a) Write the actuarial commutation functions that are equivalent to the following statements: i) A certain life insurance policy pays RM10,000 if the insured dies before the age of 55, and RM15,000 if the insured survives to aged 55. The coverage is offered to a 32-year-old with a twenty-year premium payment. ii) Net single premium for a person aged 23 for an increasing whole life insurance policy with a death benefit of RM5,000 payable in the first policy year and increasing by RM2,000 per year. (5 marks) b) A 35-year-old man wishes to provide a RM12,000-per-year life annuity, with the first payment due when he turns 60. If his contract stipulates that no money will be returned in the event of his death, what annual payment should he deposit with an insurance company at the beginning of each year for the next 25 years? (10 marks) Table II - Commutation Columns - 1958 CSO - 3% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 68 737.864 16 471.864 13 787.524 12 837.749 11 934.192 11 156.965 10 417.328 9 789.464 9 266.745 8 839.092 8 571.528 8 449.523 8 392.725 8 525.775 8 704.932 8 864.550 9064.961 9 243.829 9 346.988 9 327.222 9 299.603 9 214.012 9 075.863 8 936.960 8 751.644 8 569.542 8 432.941 8 296.154 8 200.069 8 140.858 8 076.941 8 045.567 8 007.661 7 998.081 8 014.251 8 117.923 8 269.054 8 492.305 8 838.258 9 237.171 9709.221 Mx 1 583 601.456 1 514 863.592 1 498 391.728 1 484 604.204 1 471 766.455 1 459 832.263 1 448 675.298 1 438 257.970 1 428 468.506 1 419 201.761 1 410 362.669 1 401 791.141 1 393 341.618 1 384 948.893 1 376 423.118 1 367 718.186 1 358 853.636 1 349 788.675 1 340 544.846 1 331 197.858 1 321 870.636 1 312 571.033 1 303 357.021 1 294 281.158 1 285 344.198 1 276 592.554 1 268 023.012 1 259 590.071 1 251 293.917 1 243 093.848 1 234 952.990 1 226 876.049 1 218 830.482 1 210 822.821 1 202 824.740 1 194 810.489 1 186 692.566 1 178 423.512 1 169 931.207 1 161 092.949 1 151 855.778 Rx 85 672 418.432 84 088 816.976 82 573 953.384 81 075 561.656 79 590 957.452 78 119 190.997 76 659 358.734 75 210 683.436 73 772 425.466 72 343 956.960 70 924 755.199 69 514 392.530 68 112 601.389 66 719 259.771 65 334 310.878 63 957 887.760 62 590 169.574 61 231 315.938 59 881 527.263 58 540 982.417 57 209 784.559 55 887 913.923 54 575 342.890 53 271 985.869 51 977 704.711 50 692 360.513 49 415 767.959 48 147 744.947 46 888 154.876 45 636 860.959 44 393 767.111 43 158 814.121 41 931 938.072 40 713 107.590 39 502 284.769 38 299 460.029 37 104 649.540 35 917 956.974 34 739 533.462 33 569 602.255 32 408 509.306 21 22 23 24 25 26 27 28 29 30 31 32 33 35 36 37 38 39 40 Table ll - Commutation Columns - 1958 CSO - 3% 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 10 218.176 10 731.609 11 271.289 11 831.248 12 429.129 13 079.355 13 772.152 14 518.518 15 306.897 16 145.109 17 020.413 17 902.007 18 814.279 19 743.028 20 690.546 21 672.210 22 683.398 23 717.295 24 752.177 25 804.703 26 836.036 27 846.132 28 830.119 29 779.577 30 692.340 31 569.313 32 395.427 33 150.537 33 751.833 34 140.262 34 253.619 34 069.048 33 584.287 32 889.905 32 050.095 31 116.905 30 109.191 29 022.371 27 787.431 26 354.463 Mx 1 142 146.557 1 131 928.381 1 121 196.772 1 109 925.483 1 098 094.235 1 085 665.106 1 072 585.751 1 058 813.599 1 044 295.081 1 028 988.184 1 012 843.075 995 822.662 977 920.655 959 106.376 939 363.348 918 672.802 897 000.592 874 317.194 850 599.899 825 847.722 800 043.019 773 206.983 745 360.851 716 530.732 686 751.155 656 058.815 624 489.502 592 094.075 558 943.538 525 191.705 491 051.443 456 797.824 422 728.776 389 144.489 356 254.584 324 204.489 293 087.584 262 978.393 233 956.022 206 168.591 Rx 31 256 653.528 30 114 506.971 28 982 578.590 27 861 381.818 26 751 456.335 25 653 362.100 24 567 696.994 23 495 111.243 22 436 297.644 21 392 002.563 20 363 014.379 19 350 171.304 18 354 348.642 17 376 427.987 16 417 321.611 15 477 958.263 14 559 285.461 13 662 284.869 12 787 967.675 11 937 367.776 11 111 520.054 10 311 477.035 9 538 270.052 8 792 909.201 8 076 378.469 7 389 627.314 6 733 568.499 6 109 078.997 5 516 984.922 4 958 041.384 4 432 849.679 3 941 798.236 3 485 000.412 3 062 271.636 2 673 127.147 2 316 872.563 1 992 668.074 1 699 580.490 1 436 602.097 1 202 646.075 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 a) Write the actuarial commutation functions that are equivalent to the following statements: i) A certain life insurance policy pays RM10,000 if the insured dies before the age of 55, and RM15,000 if the insured survives to aged 55. The coverage is offered to a 32-year-old with a twenty-year premium payment. ii) Net single premium for a person aged 23 for an increasing whole life insurance policy with a death benefit of RM5,000 payable in the first policy year and increasing by RM2,000 per year. (5 marks) b) A 35-year-old man wishes to provide a RM12,000-per-year life annuity, with the first payment due when he turns 60. If his contract stipulates that no money will be returned in the event of his death, what annual payment should he deposit with an insurance company at the beginning of each year for the next 25 years? (10 marks) Table II - Commutation Columns - 1958 CSO - 3% 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 68 737.864 16 471.864 13 787.524 12 837.749 11 934.192 11 156.965 10 417.328 9 789.464 9 266.745 8 839.092 8 571.528 8 449.523 8 392.725 8 525.775 8 704.932 8 864.550 9064.961 9 243.829 9 346.988 9 327.222 9 299.603 9 214.012 9 075.863 8 936.960 8 751.644 8 569.542 8 432.941 8 296.154 8 200.069 8 140.858 8 076.941 8 045.567 8 007.661 7 998.081 8 014.251 8 117.923 8 269.054 8 492.305 8 838.258 9 237.171 9709.221 Mx 1 583 601.456 1 514 863.592 1 498 391.728 1 484 604.204 1 471 766.455 1 459 832.263 1 448 675.298 1 438 257.970 1 428 468.506 1 419 201.761 1 410 362.669 1 401 791.141 1 393 341.618 1 384 948.893 1 376 423.118 1 367 718.186 1 358 853.636 1 349 788.675 1 340 544.846 1 331 197.858 1 321 870.636 1 312 571.033 1 303 357.021 1 294 281.158 1 285 344.198 1 276 592.554 1 268 023.012 1 259 590.071 1 251 293.917 1 243 093.848 1 234 952.990 1 226 876.049 1 218 830.482 1 210 822.821 1 202 824.740 1 194 810.489 1 186 692.566 1 178 423.512 1 169 931.207 1 161 092.949 1 151 855.778 Rx 85 672 418.432 84 088 816.976 82 573 953.384 81 075 561.656 79 590 957.452 78 119 190.997 76 659 358.734 75 210 683.436 73 772 425.466 72 343 956.960 70 924 755.199 69 514 392.530 68 112 601.389 66 719 259.771 65 334 310.878 63 957 887.760 62 590 169.574 61 231 315.938 59 881 527.263 58 540 982.417 57 209 784.559 55 887 913.923 54 575 342.890 53 271 985.869 51 977 704.711 50 692 360.513 49 415 767.959 48 147 744.947 46 888 154.876 45 636 860.959 44 393 767.111 43 158 814.121 41 931 938.072 40 713 107.590 39 502 284.769 38 299 460.029 37 104 649.540 35 917 956.974 34 739 533.462 33 569 602.255 32 408 509.306 21 22 23 24 25 26 27 28 29 30 31 32 33 35 36 37 38 39 40 Table ll - Commutation Columns - 1958 CSO - 3% 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 10 218.176 10 731.609 11 271.289 11 831.248 12 429.129 13 079.355 13 772.152 14 518.518 15 306.897 16 145.109 17 020.413 17 902.007 18 814.279 19 743.028 20 690.546 21 672.210 22 683.398 23 717.295 24 752.177 25 804.703 26 836.036 27 846.132 28 830.119 29 779.577 30 692.340 31 569.313 32 395.427 33 150.537 33 751.833 34 140.262 34 253.619 34 069.048 33 584.287 32 889.905 32 050.095 31 116.905 30 109.191 29 022.371 27 787.431 26 354.463 Mx 1 142 146.557 1 131 928.381 1 121 196.772 1 109 925.483 1 098 094.235 1 085 665.106 1 072 585.751 1 058 813.599 1 044 295.081 1 028 988.184 1 012 843.075 995 822.662 977 920.655 959 106.376 939 363.348 918 672.802 897 000.592 874 317.194 850 599.899 825 847.722 800 043.019 773 206.983 745 360.851 716 530.732 686 751.155 656 058.815 624 489.502 592 094.075 558 943.538 525 191.705 491 051.443 456 797.824 422 728.776 389 144.489 356 254.584 324 204.489 293 087.584 262 978.393 233 956.022 206 168.591 Rx 31 256 653.528 30 114 506.971 28 982 578.590 27 861 381.818 26 751 456.335 25 653 362.100 24 567 696.994 23 495 111.243 22 436 297.644 21 392 002.563 20 363 014.379 19 350 171.304 18 354 348.642 17 376 427.987 16 417 321.611 15 477 958.263 14 559 285.461 13 662 284.869 12 787 967.675 11 937 367.776 11 111 520.054 10 311 477.035 9 538 270.052 8 792 909.201 8 076 378.469 7 389 627.314 6 733 568.499 6 109 078.997 5 516 984.922 4 958 041.384 4 432 849.679 3 941 798.236 3 485 000.412 3 062 271.636 2 673 127.147 2 316 872.563 1 992 668.074 1 699 580.490 1 436 602.097 1 202 646.075 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80