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6. Use the file GSB 519 Male Survivors found under Content, Course Files in D2L. You will see male survivors from 100,000 newbom male babies (i.e., age 0) to age 111. At age 60, there are 84654 male survivors from the original 100,000 newboms. Suppose a male who is alive at age has a life pension (a private or a public pension) of S48,000 per year. However, each payment of S48,000 only is paid if the pensioner survives a complete year. Suppose also that the appropriate discount rate is .05 per year. Use Excel to calculate the actuarial present value of the pension at age 60. $48.000 The first calculation in Excel is (83582/84654) where (83582/84654) is the (1.05) probability that a 60-year-old male survives to age 61. The second calculation in Excel is $48.000 (82458/84654) where (82458/84654) is the probability that a 60-year-old male survives to age 62. Keep doing the same type of calculations until there are no survivors in the file GSB 519 Survivors. Sum all of your calculations, and you have the actuarial present value of the pension. This sum is called "actuarial present value for the following reasons: "present value because of the discounting in the problem and "actuarial" because each calculation is weighted by the probability of survival. (1.05) [Pensions usually are paid each month. A pension of $48,000 per year likely would be paid as $4,000 per month. However, using monthly payments in this problem does not add to understanding the structure and meaning of the problem. It only means that we would have monthly rather than yearly calculations. So, we will stay with annual payments of $48,000 but paid only of a person survives.] Arial y 10 V Paste [Copy Format Painter BI U V V a var Clipboard 2 Font G40 fr C D E F G H 38 39 40 41 42 43 44 12 45 46 47 48 A B 3 Age Survivors 4 0 100000 5 1 99249 6 2 99193 7 3 99155 8 4 99126 9 5 99102 10 6 99083 11 7 99066 8 99051 13 9 99035 14 10 99019 15 11 99001 16 12 98983 17 13 98963 18 14 98938 19 15 98906 20 16 98860 21 17 98791 22 18 98700 23 19 98580 24 20 98444 25 21 98311 26 22 98163 27 23 98023 28 24 97888 29 25 97752 30 26 97624 31 22 97489 32 28 97359 33 29 97224 34 30 97092 35 31 96954 36 32 968 19 37 33 96677 38 34 96522 39 35 96369 40 36 96180 41 37 95997 Sheet1 50 $1 52 53 34 55 56 S7 58 59 60 61 95791 95569 95337 95087 94825 94542 94229 93892 93529 93142 92713 92254 91768 91247 90707 90127 89527 88839 88161 87832 86542 85600 84654 83582 82458 81231 79920 78506 76988 75391 73665 71830 69875 67824 65652 63335 60880 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 58335 55655 52874 50001 47012 43928 40856 37568 34457 31192 27975 24820 21766 18852 16113 13580 11277 9218 7412 5857 4546 3462 2586 1893 1357 953 600 400 200 100 50 30 15 7 3 1 63 64 65 66 62 68 69 TO 71 72 73 74 Sheet2 Sheet3 Type here to search e 6. The actuarial present value of the pension is 6. Use the file GSB 519 Male Survivors found under Content, Course Files in D2L. You will see male survivors from 100,000 newborn male babies (i.e., age 0) to age 111. At age 60, there are 84654 male survivors from the original 100,000 newborns. Suppose a male who is alive at age has a life pension (a private or a public pension) of $48,000 per year. However, each payment of $48,000 only is paid if the pensioner survives a complete year. Suppose also that the appropriate discount rate is .05 per year. Use Excel to calculate the actuarial present value of the pension at age 60. $48,000 The first calculation in Excel is (83582/84654) where (83582/84654) is the (1.05) probability that a 60-year-old male survives to age 61. The second calculation in Excel is $48,000 (1.05) (82458/84654) where (82458/84654) is the probability that a 60-year-old male survives to age 62. Keep doing the same type of calculations until there are no survivors in the file GSB 519 Survivors. Sum all of your calculations, and you have the actuarial present value of the pension. This sum is called "actuarial present value for the following reasons: "present value because of the discounting in the problem and "actuarial" because each calculation is weighted by the probability of survival. [Pensions usually are paid each month. A pension of $48,000 per year likely would be paid as $4,000 per month. However, using monthly payments in this problem does not add to understanding the structure and meaning of the problem. It only means that we would have monthly rather than yearly calculations. So, we will stay with annual payments of $48,000 but paid only of a person survives.] A 1 2 3 Age 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 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 B Number of Survivors 100000 99249 99193 99155 99126 99102 99083 99066 99051 99035 99019 99001 98983 98963 98938 98906 98860 98791 98700 98580 98444 98311 98163 98023 97888 97752 97624 97489 97359 97224 97092 96954 96818 96677 96522 96359 23 24 25 26 27 28 29 30 31 32 33 34 35 34 55 36 9 38 39 40 4] 42 43 44 45 46 47 48 49 50 51 52 53 54 4 48 49 50 1 12: 53 54 55 16 522 96359 95180 95997 979|| 97569 95337 9507 0423 94542 24229 99992 93529 93 142 92713 92254 91768 91247 90707 90127 19527 88839 88161 87382 B6542 85600 4654 63592 82458 81271 9921 79506 6968 T-91 T2555 TIBOD 5995 5721 SEE 33 9 60 57 58 59 5] El 62 6 54 E5 BE b 68 E TO 1 2 4 6 16 4 65 56 fig 69 70 7L | 72 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 A 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 B 52874 50001 47012 43928 40856 37568 34457 31192 27975 24820 21766 18852 16113 13580 11277 9218 7412 5857 4546 3462 2586 1893 1357 953 600 400 200 100 50 30 15 7 3 1 0 110 111 112 113 114 115 116 110 111