Question 2 A male customer of 35 years old wants to purchase a two-year term life insurance policy from your insurance company Nova Life. Premium will be received at beginning of each year, and claim of $80,000 would be paid in the middle of the year if ever death occurs. With an annual interest rate of 6%, and using the Nova Scotia Life Table, what minimum premium will you charge on the policy? Life table, Nova Scotia, 2000 to 2002 (males) cumulative/unconditional conditional prob. of dying during the next year q. Exact agex surviving rate P. #living IK [= 1x1 dx-1) prob. of surviving to x dead death rate de q [= data] [= d./u] [= 1-9] [= L / 100,000) 0 1 2 3 4 100,000 99,437 99,398 99,373 99,349 563 0.0056300 39 0.0003922 25 0.0002515 24 0.0002415 24 0.0002416 0.99437 0.99961 0.99975 0.99976 0.99976 1.00000 0.99437 0.99398 0.99373 0.99349 [= (-6)/] 0.0056300 0.0003922 0.0002515 0.0002415 0.0002416 5 6 7 8 9 99,325 99,310 99,298 99,287 99,277 15 0.0001510 12 0.0001208 11 0.0001108 10 0.0001007 11 0.0001108 0.99985 0.99988 0.99989 0.99990 0.99989 0.99325 0.99310 0.99298 0.99287 0.99277 0.0001510 0.0001208 0.0001108 0.0001007 0.0001108 10 11 12 13 14 99,266 99,255 99,245 99,230 99,211 11 0.0001108 10 0.0001008 15 0.0001511 19 0.0001915 26 0.0002621 0.99989 0.99990 0.99985 0.99981 0.99974 0.99266 0.99255 0.99245 0.99230 0.99211 0.0001108 0.0001008 0.0001511 0.0001915 0.0002621 15 16 17 99,185 99,150 99,108 99,057 98,999 35 0.0003529 42 0.0004236 51 0.0005146 58 0.0005855 66 0.0006667 0.99965 0.99958 0.99949 0.99941 0.99933 0.99185 0.99150 0.99108 0.99057 0.98999 0.0003529 0.0004236 0.0005146 0.0005855 0.0006667 18 19 20 21 22 98,933 98,858 98,776 98,690 98,603 75 0.0007581 82 0.0008295 86 0.0008707 87 0.0008815 86 0.0008722 0.99924 0.99917 0.99913 0.99912 0.99913 0.98933 0.98858 0.98776 0.98690 0.98603 0.0007581 0.0008295 0.0008707 0.0008815 0.0008722 23 24 25 26 27 28 29 98,517 98,433 98,352 98,273 98,195 84 0.0008526 81 0.0008229 79 0.0008032 78 0.0007937 75 0.0007638 0.99915 0.99918 0.99920 0.99921 0.99924 0.98517 0.98433 0.98352 0.98273 0.98195 0.0008526 0.0008229 0.0008032 0.0007937 0.0007638 2 30 31 32 33 98,120 98,047 97974 97,898 97,815 73 0.0007440 73 0.0007445 76 0.0007757 83 0.0008478 94 0.0009610 0.99926 0.99926 0.99922 0.99915 0.99904 0.98120 0.98047 0.97974 0.97898 097815 0.0007440 0.0007445 0.007757 0.0008478 0.0009610 5 Eng 97,721 97,615 97.496 97.364 97.221 106 0.0010847 119 0.001211 132 0.0013539 143 0.01.68/ 153 0.0015737 0.99892 0.99878 0.99865 0.99853 0.99843 097721 197615 0.97496 0.97364 097221 0.0010847 0.0012 191 0.0013539 0.0014687 0.0015737 40 41 42 43 44 97,068 96,903 196.725 96.532 96.323 165 0.00 16998 178 0.0018369 193 0.0019953 209 0.0021651 228 0.0023670 0.99830 0.99816 0.99800 0.99783 0.99763 0.97068 0.96903 0.96725 0.96532 0.96323 0.0016998 0.0018369 0.0019953 0.0021651 0.0023670 sss9 96.095 95,846 95.577 95.284 94.969 249 0.0025912 269 0.0028066 293 0.0030656 315 0.0033059 3386 0.0035380 0.99741 0.99719 0.99693 0.99669 0.99646 0.96095 0.95846 0.9577 0.95288 02ASES 0.0025912 0.0028066 0.0030656 0.0033059 0.0035380 50 51 52 53 54 94,633 94,272 93,883 93.458 92,990 361 0.0038147 389 0.0041264 425 0.0045269 468 0.0050076 514 0.0055275 0.99619 0.99587 0.99547 0.99499 0.99447 094633 0.94272 0.93883 0.93458 0.92990 0.0038147 0.0041264 0.0045269 0.0050076 0.0055275 55 56 57 58 9 92.476 91,910 91,284 90,589 89,816 566 0.0061205 626 0.0068110 695 0.0076136 773 0.0065330 257 0.0095417 0.99388 0.99319 0.99239 0.99147 199046 0.92476 0.91910 0.91284 0.90589 0.89816 0.0061205 0.0068110 0.0076136 0.0085330 0.0095-17 100 101 102 103 104 303 168 89 45 22 135 0.4455446 79 0.4702381 4 0.4943820 23 05111111 12 0.5454545 0.55446 0.52976 0.50562 0.48889 0.45455 10.00303 0.00168 0.00089 0.00045 0.00022 0.4455446 0.4702381 0.4943820 0.5111111 0.5454545 Lu | Question 2 A male customer of 35 years old wants to purchase a two-year term life insurance policy from your insurance company Nova Life. Premium will be received at beginning of each year, and claim of $80,000 would be paid in the middle of the year if ever death occurs. With an annual interest rate of 6%, and using the Nova Scotia Life Table, what minimum premium will you charge on the policy? Life table, Nova Scotia, 2000 to 2002 (males) cumulative/unconditional conditional prob. of dying during the next year q. Exact agex surviving rate P. #living IK [= 1x1 dx-1) prob. of surviving to x dead death rate de q [= data] [= d./u] [= 1-9] [= L / 100,000) 0 1 2 3 4 100,000 99,437 99,398 99,373 99,349 563 0.0056300 39 0.0003922 25 0.0002515 24 0.0002415 24 0.0002416 0.99437 0.99961 0.99975 0.99976 0.99976 1.00000 0.99437 0.99398 0.99373 0.99349 [= (-6)/] 0.0056300 0.0003922 0.0002515 0.0002415 0.0002416 5 6 7 8 9 99,325 99,310 99,298 99,287 99,277 15 0.0001510 12 0.0001208 11 0.0001108 10 0.0001007 11 0.0001108 0.99985 0.99988 0.99989 0.99990 0.99989 0.99325 0.99310 0.99298 0.99287 0.99277 0.0001510 0.0001208 0.0001108 0.0001007 0.0001108 10 11 12 13 14 99,266 99,255 99,245 99,230 99,211 11 0.0001108 10 0.0001008 15 0.0001511 19 0.0001915 26 0.0002621 0.99989 0.99990 0.99985 0.99981 0.99974 0.99266 0.99255 0.99245 0.99230 0.99211 0.0001108 0.0001008 0.0001511 0.0001915 0.0002621 15 16 17 99,185 99,150 99,108 99,057 98,999 35 0.0003529 42 0.0004236 51 0.0005146 58 0.0005855 66 0.0006667 0.99965 0.99958 0.99949 0.99941 0.99933 0.99185 0.99150 0.99108 0.99057 0.98999 0.0003529 0.0004236 0.0005146 0.0005855 0.0006667 18 19 20 21 22 98,933 98,858 98,776 98,690 98,603 75 0.0007581 82 0.0008295 86 0.0008707 87 0.0008815 86 0.0008722 0.99924 0.99917 0.99913 0.99912 0.99913 0.98933 0.98858 0.98776 0.98690 0.98603 0.0007581 0.0008295 0.0008707 0.0008815 0.0008722 23 24 25 26 27 28 29 98,517 98,433 98,352 98,273 98,195 84 0.0008526 81 0.0008229 79 0.0008032 78 0.0007937 75 0.0007638 0.99915 0.99918 0.99920 0.99921 0.99924 0.98517 0.98433 0.98352 0.98273 0.98195 0.0008526 0.0008229 0.0008032 0.0007937 0.0007638 2 30 31 32 33 98,120 98,047 97974 97,898 97,815 73 0.0007440 73 0.0007445 76 0.0007757 83 0.0008478 94 0.0009610 0.99926 0.99926 0.99922 0.99915 0.99904 0.98120 0.98047 0.97974 0.97898 097815 0.0007440 0.0007445 0.007757 0.0008478 0.0009610 5 Eng 97,721 97,615 97.496 97.364 97.221 106 0.0010847 119 0.001211 132 0.0013539 143 0.01.68/ 153 0.0015737 0.99892 0.99878 0.99865 0.99853 0.99843 097721 197615 0.97496 0.97364 097221 0.0010847 0.0012 191 0.0013539 0.0014687 0.0015737 40 41 42 43 44 97,068 96,903 196.725 96.532 96.323 165 0.00 16998 178 0.0018369 193 0.0019953 209 0.0021651 228 0.0023670 0.99830 0.99816 0.99800 0.99783 0.99763 0.97068 0.96903 0.96725 0.96532 0.96323 0.0016998 0.0018369 0.0019953 0.0021651 0.0023670 sss9 96.095 95,846 95.577 95.284 94.969 249 0.0025912 269 0.0028066 293 0.0030656 315 0.0033059 3386 0.0035380 0.99741 0.99719 0.99693 0.99669 0.99646 0.96095 0.95846 0.9577 0.95288 02ASES 0.0025912 0.0028066 0.0030656 0.0033059 0.0035380 50 51 52 53 54 94,633 94,272 93,883 93.458 92,990 361 0.0038147 389 0.0041264 425 0.0045269 468 0.0050076 514 0.0055275 0.99619 0.99587 0.99547 0.99499 0.99447 094633 0.94272 0.93883 0.93458 0.92990 0.0038147 0.0041264 0.0045269 0.0050076 0.0055275 55 56 57 58 9 92.476 91,910 91,284 90,589 89,816 566 0.0061205 626 0.0068110 695 0.0076136 773 0.0065330 257 0.0095417 0.99388 0.99319 0.99239 0.99147 199046 0.92476 0.91910 0.91284 0.90589 0.89816 0.0061205 0.0068110 0.0076136 0.0085330 0.0095-17 100 101 102 103 104 303 168 89 45 22 135 0.4455446 79 0.4702381 4 0.4943820 23 05111111 12 0.5454545 0.55446 0.52976 0.50562 0.48889 0.45455 10.00303 0.00168 0.00089 0.00045 0.00022 0.4455446 0.4702381 0.4943820 0.5111111 0.5454545 Lu |