Question

1 Approved Answer

Posted on Jul 01, 2024

Using the 2001 mortality tables (Table 2 is male and Table 3 is female); find the following probabilities: 1. A male age 20 will die

Using the 2001 mortality tables (Table 2 is male and Table 3 is female); find the following probabilities:

1. A male age 20 will die before age 60.

2. Both a male age 60 and a female age 63 will die within one year. (Assume the deaths are independent).

3. A female age 50 and a male age 52 will both be alive after 10 years.

4. For a person of your age and gender, the probability of living to age 80.

5. For a person of your age and gender, calculate the net single premium for a 1-year term insurance policy with a face amount = $500,000. Assume the interest rate is 4%.

LEWK3_2001 4 og 27 LEWK3_2001 5 og 27 Table 2. Life table for males: United States, 2001 Table 2. Life table for males: United States, 2001 Total Total Probablety Person-years number of Probablety Number Person-years number of Number Expectation of dying Number dying lived person-years Expectation of dying Number dying lived person-years between between lived above of life between surviving to between between lived above of life between surviving to age x at age x ages x to x+1 age x ages x to x+1 ages x to x+1 age x at age x ages x to x+1 age> ages x to x+1 ages x to x+1 1(x ) d(x) L(x) T(x) e (x ) Age q(x) 1(x ) d(x) L(x) T(x) e(x) Age q(x) 219 95,679 3,697,109 38.6 0-1 0.00751 100,000 95,788 751 99,344 7,426,45 74.3 38-39 0.002283 99,249 56 99,220 7,327,107 73.8 39-40 0.002444 95,569 234 95,452 3,601,430 37.7 1-2 0.000568 37 99,173 7,227,887 72.9 40-41 0.002611 95,336 249 95,211 3,505,978 36.8 2-3 0.000378 99,192 95,087 266 94,954 3,410,767 35.9 3-4 0.000282 99,155 28 99,141 7,128,713 71.9 41-42 0.002793 42-43 0.003004 94,821 285 94,679 3,315,813 35.0 4-5 .00023 99,127 24 99,115 7,029,573 70.9 308 94,382 3,221,134 34.1 5- 6 0.000201 99,103 20 99.09: 6,930,458 69 9 43-44 0.00325 94,536 94,061 3,126,752 33.2 6-7 0.000186 99,083 18 99,074 6,831,364 68.9 44-45 0.003554 94,228 335 93,893 365 93,711 3,032,691 32.3 7-8 0.000172 99,065 17 99,056 6,732,290 68.0 45-46 0.003886 16-47 0.004237 93,528 396 93,33 2,938,980 31.4 8-9 0.000152 99,048 15 99,040 5,633,234 67.0 427 92,918 2,845,650 30.6 9-10 0.000127 99,033 13 99,026 6,534,194 66.0 47-48 0.004589 93,132 456 92,477 2,752,731 29.7 10-11 0.000109 99,020 11 99,015 6,435,167 65.0 48-49 0.004921 92,705 49-50 0.005236 92,249 483 92,007 2,660,255 28.8 11-12 0.000117 99,009 12 99,004 6,336,152 64.0 17 6,237,149 50-51 0.005556 91,766 510 91,511 2,568,24 28.0 12-13 .000172 98,998 98,98 63.0 91,256 539 90,986 2,476,737 27.1 13- 14 0.000288 98,981 29 98,967 6,138,160 62.0 51-52 0.005909 26.3 14-15 .000449 98,952 44 98,930 6,039,193 61.0 52-53 0.006309 90,716 572 0,430 2,385,751 12 89,838 2,295,320 25.5 15-16 0.000627 98,908 62 98,877 5,940,263 60.1 53-54 0.006793 90,144 54-55 0.007382 89,532 661 89,201 2,205,482 24.6 16-17 .000797 98,846 79 98,806 5,841,386 59.1 55-56 0.008093 88,871 719 88,511 2,116,281 23.8 17-18 0.000952 98,767 94 98,720 5,742,580 58 .1 87,759 2,027,770 23.0 18-19 0.001080 98,673 107 98,620 5,643,860 57.2 56-57 0.008903 88,152 785 22.2 19-20 0.001183 98,566 117 98,508 5,545,240 56.3 57-58 0.009781 87,367 354 86,940 1,940,011 5,446,732 55.3 58-59 0.010663 86,512 922 36,051 1,853,071 21.4 20-21 0.001288 98,450 127 98,38 59-60 0.011545 85,590 988 85,096 1,767,020 20.6 21-22 0.001391 98,323 137 98,255 5,348,345 54.4 1,681,924 98,186 5,250,091 0.012504 84,602 1,058 19.9 22-23 0.001455 143 98,115 53.5 60-61 84,073 19.1 23-24 0.001467 98,043 144 97,971 5,151,976 52.5 61-62 0.013607 83,544 1,137 82,976 1,597,851 81,797 1,514,876 18.4 24-25 0.001441 97,900 141 97,829 5,054,004 51.6 62-63 0.014812 32,407 1,221 0.001401 97,758 137 97,690 4,956,175 50.7 63-64 0.016133 81,186 1,310 80,532 1,433,079 17.7 25-26 0.017580 79,877 1,404 79,175 1,352,547 16.9 26-27 0.001369 97,621 134 97,555 4,858,485 49.8 64-65 16.2 27-28 0.001347 97,488 131 97,422 4,760,931 48.8 65-66 0.019115 78,472 1,500 7,722 1,273,373 4,663,509 47.9 66-67 0.020802 76,972 1,601 76,172 1,195,650 15.5 28-29 0.001347 97,356 131 97,291 57-68 0.022714 75,371 1,712 74,515 1,119,478 14.9 29-30 0.001366 97,225 133 97,159 4,566,218 47.0 1,834 72,742 1,044,963 14.2 30-31 0.001390 97,093 135 97,025 4,469,059 46.0 68-69 0.024896 73,659 972,221 13.5 31-32 0.001421 96,958 138 96,889 4,372,034 45.1 69-70 0.027275 71,825 1,959 70,846 32-33 .001492 96,820 144 96,74 4,275,145 44.2 70-71 0.029698 69,866 2,075 58,829 901,375 12.9 12.3 0.001575 96,675 96,59 4,178,397 66,699 832,546 33 - 34 152 43.2 71-72 0.03223 67,791 2,185 2,306 $4,453 765,847 11.7 34-35 0.001697 96,523 164 96,441 4,081,798 42.3 72-73 0.035146 65,606 63,300 2,440 62,081 701,394 11.1 35-36 0.001835 96,359 177 96,271 3,985,357 41.4 73-74 0.038542 190 96,08 3,889,086 40.4 74-75 0.042236 60,861 2,571 59,575 639,313 10.5 36-37 0.001978 96,183 0.046267 58,290 2,697 56,942 9.9 75-76 579,738 37-38 0.002129 95,992 204 95,890 3,792,999 39.5 Source: CDC/NCHS, National Vital Statistics System, Mortality. Source: CDC/NCHS, National Vital Statistics System, Mortality.Page 6 of 27 7 of 27 6 og 27 LEWK3_2001 LEWK3_2001 Table 3. Life table for females: United States, 2001 Table 2. Life table for males: United States, 2001 Total Total Probablety Number Person-years number of Probablety Number Person-years number of Number dying lived person-years Expectation of dying Number dying lived person-years Expectation of dying lived above of life between surviving to between between lived above of life between surviving to between between age x ages x to x+1 ages x to x+1 age x at age x ages x to x+1 age> ages x to x+1 ages x to x+1 age x at age x ages x to x+1 q(x) 1(x) d(x) L(X) T(x) e(x) Age q(x) 1(x) d(x) L(x) T(x) e(x) Age 614 99,467 7,953,894 79.5 76-77 0.050644 55,59 2,815 54,185 522,796 9.4 0-1 0.006139 100,000 1-2 0.000477 99,386 47 99,362 7,854,427 79.0 77-78 0.055222 52,778 2,914 51,321 468,610 8. 417,290 8.4 2-3 0.000294 99,339 29 99,324 7,755,064 78.1 78-79 0.060335 49,863 3,009 48,359 22 99,299 7,655,740 77.1 79-80 0.065996 46,855 3,092 45,309 368,931 7.9 3- 4 0.000220 99,310 4-5 0.000177 99,28 18 99,279 7,556,442 76.1 80-81 0.072380 43,762 3,168 42,179 323,622 7.4 75.1 40,595 3,24 38,971 281,444 6.9 5-6 0.000164 99,270 16 99,262 7,457,163 81-82 0.079997 242,472 6.5 6-7 0.000149 99,254 15 99,247 7,357,901 74.1 82-83 0.088553 37,347 3,307 35,694 6.1 7-8 0.000138 99,239 14 99,232 7,258,654 73.1 83-84 0.097926 34,040 3,33 32,374 206,779 7,159,422 72.2 84-85 .10810 30,707 3,31 29,047 174,405 5.7 8-9 0.000127 99,225 13 99,219 9-10 0.000117 99,213 12 99,207 7,060,203 71.2 85-86 0.119111 27,387 3,26 25,756 145,358 5.3 6,960,995 5.0 10-11 0.000111 99,201 11 99,196 70.2 86-87 0.130979 24,125 3,160 22,545 119,602 0.143720 20,965 3,013 19,459 97,056 4.6 11-12 0.000115 99,190 11 99,185 6,861,800 69.2 87-88 12-13 0.000134 99,179 13 99,172 6,762,615 58.2 88-89 0.157336 17,952 2,825 16,540 77,597 4.3 13,828 51,058 4.0 13-14 0.000174 99,166 17 99,157 6,663,44 67.2 89-90 0.171818 15,128 ,59 14-15 0.000229 99,148 23 99,137 6,564,286 66.2 90-91 0.187144 12,528 2,345 11,356 47,229 3.8 99,111 6,465,149 65.2 91-92 0.203275 10,184 2,070 9,149 35,873 3.5 15-16 0.000293 99,126 29 35 99,079 6,366,038 64.2 92-93 0.220158 8,114 1,786 7,221 26,724 3.3 16-17 0.000355 99,096 63.3 93-94 0.237724 17-18 0.000402 99,061 40 99,041 6,266,959 6,327 1,504 5,57 19,504 3.1 2.9 18-19 0.000428 99,021 42 99,000 6,167,918 62.3 94-95 0.255888 4,823 1,234 4,206 13,929 3,589 985 3,096 9,727 2.7 19-20 0.000436 98,979 43 98,958 6,068,918 61.3 95-96 0.274552 44 98,914 5,969,960 60.3 96-97 0.293604 2,604 764 2,22 6,626 2.5 20-21 0.000442 98,936 59.4 0.312923 1.839 576 1,551 ,405 2.4 21-22 0.000453 98,892 45 98,870 5,871,046 37-98 46 5,772,176 58.4 98-99 0.332381 1,264 420 1,054 2,853 2.3 22-23 0.000463 98,847 98,825 23-24 0.000476 98,802 47 98,778 5,673,352 57.4 99-100 0.351845 844 297 695 1,80 2.1 20 24-25 0.000492 98,755 49 98,730 5,574,574 56.4 100 and over 1.000000 547 547 1,104 1,104 25-26 0.000511 98,706 98,681 5,475,843 55.5 26-27 0.000533 98,656 98,629 5,377,163 54.5 27-28 0.000557 98,603 98,576 5,278,533 53.5 0.000583 98,54 98,519 5,179,95 52.6 28-29 29-30 0.000611 98,491 98,461 5,081,438 51.6 30-31 0.000642 98,430 98,399 4,982,978 50.6 31-32 0.000680 98,367 98,334 4,884,579 49.7 32-33 0.000737 98,300 72 98,264 4,786,245 48.7 33-34 0.000804 98,228 79 98,188 4,687,981 47.7 34-35 0.000888 98,149 87 98,105 4,589,792 46.8 35-36 0.000979 98,062 96 98,014 4,491,687 45.8 36-37 0.001072 97,966 105 97,913 4,393,673 14.8 37-38 0.001172 97,861 115 97,803 4,295,760 43.9 Source: CDC/NCHS, National Vital Statistics System, Mortality. Source: CDC/NCHS, National Vital Statistics System, Mortality.8 of 27 LEWK3_2001 9 of 27 LEWK3_2001 Table 3. Life table for females: United States, 2001 Table 3. Life table for females: United States, 2001 Total Total Number Probablety Person-years number of Probablety Person-years number of Number person-years Expectation of dying Number dying lived person-years Expectation of dying Number dying lived of life between surviving to between between lived above of life between surviving to between between lived above age x ages x to x+1 ages x to x+1 age x at age x ages x to x+1 age > ages x to x+1 ages x to x+1 age x at age x ages x to x+1 e (x ) Age q(x) 1(x) d(x) L(X) T(x) e(x) Age q(x) 1(x ) d(x) L(x) T(x) 790,042 11.4 38-39 0.00127 17,746 125 97,684 4,197,957 42.9 76-77 0.033381 69,309 2,314 68,152 97,553 4,100,273 42.0 77-78 0.036700 66,995 2,459 65,766 721,890 10.8 39-40 0.001391 97,621 136 4,002,720 41.1 78-79 0.040487 64,536 2,613 63,230 656,124 10.2 40-41 0.001510 97,485 147 97,412 61,924 2,783 60,532 592,894 9.6 41-42 0.001634 97,338 159 97,25 3,905,308 40.1 79-80 0.044935 0.049727 59,141 2,941 57,671 532,361 9.0 42-43 .001762 97,179 171 97,09 3,808,049 39.2 80-81 0.055103 56,200 3,097 54,652 474,691 3.4 43-44 0.001896 97,008 184 96,916 3,710,956 38 .3 81-82 51,469 420,039 7.9 44-45 0.002042 96,824 198 96,725 3,614,040 37.3 82-83 0.061550 53,103 3,269 83-84 0.068637 49,835 3,421 48,125 368,570 7.4 45-46 0.002202 96,626 213 96,520 3,517,315 36.4 0.076890 46,414 3,569 44,630 320,445 6.9 46-47 0.002379 96,413 229 96,29 3,420,796 35.5 84-85 85-86 0.08608 42,846 3,688 41,001 275,816 6.4 47-48 0.002572 96,184 247 96,060 3,324,497 34.6 39,157 3,764 37,275 234,814 6.0 48-49 0.002779 95,937 267 95,803 3,228,437 33.7 86-87 0.096130 33,497 197,539 5.6 49-50 0.002995 95,670 287 95,527 3,132,633 32.7 87-88 0.107126 35,393 3,791 31.8 88-89 0.119117 31,601 3,764 29,71 164,042 5.2 50-51 0.003223 95,383 307 95,230 3,037,107 2,941,877 30.9 89-90 0.132134 27,83 3,678 25,998 134,323 4.8 51-52 0.003470 95,076 330 94,911 94,746 355 94,56 2,846,966 30.0 90-91 0.146194 24,159 3,532 22,393 108,325 4.5 52-53 0.003748 53-54 0.004079 94,391 385 94,198 2,752,397 29.2 91-92 0.161298 20,627 3,327 18,963 35,932 4.2 2,658,199 28.3 92-93 0.177431 17,300 3,070 15,765 56,969 3.9 54-55 .004479 94,006 421 93,79 3 .6 55-56 0.004963 93,585 464 93,353 2,564,403 27.4 93-94 0.194556 14,230 2,769 12,846 51,204 94-95 0.212615 11,462 2,437 10,243 38,357 3.3 56-57 0.005516 93,120 514 92,864 2,471,051 26.5 92,324 2,378,187 25.7 95-96 0.231529 9,02 2,090 7,980 28,114 3.1 57-58 0.006109 92,607 566 6,935 1,742 6,064 20,134 2.9 58-59 0.006696 92,041 616 91,73 2,285,863 24.8 96-97 0.251194 24.0 97-98 0.271488 5,193 1,410 4,488 14,070 2.7 59- 60 0.007276 91,425 665 91,092 2,194,130 23.2 98-99 0.292268 3,783 1.106 3,230 9,582 2.5 60-61 0.007915 90,760 718 90,400 2,103,038 90,041 779 39,652 2,012,638 22.4 99-100 0.313377 2,678 839 2,258 6,351 2.4 61-62 0.008654 1,922,986 21.5 100 and over 1.000000 1,838 1,838 4,093 4,093 2.2 62-63 0.009453 89,262 844 88,84 63-64 0.010314 88,418 912 87,962 1,834,146 20.7 64-65 0.011250 87,506 984 87,014 1,746,184 20.0 65-66 0.012265 86,522 1,061 85,991 1,659,170 19.2 66-67 0.013396 85,460 ,14 84,888 1,573,179 18.4 57-68 0.014652 84,316 1,23 83.69 1,488,291 17.7 68-69 0.016039 83,080 1,333 82,414 1,404,593 16.9 69-70 0.017547 81,748 1,434 81,031 1,322,179 16.2 70-71 0.019110 30,313 1,535 79,546 1,241,148 15.5 71-72 0.020753 78,779 1,635 77,961 1,161,602 14.7 72-73 0.022705 77,144 1,752 76,26 1,083,641 14.0 73-74 0.025045 75,392 1,88 74,448 1,007,373 13.4 74-75 0.027576 73,504 2,02 72,491 932,925 12.7 75-76 0.030335 71,477 2,168 70,393 860,435 12.0 Source: CDC/NCHS, National Vital Statistics System, Mortality. Source: CDC/NCHS, National Vital Statistics System, Mortality