.033 9.925 74 0.62870 0.63306 9.654 9.541 75 0.64322 0.64772 9.276 9.159 76 0.65765 0.66222 8.901 8.782 77 0.67197 0.67653 8.529 8.410 78 0.68613 0.69062 8.161 8.044 79 0.70005 0.70445 7.799 7.684 80 0.71360 0.71800 7.446 7.332 81 0.72672 0.73123 7.105 6.988 82 0.73942 0.74413 6.775 6.652 83 0.75173 0.75668 6.455 6.326 84 0.76365 0.76884 6.145 6.010 85 0.77518 0.78060 5.845 5.704 86 0.78629 0.79195 5.556 5.409 87 0.79698 0.80287 5.279 5.125 88 0.80724 0.81336 5.012 4.853 89 0.81705 0.82340 4.757 4.592 90 0.82642 0.83299 4.513 4.342 91 0.84213 4.105 92 0.85081 3.879 93 0.85905 3.665 94 0.86683 3.462 95 0.87417 3.272 96 0.88106 3.092 97 0.88751 2.925 98 0.89351 2.769 99 0.89904 2.625 100 0.90404 2.495 Age x 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 99 100 58 AMCOO Male Life Functions (4%) Age x NX-1+1 59 60 61 62 63 64 65 66 Agex N. 17 121013.22 121014.86 18 115879.55 115880.77 115881.13 19 110945.59 110946.76 110947.11 20 106203.56 106204.70 106205.03 21 101646.03 101647.13 101647.45 22 97265.82 97266.89 97267.20 23 93056.05 93057.08 93057.39 24 89010.09 89011.10 89011.39 25 85121.59 85122.57 85122.86 26 81384.45 81385.41 81385.69 27 77792.78 77793.72 77793.99 28 74340.96 74341.87 74342.13 29 71023.58 71024.44 71024.70 30 67835.43 67836.24 67836.49 31 64771.51 64772.26 64772.48 32 61827.01 61827.70 61827.89 33 58997.30 58997.93 58998.09 34 56277.95 56278.53 56278.66 35 53664.69 53665.23 53665.34 36 51153.45 51153.95 51154.04 37 48740.30 48740.77 48740.84 38 46421.48 46421.92 46421.97 39 44193.38 44193.79 44193.82 40 42052.51 42052.91 42052.93 41 39995.55 39995.95 39995.96 42 38019.32 38019.72 38019.72 43 36120.76 36121.17 36121.17 44 34296.94 34297.35 34297.35 45 32545.06 32545.48 32545.48 46 30862.41 30862.85 30862.85 47 29246.43 29246.89 29246.89 48 27694.65 27695.14 27695.14 49 26204.72 26205.24 26205.24 50 24774.37 24774.94 24774.94 51 23401.47 23402.08 23402.08 52 22083.94 22084.61 22084.61 53 20819.83 20820.58 20820.58 54 19607.27 19608.12 19608.13 55 18444.47 18445.44 18445.47 56 17329.76 17330.87 17330.93 57 16261.53 16262.80 16262.89 58 15238.27 15239.71 15239.85 Age x 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 51 52 53 54 55 56 57 58 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 99 100 Nu N 14258.53 14260.18 14260.36 13320.96 13322.83 13323.07 12424.28 12426.38 12426.69 11567.26 11569.63 11570.01 10748.78 10751.44 10751.90 9967.77 9970.73 9971.28 9223.22 9226.50 9227.15 8514.21 8517.82 8518.56 7839.85 7843.79 7844.64 7199.32 7203.60 7204.55 6591.87 6596.47 6597.52 6016.77 6021.68 6022.82 5473.35 5478.53 5479.75 4960.98 4966.38 4967.67 4479.04 4484.61 4485.94 4026.96 4032.62 4033.96 3604.16 3609.81 3611.14 3210.07 3215.62 3216.88 2844.13 2849.44 2850.58 2505.65 2510.66 2511.63 2193.87 2198.61 2199.39 1907.94 1912.56 1913.17 1647.13 1651.72 1652.24 1410.71 1415.31 1415.80 1197.92 1202.49 1202.97 1007.84 1012.34 1012.82 839.45 843.83 844.31 691.61 695.84 696.30 563.10 567.14 567.58 452.62 456.42 456.84 358.78 362.31 362.70 280.12 283.35 283.71 218.05 218.37 165.17 122.59 89.14 63.39 44.02 29.78 19.60 12.52 7.75 Age : 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 99 100 Question 5 [15 marks). Thomas Brown plans to retire at age 67 with a pension of 30,000 per year, paid annually in advance during his remaining lifetime. Assume an effective annual interest rate of 4% and the mortality given by table AMCOO select values. You can find the table in the appendix. (a) Show that the expected present value of the pension at retirement is approximately 369,659. (b) In order to cover the cost of the pension, Thomas wants to make monthly payments in arrears starting at age 30 until retirement. What are the monthly premiums assuming he survives until retirement? (c) How does the expected present value in (a) change when he switches to a pension of 2,500 paid monthly in advance during his remaining lifetime? Give reasons. [6] [5] AMCOO Male Life Table 1-1+1 Age x 17 18 19 Agex 17 9997.5094 10000.0000 18 9992.9305 9994.6901 9995.4200 19 9988.3337 9990.1025 9990.8321 20 9983.6991 9985.4871 9986.2163 21 9979.0567 9980.8438 9981.5827 22 9974.3666 9976.1827 9976.9213 23 9969.6487 9971.4740 9972.2222 24 9964.8832 9966.7276 9967.4854 25 9960.0701 9961.9336 9962.7010 26 9955.1996 9957.0921 9957.8691 27 9950.2618 9952.1832 9952.9698 28 9945.2469 9947.1972 9947.9933 29 9940.1847 9942. 1340 9942.9398 30 9935.0655 9936.9939 9937.7794 31 9929.8794 9931.7671 9932.5024 32 9924.5767 9926.4238 9927.0892 33 9919.1182 9920.9344 9921.5201 34 9913.4841 9915.2596 9915.7755 35 9907.6152 9909.3799 9909.8162 36 9901.4922 9903.2460 9903.6126 37 9895.0760 9896.8385 9897.1357 38 9888.3275 9890.1087 9890.3363 39 9881.1880 9882.9977 9883.1559 40 9873.5893 9875.4570 9875.5558 41 9865.4534 9867.4085 9867.4578 42 9856.7223 9858.7745 9858.7942 43 9847.3090 9849.4875 9849.4875 44 9837.1169 9839.4312 9839.4312 45 9826.0499 9828.5291 9828.5291 46 9813.9735 9816.6562 9816.6562 47 9800.7439 9803.6786 9803.6786 48 9786.2090 9789.4437 9789.4437 49 9770.1885 9773.7708 9773.7708 50 9752.4550 9756.4712 9756.4712 51 9732.8031 9737.3192 9737.3192 52 9710.9228 9716.0627 9716.0627 53 9686.5083 9692.4138 9692.4332 54 9659.2100 9666.0213 9666.1182 55 9628.6170 9636.5205 9636.7719 56 9594.3554 9603.4960 9604.0069 57 9555.9547 9566.5317 9567.3964 58 9512.9284 9525.1558 9526.4767 = = = = = = = = = = = = = = = = = = = = = = = = G T = + = = = = = = = = = = = = Ages 59 9464.7096 9478.8531 9480.7305 60 9410.6849 9427.0212 9429.5820 61 9350.1805 9369.0144 9372.4010 62 9282.4873 9304.1589 9308.5187 63 9206.8320 9231.7028 9237.1968 64 9122.3956 9150.8360 9157.6369 65 9028.3257 9060.7100 9069.0001 66 8923.7129 8960.4327 8970.3747 67 8807.6361 8849.0571 8860.8106 68 8679.1539 8725.6105 8739.3111 69 8537.3365 8589.1250 8604.8568 70 8381.2654 8438.6022 8456.4058 71 8210.1056 8273.0800 8292.9181 72 8023.0608 8091.6666 8113.3848 73 7819.4936 7893.5124 7916.8461 74 7598.8879 7677.9138 7702.4263 75 7360.9680 7444.3113 7469.3894 76 7105.6585 7192.3651 7217.1705 77 6833.2053 6921.9772 6945.4296 78 6543.2750 6633.3614 6654.1244 79 6234.6920 6326.2215 6343.5631 80 5905.8869 6000.3050 6014.4463 81 5557.1270 5655.4241 5667.9541 82 5191.0860 5293.5691 5305.7888 83 4811.5773 4917.5469 4930-2080 84 4422.4381 4531.0383 4544.0494 85 4027.2597 4137.4915 4150.7347 86 3630.1730 3740.8772 3754.2191 87 3235.7358 3345.6473 3358.9374 88 2848.8406 2956.5986 2969.6769 89 2474.5254 2578.7306 2591.4291 90 2117.7709 2217.0436 2229.1940 91 1876.3069 1887.7528 92 1571.4202 93 1283.8047 94 1027.5920 95 804.3661 96 614.5164 97 457.2229 98 330.5502 99 231.6268 100 156.9026 Agex 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 99 100 AMCOO Male Life Functions (4%) Del+1 D. D--]+1 D. Agex 17 18 19 20 22 23 24 25 26 12 3 Age x D. 17 5132.45 5133.73 15 4932.79 4933.6 4934.02 19 4740.89 4741.73 4742.07 20 4556.43 4557,54557.58 21 4379.154379.93 4380.25 22 4208.74 4209.50 4209.82 23 4044.95 4045.9 4045.9 24 3887.51 3888.23 3888.53 25 3736.19 3736.89 3737.18 26 3590.73 3591.42 3591.70 27 3450.92 3451.58 3451.85 3316.52 3317.17 3317.43 3187.33 3187.96 3188.22 300 3063.173063.76 3064.00 31 2943.81 2944.37 294.59 32 2829.08 2829.61 2829.80 33 2718.77 2719.27 2719.43 34 2612.72 2613.19 2613.32 2510.74 | 2511.19 2511.30 2412.68 | 2413.11 241320 7 2318.39 23 18.80 2313.87 38 2227.70 2228.10 2228.15 2140.47 2140.86 2140.90 40 2056.56 2056.95 2056.97 41 1975.83 1976.22 1976.23 42 1898.16 1898.55 1898.56 43 1823.41 1823.81 1823.81 44 1751.46 1751.87 1751.87 45 16582.20 1682.63 1682.63 46 1615.52 1615.96 1615.96 47 1551.29 1551.75 1551.75 48 1489.41 1489.90 1489.90 49 1429.78 1430.30 1430.30 500 1372.29 1372.86 1372.86 51 1316.85 1317.47 1317.47 52 1263.36 | 1264.03 1264.05 53 1211.71 1212.45 1212.46 4 1161.83 1162.65 1162.66 5 1113.60 1114.52 1114.55 56 1066.96 1067.98 1068.05 57 102 1.82 1022.95 1023.04 58 978.049 97935 979.49 Agex D. Agex 30 935.71 937.11 937.29 59 60 94.58 896.14 896.38 60 61 854.65 856.37856.68 61 62 15.83 ALTI 818.11 62 67 778.05 780.16 780.62 63 64 741.27 743.58 74.13 64 65 105.41 07.94 708.59 65 6 670.42 673.18 673.92 66 67 636.25 639.24 640.00 67 68 602.85 606.08 07.03 68 69 570.19 573.65 574.70 69 0 538.24 541.92 543.07 0 1 1506.97 510.86 512.08 71 72 476.36 480.44 48173 72 73 46.42 450.65 451.98 73 74 417.14 421.48 422.82 74 75 388.54 392.94 394.26 75 76 360.64 365.0M 366.30 76 333.47 37.80 33895 TT 78 307.04 311.27 31224 78 79 28131 285.44 286.22 79 80 256.11 260.32 260.93 800 81 231.82 255.92 236.44 8L A2 208.22 212.33 212.82 82 83 185.58 189.66 190.15 83 84 164.01 168.03 168.52 84 85 143.6L 14754 148.0L 85 56 124.47 128.26 128.72 6 87 106.68 I10.30 I10.74 87 88 90.31 93.73 4.14 88 89 75.43 78.60 78.99 89 90 62.07 64.95 65.34 90 91 52.88 53.20 91 97 42.58 92 93 13.45 93 4 15.74 94 95 19.38 95 96 14.23 6 7 10.18 97 98 7.108 98 99 4.77 9 100 3. II 1000 42 43 44 45 52 53 4 55 516 57 58 AMC00 Male Life Functions (4%) Mis lll M-1|- 12 | Agex M. M. Agex 17 478.10 479.31 17 18 475.89 476.71 477.05 18 19 473.75 474.54 474.88 19 20 471.68 472.45 472.77 20 21 469.68 470.42 470.74 21 467.74 468.47 468.7 17 23 465.87 466.57 466.86 23 24 464.005 464.73 465.02 24 25 462.28 462.94 463.22 15 26 46056 61.21 461.48 26 27 458.89 459.52 459.78 27 28 457.25 457.86 458.12 28 29 455.66 456.25 456.50 29 30 454.11 454.07 454.91 30 31 452.60 453.13 453.34 31 32 45L12 451.62 451.800 32 33 449.65 450.12 450.27 33 4 448.18 448.63 448.76 4 35 446.72 47.14 47.15 35 36 445.24 45.65 445.74 36 37 43.76 444.15 444.22 7 38 42.25 42.4 442.69 38 9 440.72 41.10 41.13 400 439.16 439.53 439.5 40 41 437.54 43792 437.93 41 42 435.88 436.26 436.26 42 43 434.15 434.54 434.4 43 4 432.35 432.75 432.75 45 430.47 430.88 430.88 45 46 428.50 428.92 428.92 46 47 426.42 426.87 426.87 47 48 424.23 424.70 424.70 48 49 42191 422.41 422.41 30 419.43 419.98 419.98 50 51 416.80 417.39 417.39 51 52 413.98 414.62 414.62 52 53 410.95 411.66 411.66 53 407.70 408.49 408.50 4 55 404.20 05.08 405.10 55 56 400.43 401.41 401.46 57 396.37 7.46 97.55 57 92.01 393.21 393.34 58 Agex M M, M Agex 50 387300 388.64 388.82 9 60 382.24383.72 383.95 60 61 376.79 378.43 378.73 61 62 370.93 372.74 373.11 62 63 34.6M 36.64 367.09 63 64 357.89 360.00 360.62 64 65 350.67 353.07 153.70 65 66 4295 45.57 46.29 67 34.71 337.55 33837 67 68 325.95 329.02 329.93 69 316.66 31994 120.95 69 70 306.83 310.32 11.42 70 1 106.46 300.15 301.32 1 72 285.56 289.42 290.66 T2 73 274.15 28.16 279.44 73 74 262.26 26.38 267.67 14 75 249.92 254.10 255.37 76 137.17 241.36 24257 76 77 224.18 228.21 2011 78 210.67 21470 215.64 73 79 196.93 20NO.83 201.63 79 80 182.84 186.76 18735 80 81 168.47 129 1290 AL 82 153.96 157.90 15837 A. 83 19.50 143.41 143.88 83 84 125.24 129.10 12956 84 85 111.32 115.0% 115.4 85 86 97.87 101.50 101.94 36 87 85.02 88.49 35.91 87 88 72.90 76.17 76.57 33 89 61.63 4.67 65.04 89 51.30 4.08 4.42 90 91 4.49 4.30 91 92 36.23 92 93 28.74 93 94 22.32 94 95 16.94 95 96 1254 96 97 9.0M 97 98 6.33 98 99 4.29 99 100 281 100 4 58 AMC00 Male Life Functions (4%) Mis lll M-1|- 12 | Agex M. M. Agex 17 478.10 479.31 17 18 475.89 476.71 477.05 18 19 473.75 474.54 474.88 19 20 471.68 472.45 472.77 20 21 469.68 470.42 470.74 21 467.74 468.47 468.7 17 23 465.87 466.57 466.86 23 24 464.005 464.73 465.02 24 25 462.28 462.94 463.22 15 26 46056 61.21 461.48 26 27 458.89 459.52 459.78 27 28 457.25 457.86 458.12 28 29 455.66 456.25 456.50 29 30 454.11 454.07 454.91 30 31 452.60 453.13 453.34 31 32 45L12 451.62 451.800 32 33 449.65 450.12 450.27 33 4 448.18 448.63 448.76 4 35 446.72 47.14 47.15 35 36 445.24 45.65 445.74 36 37 43.76 444.15 444.22 7 38 42.25 42.4 442.69 38 9 440.72 41.10 41.13 400 439.16 439.53 439.5 40 41 437.54 43792 437.93 41 42 435.88 436.26 436.26 42 43 434.15 434.54 434.4 43 4 432.35 432.75 432.75 45 430.47 430.88 430.88 45 46 428.50 428.92 428.92 46 47 426.42 426.87 426.87 47 48 424.23 424.70 424.70 48 49 42191 422.41 422.41 30 419.43 419.98 419.98 50 51 416.80 417.39 417.39 51 52 413.98 414.62 414.62 52 53 410.95 411.66 411.66 53 407.70 408.49 408.50 4 55 404.20 05.08 405.10 55 56 400.43 401.41 401.46 57 396.37 7.46 97.55 57 92.01 393.21 393.34 58 Agex M M, M Agex 50 387300 388.64 388.82 9 60 382.24383.72 383.95 60 61 376.79 378.43 378.73 61 62 370.93 372.74 373.11 62 63 34.6M 36.64 367.09 63 64 357.89 360.00 360.62 64 65 350.67 353.07 153.70 65 66 4295 45.57 46.29 67 34.71 337.55 33837 67 68 325.95 329.02 329.93 69 316.66 31994 120.95 69 70 306.83 310.32 11.42 70 1 106.46 300.15 301.32 1 72 285.56 289.42 290.66 T2 73 274.15 28.16 279.44 73 74 262.26 26.38 267.67 14 75 249.92 254.10 255.37 76 137.17 241.36 24257 76 77 224.18 228.21 2011 78 210.67 21470 215.64 73 79 196.93 20NO.83 201.63 79 80 182.84 186.76 18735 80 81 168.47 129 1290 AL 82 153.96 157.90 15837 A. 83 19.50 143.41 143.88 83 84 125.24 129.10 12956 84 85 111.32 115.0% 115.4 85 86 97.87 101.50 101.94 36 87 85.02 88.49 35.91 87 88 72.90 76.17 76.57 33 89 61.63 4.67 65.04 89 51.30 4.08 4.42 90 91 4.49 4.30 91 92 36.23 92 93 28.74 93 94 22.32 94 95 16.94 95 96 1254 96 97 9.0M 97 98 6.33 98 99 4.29 99 100 281 100 4 58 AMCOO Male Life Functions (4%) Agex A, 17 0.09315 0.09337 23.578 23.572 18 0.09647 0.09669 23.492 23.486 19 0.09993 0.10014 23.402 23.396 20 0.10352 0.10373 23.309 23.303 21 0.10725 0.10747 23.211 23.206 22 0.11114 0.11135 23.110 23.105 23 0.11517 0.11539 23.005 23.000 24 0.11937 0.11959 22.896 22.891 25 0.12373 0.12395 22.783 22.777 26 0.12826 0.12848 22.665 22.659 27 0.13297 0.13320 22.543 22.537 28 0.13787 0.13809 22.415 22.410 29 0.14296 0.14318 22.283 22.277 30 0.14825 0.14847 22.146 22.140 31 0.15375 0.15396 22.003 21.997 32 0.15946 0.15966 21.854 21.849 33 0.16539 0.16558 21.700 21.695 34 0.17154 0.17172 21.540 21.535 35 0.17792 0.17809 21.374 21.370 36 0.18454 0.18471 21.202 21.198 37 0.19141 0.19157 21.023 21.019 38 0.19853 0.19868 20.838 20.834 39 0.20590 0.20605 20.647 20.643 40 0.21354 0.21369 20.448 20.444 41 0.22145 0.22160 20.242 20.238 42 0.22963 0.22978 20.030 20.026 43 0.23810 0.23826 19.809 19.805 44 0.24685 0.24702 19.582 19.578 45 0.25590 0.25608 19.347 19.342 46 0.26524 0.26543 19.104 19.099 47 0.27488 0.27509 18.853 18.848 48 0.28483 0.28506 18.594 18.589 49 0.29508 0.29533 18.328 18.321 50 0.30564 0.30591 18.053 18.046 51 0.31651 0.31681 17.771 17.763 52 0.32768 0.32801 17.480 17.472 53 0.33915 0.33953 17.182 17.172 54 0.35091 0.35135 16.876 16.865 55 0.36297 0.36347 16.563 16.550 56 0.37530 0.37589 16.242 16.227 57 0.38791 0.38859 15.914 15.897 58 0.40079 0.40158 15.580 15.559 Agex 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 51 52 53 54 55 56 57 Agex A A, 59 0.41391 0.41483 15.238 15.214 60 0.42728 0.42834 14.891 14.863 61 0.44087 0.44209 14.537 14.506 62 0.45467 0.45607 14.179 14.142 63 0.46866 0.47025 13.815 13.774 64 0.48281 0.48462 13.447 13.400 65 0.49711 0.49916 13.075 13.022 66 0.51154 0.51384 12.700 12.640 67 0.52608 0.52863 12.322 12.256 68 0.54069 0.54352 11.942 11.869 69 0.55536 0.55847 11.561 11.480 70 0.57005 0.57345 11.179 11.090 71 0.58476 0.58843 10.796 10.701 72 0.59945 0.60338 10.414 10.312 73 0.61411 0.61827 10.033 9.925 74 0.62870 0.63306 9.654 9.541 75 0.64322 0.64772 9.276 9.159 76 0.65765 0.66222 8.901 8.782 77 0.67197 0.67653 8.529 8.410 78 0.68613 0.69062 8.161 8.044 79 0.70005 0.70445 7.799 7.684 80 0.71360 0.71800 7.446 7.332 81 0.72672 0.73123 7.105 6.988 82 0.73942 0.74413 6.775 6.652 83 0.75173 0.75668 6.455 6.326 84 0.76365 0.76884 6.145 6.010 85 0.77518 0.78060 5.845 5.704 86 0.78629 0.79195 5.556 5.409 87 0.79698 0.80287 5.279 5.125 88 0.80724 0.81336 5.012 4.853 89 0.81705 0.82340 4.757 4.592 90 0.82642 0.83299 4.513 4.342 91 0.84213 4.105 92 0.85081 3.879 93 0.85905 3.665 94 0.86683 3.462 95 0.87417 3.272 96 0.88106 3.092 97 0.88751 2.925 98 0.89351 2.769 99 0.89904 2.625 100 0.90404 2.495 Age x 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 99 100 58 AMCOO Male Life Functions (4%) Age x NX-1+1 59 60 61 62 63 64 65 66 Agex N. 17 121013.22 121014.86 18 115879.55 115880.77 115881.13 19 110945.59 110946.76 110947.11 20 106203.56 106204.70 106205.03 21 101646.03 101647.13 101647.45 22 97265.82 97266.89 97267.20 23 93056.05 93057.08 93057.39 24 89010.09 89011.10 89011.39 25 85121.59 85122.57 85122.86 26 81384.45 81385.41 81385.69 27 77792.78 77793.72 77793.99 28 74340.96 74341.87 74342.13 29 71023.58 71024.44 71024.70 30 67835.43 67836.24 67836.49 31 64771.51 64772.26 64772.48 32 61827.01 61827.70 61827.89 33 58997.30 58997.93 58998.09 34 56277.95 56278.53 56278.66 35 53664.69 53665.23 53665.34 36 51153.45 51153.95 51154.04 37 48740.30 48740.77 48740.84 38 46421.48 46421.92 46421.97 39 44193.38 44193.79 44193.82 40 42052.51 42052.91 42052.93 41 39995.55 39995.95 39995.96 42 38019.32 38019.72 38019.72 43 36120.76 36121.17 36121.17 44 34296.94 34297.35 34297.35 45 32545.06 32545.48 32545.48 46 30862.41 30862.85 30862.85 47 29246.43 29246.89 29246.89 48 27694.65 27695.14 27695.14 49 26204.72 26205.24 26205.24 50 24774.37 24774.94 24774.94 51 23401.47 23402.08 23402.08 52 22083.94 22084.61 22084.61 53 20819.83 20820.58 20820.58 54 19607.27 19608.12 19608.13 55 18444.47 18445.44 18445.47 56 17329.76 17330.87 17330.93 57 16261.53 16262.80 16262.89 58 15238.27 15239.71 15239.85 Age x 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 51 52 53 54 55 56 57 58 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 99 100 Nu N 14258.53 14260.18 14260.36 13320.96 13322.83 13323.07 12424.28 12426.38 12426.69 11567.26 11569.63 11570.01 10748.78 10751.44 10751.90 9967.77 9970.73 9971.28 9223.22 9226.50 9227.15 8514.21 8517.82 8518.56 7839.85 7843.79 7844.64 7199.32 7203.60 7204.55 6591.87 6596.47 6597.52 6016.77 6021.68 6022.82 5473.35 5478.53 5479.75 4960.98 4966.38 4967.67 4479.04 4484.61 4485.94 4026.96 4032.62 4033.96 3604.16 3609.81 3611.14 3210.07 3215.62 3216.88 2844.13 2849.44 2850.58 2505.65 2510.66 2511.63 2193.87 2198.61 2199.39 1907.94 1912.56 1913.17 1647.13 1651.72 1652.24 1410.71 1415.31 1415.80 1197.92 1202.49 1202.97 1007.84 1012.34 1012.82 839.45 843.83 844.31 691.61 695.84 696.30 563.10 567.14 567.58 452.62 456.42 456.84 358.78 362.31 362.70 280.12 283.35 283.71 218.05 218.37 165.17 122.59 89.14 63.39 44.02 29.78 19.60 12.52 7.75 Age : 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 99 100