2. A fully discrete whole life insurance of $100,000 is issued to a select life aged (65). Premiums are paid annually in advance for at most 10 years. . Interest is 5% per year. Initial expenses are 50% of the premium plus $125. Renewal expenses are 5% of the premiums from the 2nd premium onwards. Expenses of 200 on the benefit sum insured. Use Table D Standard Select Survival Model in your calculations. (a) (10 pts) Calculate the premium for this policy. (b) (10 pts) Write an expression for L; and calculate its mean VI Appendu D. Tubes 585 Appendix D. Tubles Table D 2 Standard Select Surwiwal Model 5% per year Table D.2 (Cont.) PAI Il to Frig 50 19.967 19.921 19.872 19.820 19.756 0.01918 0.051-10 0.05373 0.05618 0.05874 0.00576 0.00510 0.00048 0.00589 0.00734 31 0.78255 0.78254 0.78252 0.78249 0.78247 10 0.61227 0.61223 0.61218 0.61213 0.61208 0.37441 0.37431 0.37419 0.37406 0.37392 20 21 22 23 24 50 51 52 53 54 17.028 16.850 16.665 16472 16 273 PARI 0,05087 0.05495 0.03933 0.06104 0.06909 0.18913 0.19761 0.20642 0.21558 072509 SEL 0.77791 0.77732 0.7700 0.77591 0.77507 0.60196 0.60006 0.59919 0.59735 0.59572 0.3483 0.34512 0.14156 0.33700 0.33320 is ES 1 19.710 19.651 19.589 19.54 19.456 0.06143 0.06424 0.06720 0.07029 0.07353 0.00783 0.01837 0.00895 0.00959 0.01025 0.78344 0.78241 0.78237 0.78233 0.78219 0.61201 0.61194 0.61186 0.61177 0.117 0.37375 0.37356 0.37336 0.37312 037286 25 26 27 28 29 55 56 57 S8 59 16.066 15.851 15.628 15 398 15.160 0.23496 0.24519 0.25579 0.26677 0.27811 0.07451 0.0031 0.08653 0.09317 010 0.77413 0.77307 0.77189 0.77056 0790 0.59366 0.59135 0.58877 0.38588 3.03 032312 0.32393 0.31697 0.31041 0.30319 55 56 57 38 19.384 19310 19.272 19.150 19.044 0.07693 0.00049 0.08421 0.06E11 0.09220 0.01104 0.01186 0.01276 0,01373 0.01479 0.78224 0.78218 0.78211 0.78204 0.78196 0.61156 0.61143 0.61128 0.61112 0.61094 037256 0.37223 0.37186 0.37144 0.37097 30 31 32 33 34 60 61 62 63 64 H013 14.659 14.397 14.127 13.850 0.28984 0.30194 031 HZ 0.32727 0.34049 0.10781 0.11386 0.1241 0.13350 0.14313 0.76739 0.76552 0.76341 0.76105 0.75841 0.5794 0.57301 0.57051 0.56550 (1.35993 0.29528 0.28663 0.27721 0.26700 0.23596 61 62 63 , 18.974 18.800 18.72 1679 1572 0.09647 0.10094 0.10562 0.11051 5.1 1563 0.01594 0.01720 0.01856 0.02004 0.0216 0.78187 0.78176 0.78165 0.78152 0.78137 0.61074 0.01051 0.61025 0.60996 0.60463 0.37044 0.36985 0.36919 0.36844 030761 35 36 37 38 39 2938 13.564 13.272 12.972 12.045 12.351 035407 0.36801 0.38230 0.39692 041180 0.15333 0.16411 0.17548 0.18746 0.20005 0.75545 0.75214 0.74844 0.74429 0.73906 0:55371 U.S4082 05397 0.53170 0.3214 0.2 H11 0233 0.21797 0.20377 0 1891 00 67 68 09 10 18.400 18342 18.220 18.092 17.95 0.130 0.13656 0.13240 0 13849 014485 0.0233 0.02527 0.02731 0.00952 0.03191 0.78121 0.78102 0.78082 0.78058 0.78032 0.6027 0.60886 0.608-10 0.60788 0.607.10 0.36667 0.36562 0.16-144 0.36312 046165 = 997 70 21 72 73 74 12.031 11.705 11.374 11.037 10.606 0.42710 0.44262 0-45840 0.47412 0.49065 0.21320 0.22709 0.24154 0.25662 077229 0.73430 0.72873 0.72330 0.71515 0.70719 0.51 103 0.1946 0.48719 0.47355 0-45867 0.17350 0.15767 0.14100 0.12518 0.10951 20 71 72 23 74 17.819 17.673 17.522 17.361 0.15149 0.15841 0.16563 0.17314 0.03450 0.03730 0.04032 0.0435 0.78003 0.77970 0.77932 0.77891 0.60664 0.60591 0.60509 0.60416 0.35999 0.JSNIS 0.35608 0.35377 S 97 21 1 75 76 77 78 10.352 10.004 9.654 0.50706 0.52362 0.54030 0.55704 0.28850 0.JOS41 0.33280 0.31072 0.69833 0.68854 0.07768 0.60568 #250 0.42501 0.40618 0.38000 E 0.09403 0.07930 0.186531 0.05258 Ani 75 76 27 78 10 985 Appendix D. Tables 587 The D. 3 Standard Ultimate Sur Model, 1 = 5% per year Appende D. Tables Table D 3 (Com 10 20 + A 'VE 5E, RE WE 20 21 22 19.966 19920 19.871 15819 19.763 0.04922 0.25144 0.05378 0.05633 0570 DISSO 0.00614 0.00552 0.00694 0.00739 078252 0.78250 2.78245 0.78345 0.78243 0.61224 0.61220 0.61215 0.61210 0.61205 0.37440 0.37429 0.37417 0.3740 0.37390 50 51 52 53 54 17.025 16.846 16.661 16.168 16.268 0.1893 0.19780 0.20664 0.215R2 0.22535 0.05108 0.05517 005957 0.06430 0.06938 0.77772 0.77711 0.77643 0.77566 0.77479 0.01 0.610 0302 059756 59550 0.14824 34503 0.34116 033749 13303 SU 51 52 53 54 19.703 SS 95 55 56 YRA 19.58 19.5 1945 0.06147 0.05429 0.06725 0.07034 0.07359 0.00785 00041 0.00900 0.00964 001033 0.78240 0.78236 0.78233 0.76220 0.76224 0.61198 0.61191 0.61183 0.6174 0.61163 0.37373 0 37354 0.3734 0 37310 0.37284 57 58 59 16.000 15.8.14 15.621 15.390 15.151 0.23534 0.24550 0.25613 0.16714 0.2752 0.07433 DORD67 0.08692 0.09360 0.10073 0.77382 0.77273 0.77151 0.77017 0.76860 0.3932 0.59109 0.3818 038556 0.5029 32819 02279 31681 3100 030300 58 59 3 0.76687 057864 TE 19.30 19230 09 19 60 61 0.0759 0.0805 07 0.06817 0.09226 0.01109 0.01 192 DI 0.0079 0.0146 0.78219 0.78213 0.78206 0.78199 0.78190 0.61152 0.61139 0.61124 0.61108 06100 0.37254 0.37221 0.37183 0.37141 0.37094 31 3 32 14.904 14.649 14 386 14.115 13.816 62 63 0.2902 0.30240 031495 0.32785 03411 0.10834 0.1164 0.12506 0132 0.14092 38 1.76276 0.76033 0.75760 0.29508 0.28641 27698 036074 15569 051003 0.36496 63 HE TE 973 6:0966 35 36 35 3 33 je 65 60 101010 WOOF 1780 D1601 0.01727 0.01863 0.02012 0.02173 0.781RI 0.78170 078158 0.78145 0.78130 0.61069 0.61016 061020 060990 0.60957 0.37041 0.36982 0.36915 0.36841 0.36757 65 66 67 68 69 13.30 13.356 12954 12.06 12.130 0.15477 0.36878 0.38373 0.39783 0.11285 15 0.15420 0.16507 0.17654 1886 030133 75455 . 0.74710 14. ON 033112 31754 0.56305 254009 0.53836 0515 th 66 0.15 0.11571 1570 38 39 SMO 15556 SHEET 1200 11.00 SINCHO LETTO 30 2945 70 71 42 0.02347 0.02536 0.01741 0.02963 0.03 203 12 1. 17.950 0.78113 0704 0.78072 NH 07821 OED POSTED PINO 12065 0.13249 2.135 0.14 0.60920 0.60879 0.60832 06070 0.com 036663 0.36558 0.3640 036307 0.36159 0.17313 0.1570 0 112 It it EF 70 71 72 73 74 07201 0.72039 UTENOS 0.15968 0.7550 11.005 10.065 TECID STRONO 019215 TO CMT SISTO 74 10.13 POROSO WINSTO 25 46 47 46 64 10 0.1516 0.1556 0.16577 UTAO 17316 17.071 17.519 17.361 17.196 0.046 0.0744 0.0404 04314 0.77991 077956 O TV 7775 077827 0.60655 0.6051 0.60 0.60104 0.35994 0.59 0 35001 0.15370 35 76 12 20 20 PIB 75 76 72 if 17 SF On 0854 0.000 MS 0.00217 O. 0 09366 007887 0.04.300 0.05310 001036 0.104 021886 0.16215 WO OF TO 04 0.37 COD 29 SU ED 2. A fully discrete whole life insurance of $100,000 is issued to a select life aged (65). Premiums are paid annually in advance for at most 10 years. . Interest is 5% per year. Initial expenses are 50% of the premium plus $125. Renewal expenses are 5% of the premiums from the 2nd premium onwards. Expenses of 200 on the benefit sum insured. Use Table D Standard Select Survival Model in your calculations. (a) (10 pts) Calculate the premium for this policy. (b) (10 pts) Write an expression for L; and calculate its mean VI Appendu D. Tubes 585 Appendix D. Tubles Table D 2 Standard Select Surwiwal Model 5% per year Table D.2 (Cont.) PAI Il to Frig 50 19.967 19.921 19.872 19.820 19.756 0.01918 0.051-10 0.05373 0.05618 0.05874 0.00576 0.00510 0.00048 0.00589 0.00734 31 0.78255 0.78254 0.78252 0.78249 0.78247 10 0.61227 0.61223 0.61218 0.61213 0.61208 0.37441 0.37431 0.37419 0.37406 0.37392 20 21 22 23 24 50 51 52 53 54 17.028 16.850 16.665 16472 16 273 PARI 0,05087 0.05495 0.03933 0.06104 0.06909 0.18913 0.19761 0.20642 0.21558 072509 SEL 0.77791 0.77732 0.7700 0.77591 0.77507 0.60196 0.60006 0.59919 0.59735 0.59572 0.3483 0.34512 0.14156 0.33700 0.33320 is ES 1 19.710 19.651 19.589 19.54 19.456 0.06143 0.06424 0.06720 0.07029 0.07353 0.00783 0.01837 0.00895 0.00959 0.01025 0.78344 0.78241 0.78237 0.78233 0.78219 0.61201 0.61194 0.61186 0.61177 0.117 0.37375 0.37356 0.37336 0.37312 037286 25 26 27 28 29 55 56 57 S8 59 16.066 15.851 15.628 15 398 15.160 0.23496 0.24519 0.25579 0.26677 0.27811 0.07451 0.0031 0.08653 0.09317 010 0.77413 0.77307 0.77189 0.77056 0790 0.59366 0.59135 0.58877 0.38588 3.03 032312 0.32393 0.31697 0.31041 0.30319 55 56 57 38 19.384 19310 19.272 19.150 19.044 0.07693 0.00049 0.08421 0.06E11 0.09220 0.01104 0.01186 0.01276 0,01373 0.01479 0.78224 0.78218 0.78211 0.78204 0.78196 0.61156 0.61143 0.61128 0.61112 0.61094 037256 0.37223 0.37186 0.37144 0.37097 30 31 32 33 34 60 61 62 63 64 H013 14.659 14.397 14.127 13.850 0.28984 0.30194 031 HZ 0.32727 0.34049 0.10781 0.11386 0.1241 0.13350 0.14313 0.76739 0.76552 0.76341 0.76105 0.75841 0.5794 0.57301 0.57051 0.56550 (1.35993 0.29528 0.28663 0.27721 0.26700 0.23596 61 62 63 , 18.974 18.800 18.72 1679 1572 0.09647 0.10094 0.10562 0.11051 5.1 1563 0.01594 0.01720 0.01856 0.02004 0.0216 0.78187 0.78176 0.78165 0.78152 0.78137 0.61074 0.01051 0.61025 0.60996 0.60463 0.37044 0.36985 0.36919 0.36844 030761 35 36 37 38 39 2938 13.564 13.272 12.972 12.045 12.351 035407 0.36801 0.38230 0.39692 041180 0.15333 0.16411 0.17548 0.18746 0.20005 0.75545 0.75214 0.74844 0.74429 0.73906 0:55371 U.S4082 05397 0.53170 0.3214 0.2 H11 0233 0.21797 0.20377 0 1891 00 67 68 09 10 18.400 18342 18.220 18.092 17.95 0.130 0.13656 0.13240 0 13849 014485 0.0233 0.02527 0.02731 0.00952 0.03191 0.78121 0.78102 0.78082 0.78058 0.78032 0.6027 0.60886 0.608-10 0.60788 0.607.10 0.36667 0.36562 0.16-144 0.36312 046165 = 997 70 21 72 73 74 12.031 11.705 11.374 11.037 10.606 0.42710 0.44262 0-45840 0.47412 0.49065 0.21320 0.22709 0.24154 0.25662 077229 0.73430 0.72873 0.72330 0.71515 0.70719 0.51 103 0.1946 0.48719 0.47355 0-45867 0.17350 0.15767 0.14100 0.12518 0.10951 20 71 72 23 74 17.819 17.673 17.522 17.361 0.15149 0.15841 0.16563 0.17314 0.03450 0.03730 0.04032 0.0435 0.78003 0.77970 0.77932 0.77891 0.60664 0.60591 0.60509 0.60416 0.35999 0.JSNIS 0.35608 0.35377 S 97 21 1 75 76 77 78 10.352 10.004 9.654 0.50706 0.52362 0.54030 0.55704 0.28850 0.JOS41 0.33280 0.31072 0.69833 0.68854 0.07768 0.60568 #250 0.42501 0.40618 0.38000 E 0.09403 0.07930 0.186531 0.05258 Ani 75 76 27 78 10 985 Appendix D. Tables 587 The D. 3 Standard Ultimate Sur Model, 1 = 5% per year Appende D. Tables Table D 3 (Com 10 20 + A 'VE 5E, RE WE 20 21 22 19.966 19920 19.871 15819 19.763 0.04922 0.25144 0.05378 0.05633 0570 DISSO 0.00614 0.00552 0.00694 0.00739 078252 0.78250 2.78245 0.78345 0.78243 0.61224 0.61220 0.61215 0.61210 0.61205 0.37440 0.37429 0.37417 0.3740 0.37390 50 51 52 53 54 17.025 16.846 16.661 16.168 16.268 0.1893 0.19780 0.20664 0.215R2 0.22535 0.05108 0.05517 005957 0.06430 0.06938 0.77772 0.77711 0.77643 0.77566 0.77479 0.01 0.610 0302 059756 59550 0.14824 34503 0.34116 033749 13303 SU 51 52 53 54 19.703 SS 95 55 56 YRA 19.58 19.5 1945 0.06147 0.05429 0.06725 0.07034 0.07359 0.00785 00041 0.00900 0.00964 001033 0.78240 0.78236 0.78233 0.76220 0.76224 0.61198 0.61191 0.61183 0.6174 0.61163 0.37373 0 37354 0.3734 0 37310 0.37284 57 58 59 16.000 15.8.14 15.621 15.390 15.151 0.23534 0.24550 0.25613 0.16714 0.2752 0.07433 DORD67 0.08692 0.09360 0.10073 0.77382 0.77273 0.77151 0.77017 0.76860 0.3932 0.59109 0.3818 038556 0.5029 32819 02279 31681 3100 030300 58 59 3 0.76687 057864 TE 19.30 19230 09 19 60 61 0.0759 0.0805 07 0.06817 0.09226 0.01109 0.01 192 DI 0.0079 0.0146 0.78219 0.78213 0.78206 0.78199 0.78190 0.61152 0.61139 0.61124 0.61108 06100 0.37254 0.37221 0.37183 0.37141 0.37094 31 3 32 14.904 14.649 14 386 14.115 13.816 62 63 0.2902 0.30240 031495 0.32785 03411 0.10834 0.1164 0.12506 0132 0.14092 38 1.76276 0.76033 0.75760 0.29508 0.28641 27698 036074 15569 051003 0.36496 63 HE TE 973 6:0966 35 36 35 3 33 je 65 60 101010 WOOF 1780 D1601 0.01727 0.01863 0.02012 0.02173 0.781RI 0.78170 078158 0.78145 0.78130 0.61069 0.61016 061020 060990 0.60957 0.37041 0.36982 0.36915 0.36841 0.36757 65 66 67 68 69 13.30 13.356 12954 12.06 12.130 0.15477 0.36878 0.38373 0.39783 0.11285 15 0.15420 0.16507 0.17654 1886 030133 75455 . 0.74710 14. ON 033112 31754 0.56305 254009 0.53836 0515 th 66 0.15 0.11571 1570 38 39 SMO 15556 SHEET 1200 11.00 SINCHO LETTO 30 2945 70 71 42 0.02347 0.02536 0.01741 0.02963 0.03 203 12 1. 17.950 0.78113 0704 0.78072 NH 07821 OED POSTED PINO 12065 0.13249 2.135 0.14 0.60920 0.60879 0.60832 06070 0.com 036663 0.36558 0.3640 036307 0.36159 0.17313 0.1570 0 112 It it EF 70 71 72 73 74 07201 0.72039 UTENOS 0.15968 0.7550 11.005 10.065 TECID STRONO 019215 TO CMT SISTO 74 10.13 POROSO WINSTO 25 46 47 46 64 10 0.1516 0.1556 0.16577 UTAO 17316 17.071 17.519 17.361 17.196 0.046 0.0744 0.0404 04314 0.77991 077956 O TV 7775 077827 0.60655 0.6051 0.60 0.60104 0.35994 0.59 0 35001 0.15370 35 76 12 20 20 PIB 75 76 72 if 17 SF On 0854 0.000 MS 0.00217 O. 0 09366 007887 0.04.300 0.05310 001036 0.104 021886 0.16215 WO OF TO 04 0.37 COD 29 SU ED