Question

A 1year term insurance provides a death benet of 20, 000, payabie at the end of the policy year. On the basis of the EM BSD Table of Mortality for males and using an effective rate of interest of 5% and 5% per annumr respectively, calculate the premium for a life aged (i) 41], (ii) 50, and (iii) 601 respectively. Comment on the ordering of these premiums (including your observation and explanation on vvhy this is the case}. 2001 Commissioners Standard Ordinary (CSO) Table of Mortality Males, Composite Smoker/Nonsmoker (Ultimate Mortality Table) Probability of Number of Probability of death during Number living at deaths during living through Age (x) age x (q.) age x (1,) age x (d,) age x (Px) 0 0.00097 10,000,000 9,700 0.99903 0.00056 9,990,300 5,595 0.99944 0.00039 9,984,705 3,894 0.99961 0.00027 9,980,811 2,695 0.99973 DO LAW NH 0.00021 9,978,117 2,095 0.99979 0.00021 9,976,021 2,095 0.99979 0.00022 9,973,926 2,194 0.99978 0.00022 9,971,732 2,194 0.99978 0.00022 9,969,538 2,193 0.99978 LD 0.00023 9,967,345 2,292 0.99977 10 0.00023 9,965,052 2,292 0.99977 11 0.00027 9,962,760 2,690 0.99973 12 0.00033 9,960,070 3,287 0.99967 13 0.00039 9,956,784 3,883 0.99961 14 0.00047 9,952,901 4,678 0.99953 15 0.00061 9,948,223 6,068 0.99939 16 0.00074 9,942,154 7,357 0.99926 17 0.00087 9,934,797 8,643 0.99913 18 0.00094 9,926,154 9,331 0.99906 19 0.00098 9,916,823 9,718 0.99902 20 0.00100 9,907,105 9,907 0.99900 21 0.00100 9,897,198 9.897 0.99900 22 0.00102 9,887,300 10,085 0.99898 23 0.00103 9,877,215 10,174 0.99897 24 0.00105 9,867,042 10,360 0.99895 25 0.00107 9,856,681 10,547 0.99893 26 0.00112 9,846,135 11,028 0.99888 27 0.00117 9,835,107 11,507 0.99883 28 0.00117 9,823,600 11,494 0.99883 29 0.00115 9,812,106 11,284 0.9988530 0.00114 9,800,822 11,173 0.99886 31 0.00113 9,789.650 11,062 0.99887 32 0.00113 9,778.587 11,050 0.99887 33 0.00115 9,767,537 11,233 0.99885 34 0.00118 9,756,305 11,512 0.99882 35 0.00121 9,744.792 11,791 0.99879 36 0.00128 9,733,001 12,458 0.99872 37 0.00134 9,720.543 13,026 0.99866 38 0.00144 9,707,517 13,979 0.99856 39 0.00154 9,693,539 14,928 0.99846 40 0.00165 9,678.610 15,970 0.9983541 0.00179 9,662,641 17,296 0.99821 42 0.00196 9,645,345 18,905 0.99804 43 0.00215 9,626,440 20,697 0.99785 44 0.00239 9,605,743 22,958 0.99761 45 0.00265 9,582,785 25,394 0.99735 46 0.00290 9,557,391 27,716 0.99710 47 0.00317 9,529,674 30,209 0.99683 48 0.00333 9,499,465 31,633 0.99667 49 0.00352 9,467,832 33,327 0.99648 50 0.00376 9.434,505 35,474 0.99624 51 0.00406 9,399,032 38,160 0.99594 52 0.00447 9,360,872 41,843 0.99553 53 0.00493 9,319,028 45,943 0.99507 54 0.00550 9,273,086 51,002 0.99450 55 0.00617 9,222,084 56,900 0.99383 56 0.00688 9,165,183 63,056 0.99312 57 0.00764 9,102,127 69,540 0.99236 58 0.00827 9,032,587 74,699 0.99173 59 0.00899 8,957,887 80,531 0.99101 60 0.00986 8,877,356 87,531 0.99014 61 0.01094 8,789,825 96,161 0.98906 62 0.01225 8,693.664 106,497 0.98775 63 0.01371 8,587,167 117,730 0.98629 64 0.01524 8,469,437 129,074 0.98476 65 0.01685 8,340,363 140,535 0.98315 66 0.01847 8,199,828 151,451 0.98153 67 0.02009 8,048,377 161,692 0.97991 68 0.02185 7,886,685 172,324 0.97815 69 0.02364 7,714,361 182,367 0.97636 70 0.02577 7,531,993 194,099 0.97423 71 0.02815 7,337,894 206,562 0.97185 72 0.03132 7,131,332 223,353 0.96868 73 0.03462 6,907,979 239,154 0.96538 74 0.03808 6,668,825 253,949 0.96192 75 0.04191 6,414,876 268,847 0.95809