Consider a five-year term life insurance policy with face amount equal to $100,000 for a 40-year-old with an interest rate of 10%. 

(a). Using Table 15.3, calculate the single premium for the five-year term life insurance policy with face amount equal to $100,000 for a 40-year-old with an interest rate of 10%. 

(b). Ignoring expenses, what would be the policy's expected balance (i.e., value or a sum which should be in the account) equal after two years? 

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TABLE 15.3 1980 standard mortality table for males. Probability of Dying Number of Deaths Age 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 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 0.00418 0.00107 0.00099 0.00098 0.00095 0.00090 0.00086 0.00080 0.00076 0.00074 0.00073 0.00077 0.00085 0.00099 0.00115 0.00133 0.00151 0.00167 0.00178 0.00186 0.00190 0.00191 0.00189 0.00186 0.00182 0.00177 0.00173 0.00171 0.00170 0.00171-1 0.00173 0.00178 0.00183 0.00191 0.00200 0.00211 0.00224 0.00240 0.00258 0.00279 0.00302 0.00329 0.00356 0.00387 0.00419 0.00455 0.00492 0.00532 0.00574 0.00621 0.00671 Number of People 1000000 995820 994754 993770 992796 991853 990960 990108 989316 988564 987832 987111 986351 985513 984537 983405 982097 980614 978976 977234 975416 973563 971703 969867 968063 966301 964591 962922 961275 959641 958000 956343 954640 952893 951073 949171 947168 945047 942779 940346 937723 934891 931815 928498 924905 921029 916838 912328 907474 902265 896662 4180 1066 985 974 943 893 852 792 752 732 721 760 838 976 1132 1308 1483 1638 1743 1818 1853 1860 1837 1804 1762 1710 1669 1647 1634 1641 1657 1702 1747 1820 1902 2003 2122 2268 2432 2624 2832 3076 3317 3593 3875 4191 4511 4854 5209 5603 6017 Age 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 6 7 68 69 70 1234567 78 66 67 77 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Probability of Dying 0.00730 0.00796 0.00871 0.00956 0.01047 0.01146 0.01249 0.01359 0.01477 0.01608 0.01754 0.01919 0.02106 0.02314 0.02542 0.02785 0.03044 0.03319 0.03617 0.03951 0.04330 0.04765 0.05264 0.05819 0.06419 0.07053 0.07712 0.08390 0.09105 0.09884 0.10748 0.11725 0.12826 0.14025 0.15295 0.16609 0.17955 0.19327 0.20729 0.22177 0.23698 0.25345 0.27211 0.29590 0.32996 0.38455 0.48020 0.65798 1.00000 Number of People 890645 884144 877106 869466 861154 852138 842372 831851 820546 808427 795427 781476 766479 750337 732974 714342 694448 673309 650962 627416 602627 576533 549061 520159 489891 458445 426111 393249 360255 327454 295089 263372 232492 202673 174248 147597 123082 100983 81466 64579 50257 38347 28628 20838 14672 9831 6050 3145 1076 0 Number of Deaths 6502 7038 7640 8312 9016 9766 10521 11305 12119 13000 13952 4997 16142 17363 18632 19894 21139 22347 23545 24789 26094 27472 28903 30268 31446 32334 32862 32994 32801 32366 31716 30880 29819 28425 26651 24514 22099 19517 16887 14322 11910 9719 7790 6166 4841 3780 2905 2069 1076 TABLE 15.3 1980 standard mortality table for males. Probability of Dying Number of Deaths Age 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 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 0.00418 0.00107 0.00099 0.00098 0.00095 0.00090 0.00086 0.00080 0.00076 0.00074 0.00073 0.00077 0.00085 0.00099 0.00115 0.00133 0.00151 0.00167 0.00178 0.00186 0.00190 0.00191 0.00189 0.00186 0.00182 0.00177 0.00173 0.00171 0.00170 0.00171-1 0.00173 0.00178 0.00183 0.00191 0.00200 0.00211 0.00224 0.00240 0.00258 0.00279 0.00302 0.00329 0.00356 0.00387 0.00419 0.00455 0.00492 0.00532 0.00574 0.00621 0.00671 Number of People 1000000 995820 994754 993770 992796 991853 990960 990108 989316 988564 987832 987111 986351 985513 984537 983405 982097 980614 978976 977234 975416 973563 971703 969867 968063 966301 964591 962922 961275 959641 958000 956343 954640 952893 951073 949171 947168 945047 942779 940346 937723 934891 931815 928498 924905 921029 916838 912328 907474 902265 896662 4180 1066 985 974 943 893 852 792 752 732 721 760 838 976 1132 1308 1483 1638 1743 1818 1853 1860 1837 1804 1762 1710 1669 1647 1634 1641 1657 1702 1747 1820 1902 2003 2122 2268 2432 2624 2832 3076 3317 3593 3875 4191 4511 4854 5209 5603 6017 Age 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 6 7 68 69 70 1234567 78 66 67 77 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Probability of Dying 0.00730 0.00796 0.00871 0.00956 0.01047 0.01146 0.01249 0.01359 0.01477 0.01608 0.01754 0.01919 0.02106 0.02314 0.02542 0.02785 0.03044 0.03319 0.03617 0.03951 0.04330 0.04765 0.05264 0.05819 0.06419 0.07053 0.07712 0.08390 0.09105 0.09884 0.10748 0.11725 0.12826 0.14025 0.15295 0.16609 0.17955 0.19327 0.20729 0.22177 0.23698 0.25345 0.27211 0.29590 0.32996 0.38455 0.48020 0.65798 1.00000 Number of People 890645 884144 877106 869466 861154 852138 842372 831851 820546 808427 795427 781476 766479 750337 732974 714342 694448 673309 650962 627416 602627 576533 549061 520159 489891 458445 426111 393249 360255 327454 295089 263372 232492 202673 174248 147597 123082 100983 81466 64579 50257 38347 28628 20838 14672 9831 6050 3145 1076 0 Number of Deaths 6502 7038 7640 8312 9016 9766 10521 11305 12119 13000 13952 4997 16142 17363 18632 19894 21139 22347 23545 24789 26094 27472 28903 30268 31446 32334 32862 32994 32801 32366 31716 30880 29819 28425 26651 24514 22099 19517 16887 14322 11910 9719 7790 6166 4841 3780 2905 2069 1076