answer all questions

P. 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 $125. Renewal expenses are 5% of the premiums from the 2nd premium onwards. Expenses of 200 on the benefit sum insured. Use Table D Standard Select Survival Model in your calculations. (a) (10 pts) Calculate the premium for this policy. (b) (10 pts) Write an expression for L, and calculate its mean V. 10:12 5G. X Appendix D.pdf .. 585 Appen Dw Table 1.2 Cow.) Isip EN BE OS 15 115 16 17.028 16.850 16.668 16.473 16.273 0.1013 0.19761 0.00013 0.21555 02150 0.05087 0.05495 0.05933 0.0004 13 077791 0.7772 72065 0.72591 0.77507 0.60156 0.60066 090019 0.59755 0.59572 0.34832 0.34512 0.34150 3160 033 53 54 32 33 54 NO 0.59300 35 56 57 58 50 16.066 15831 15.626 15.398 15.160 0.13456 0.34519 0.35579 0.26673 OX 0.07451 QUOI 0.08653 0:09317 0.10035 U.23413 0.77307 0.77119 0.77136 0. 59135 OS 0.312 0.31293 031697 031041 0.101 55 50 57 38 59 0.58585 U 3205 14 19 19 1913 HAS 14.30 H.123 ESO 0.30194 031442 0.32727 0.34649 0.10781 0.115 0.12441 0.13350 0.14313 1619 076552 0761 0.76105 0.75811 OSW 0.57501 0.57051 0.56550 SSN 0.2952 0.000 0.27121 0.26700 0.25595 63 64 J 04 65 66 67 1354 13272 12.972 12.065 12.JSI 0.35407 0.36301 01230 2.15333 0.16411 0.17548 0.16746 0.2000$ 0.79145 0.75214 07544 0.7449 0.73906 55371 115466 USIT US300 052134 0.24411 0.23143 0.21797 0.20377 0.11 03 66 67 CM 041186 20 21 72 73 74 12.031 18.703 11.374 11.031 106 042710 0.44262 0.45840 047442 0.42063 0.312 0.3230 0.24154 0.25662 0.27229 0.73450 0.72623 0.72230 0.71515 0.70719 031100 0.4996 0.48719 0.47355 0.4567 017330 0.15867 OH) 0.1254 0.10951 70 71 72 ?) 74 75 76 77 18 19 10353 10.DO 9454 9.302 8.950 8592 0.00 0.52362 0.54029 0.53704 0.57382 0.01 010641 0.13280 034072 0.15912 17297 0.00 . 016776 0.66568 016345 0.617 142501 0160618 0.36000 0.345 0.34179 0.09403 0.07920 006631 005256 0.04131 0.05133 73 76 27 18 79 US . Ix Wx ir 1x ix ry dx 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 1 000 000 95 104 951 903 707 85 946 859 816 684 77 670 777 738 038 70 190 702 666 962 63430 634 602 728 57321 573 544 677 51 800 518 492 213 46 811 468 444 800 42 301 423 401 951 38 226 382 363 226 34 543 345 328 228 31 215 312 296 599 28 207 282 268 014 25 488 255 242 181 23 031 230 218 834 10665 213 207 872 10 131 203 197 455 9623 192 187 555 9141 183 178 147 8682 174 169 206 8 246 165 160 708 7832 157 152631 7438 149 144 954 7064 141 237 44 218 45 0 200 46 0 18447 0 17048 0 15749 0 14550 0 134 51 0 125 52 0 11753 0 109 54 0 102 55 0 96 56 0 9157 0 86 58 0 8359 0 84 60- 0 84 60+ 0 8561 0 86 62 0 87 63 0 8964 0 90 65 0 93 137 656 6708 134 0 95 130 719 2586 129 0 100 127 904 2 530 127 0 106 125 140 2476 124 0 113 122 428 2422 121 0 121 119 763 2369 118 0 130 117 145 2 317 116 0 140 114 572 2266 113 0 151 112042 2216 111 0 163 109 553 2 166 108 0 176 107 102 2118 106 0 190 104 688 2070 103 0 206 102 308 2023 101 0 224 99960 1976 99 0 243 97 642 1930 96 0 264 95 351 1 884 94 0 288 93 085 0 0 27926 0 65 160 0 62 6 188 210 58 700 0 56 5573 212 52 860 0 50 5018 213 47579 0 45 4515 214 42 805 0 41 4061 215 38 488 0 0 38 488 0 42 43 10:12 5.4 X Appendix D.pdf .. I Ag D. Tables Table D2 Sawar Select Surwiwal Model 39 per your PAI SEN 101 19.907 0.04918 0.78255 0.61227 03741 19.901 0.051:40 0.00610 0.78254 06123 097431 19.872 0.05373 0.00648 0.78252 0.61218 0.37419 19.820 0.05618 0.00669 2.783 0.61213 017406 19.766 0.05674 000734 0.78242 0.61208 0.37392 19.710 0.0614) 0.00783 0.7KBH 0.37375 19.651 0.00124 0.00037 0.76341 0.61194 0.37356 1059 0.66720 0.0095 0.76237 0.61186 0.37336 19.534 0.07029 0.0005 0.78213 0.61171 037312 19.256 0.07353 0.01008 0.76229 0.61167 031246 20 21 22 24 15 26 27 26 20 31 19.384 19.310 19.230 19.1 SU 19.04 0.0093 0.0019 008421 00811 0409220 001104 0.0116 0.01276 0.01373 0.01479 0.78.234 0.78215 07211 078204 0.1819 0.61156 0.61143 061128 0.61112 0.61094 0.37256 0.37221 0.3718 0.37144 0.37097 8414 L. 18.142 18.679 18.572 0.10091 0.1562 0.11091 0.113 0.01944 0.01720 OLDIES6 0.6.2004 0.00 0.78187 0.78176 0.28165 0.28152 0.78137 0.61094 0.61051 0.61025 0.60996 0.60 0.37044 0.36955 0.36919 0.3684 0.36761 35 36 17 38 39 18.460 18.342 18.220 IN 17.955 0.1360 0.13240 0.1384 14S 0.0238 0.02527 002731 003953 000191 0.78121 078102 0.78042 0.7SUS 0.78032 0.6027 0.6086 0.60640 0.00788 0.00730 0.36667 0.16562 0.36444 0.36312 0.36165 it +4 035999 199090 16OVO 45 46 17.819 17.673 17.522 IT 11.200 0.15149 0.15841 14863 0.17314 0.18098 0.03450 0.03730 0.04032 0.04358 004709 0.78005 077970 079932 077891 0.77544 0.60500 0.60416 0.60313 1008 015377 0.35120 19 P. 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 $125. Renewal expenses are 5% of the premiums from the 2nd premium onwards. Expenses of 200 on the benefit sum insured. Use Table D Standard Select Survival Model in your calculations. (a) (10 pts) Calculate the premium for this policy. (b) (10 pts) Write an expression for L, and calculate its mean V. 10:12 5G. X Appendix D.pdf .. 585 Appen Dw Table 1.2 Cow.) Isip EN BE OS 15 115 16 17.028 16.850 16.668 16.473 16.273 0.1013 0.19761 0.00013 0.21555 02150 0.05087 0.05495 0.05933 0.0004 13 077791 0.7772 72065 0.72591 0.77507 0.60156 0.60066 090019 0.59755 0.59572 0.34832 0.34512 0.34150 3160 033 53 54 32 33 54 NO 0.59300 35 56 57 58 50 16.066 15831 15.626 15.398 15.160 0.13456 0.34519 0.35579 0.26673 OX 0.07451 QUOI 0.08653 0:09317 0.10035 U.23413 0.77307 0.77119 0.77136 0. 59135 OS 0.312 0.31293 031697 031041 0.101 55 50 57 38 59 0.58585 U 3205 14 19 19 1913 HAS 14.30 H.123 ESO 0.30194 031442 0.32727 0.34649 0.10781 0.115 0.12441 0.13350 0.14313 1619 076552 0761 0.76105 0.75811 OSW 0.57501 0.57051 0.56550 SSN 0.2952 0.000 0.27121 0.26700 0.25595 63 64 J 04 65 66 67 1354 13272 12.972 12.065 12.JSI 0.35407 0.36301 01230 2.15333 0.16411 0.17548 0.16746 0.2000$ 0.79145 0.75214 07544 0.7449 0.73906 55371 115466 USIT US300 052134 0.24411 0.23143 0.21797 0.20377 0.11 03 66 67 CM 041186 20 21 72 73 74 12.031 18.703 11.374 11.031 106 042710 0.44262 0.45840 047442 0.42063 0.312 0.3230 0.24154 0.25662 0.27229 0.73450 0.72623 0.72230 0.71515 0.70719 031100 0.4996 0.48719 0.47355 0.4567 017330 0.15867 OH) 0.1254 0.10951 70 71 72 ?) 74 75 76 77 18 19 10353 10.DO 9454 9.302 8.950 8592 0.00 0.52362 0.54029 0.53704 0.57382 0.01 010641 0.13280 034072 0.15912 17297 0.00 . 016776 0.66568 016345 0.617 142501 0160618 0.36000 0.345 0.34179 0.09403 0.07920 006631 005256 0.04131 0.05133 73 76 27 18 79 US . Ix Wx ir 1x ix ry dx 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 1 000 000 95 104 951 903 707 85 946 859 816 684 77 670 777 738 038 70 190 702 666 962 63430 634 602 728 57321 573 544 677 51 800 518 492 213 46 811 468 444 800 42 301 423 401 951 38 226 382 363 226 34 543 345 328 228 31 215 312 296 599 28 207 282 268 014 25 488 255 242 181 23 031 230 218 834 10665 213 207 872 10 131 203 197 455 9623 192 187 555 9141 183 178 147 8682 174 169 206 8 246 165 160 708 7832 157 152631 7438 149 144 954 7064 141 237 44 218 45 0 200 46 0 18447 0 17048 0 15749 0 14550 0 134 51 0 125 52 0 11753 0 109 54 0 102 55 0 96 56 0 9157 0 86 58 0 8359 0 84 60- 0 84 60+ 0 8561 0 86 62 0 87 63 0 8964 0 90 65 0 93 137 656 6708 134 0 95 130 719 2586 129 0 100 127 904 2 530 127 0 106 125 140 2476 124 0 113 122 428 2422 121 0 121 119 763 2369 118 0 130 117 145 2 317 116 0 140 114 572 2266 113 0 151 112042 2216 111 0 163 109 553 2 166 108 0 176 107 102 2118 106 0 190 104 688 2070 103 0 206 102 308 2023 101 0 224 99960 1976 99 0 243 97 642 1930 96 0 264 95 351 1 884 94 0 288 93 085 0 0 27926 0 65 160 0 62 6 188 210 58 700 0 56 5573 212 52 860 0 50 5018 213 47579 0 45 4515 214 42 805 0 41 4061 215 38 488 0 0 38 488 0 42 43 10:12 5.4 X Appendix D.pdf .. I Ag D. Tables Table D2 Sawar Select Surwiwal Model 39 per your PAI SEN 101 19.907 0.04918 0.78255 0.61227 03741 19.901 0.051:40 0.00610 0.78254 06123 097431 19.872 0.05373 0.00648 0.78252 0.61218 0.37419 19.820 0.05618 0.00669 2.783 0.61213 017406 19.766 0.05674 000734 0.78242 0.61208 0.37392 19.710 0.0614) 0.00783 0.7KBH 0.37375 19.651 0.00124 0.00037 0.76341 0.61194 0.37356 1059 0.66720 0.0095 0.76237 0.61186 0.37336 19.534 0.07029 0.0005 0.78213 0.61171 037312 19.256 0.07353 0.01008 0.76229 0.61167 031246 20 21 22 24 15 26 27 26 20 31 19.384 19.310 19.230 19.1 SU 19.04 0.0093 0.0019 008421 00811 0409220 001104 0.0116 0.01276 0.01373 0.01479 0.78.234 0.78215 07211 078204 0.1819 0.61156 0.61143 061128 0.61112 0.61094 0.37256 0.37221 0.3718 0.37144 0.37097 8414 L. 18.142 18.679 18.572 0.10091 0.1562 0.11091 0.113 0.01944 0.01720 OLDIES6 0.6.2004 0.00 0.78187 0.78176 0.28165 0.28152 0.78137 0.61094 0.61051 0.61025 0.60996 0.60 0.37044 0.36955 0.36919 0.3684 0.36761 35 36 17 38 39 18.460 18.342 18.220 IN 17.955 0.1360 0.13240 0.1384 14S 0.0238 0.02527 002731 003953 000191 0.78121 078102 0.78042 0.7SUS 0.78032 0.6027 0.6086 0.60640 0.00788 0.00730 0.36667 0.16562 0.36444 0.36312 0.36165 it +4 035999 199090 16OVO 45 46 17.819 17.673 17.522 IT 11.200 0.15149 0.15841 14863 0.17314 0.18098 0.03450 0.03730 0.04032 0.04358 004709 0.78005 077970 079932 077891 0.77544 0.60500 0.60416 0.60313 1008 015377 0.35120 19