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Use the file Male Survivors. 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 60 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. The first calculation in Excel is where (83582/84654) is the probability that a 60-year-old male survives to age 61. The second calculation in Excel is 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. 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.

D 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 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 96180 95997 95791 95569 44 45 46 47 48 95337 95087 94825 94542 94229 93892 93529 93142 92713 9 1 3 4 8 2254 91768 91247 90707 90127 39527 88839 8161 87382 86542 85500 84654 83582 32458 81231 19920 78506 76988 75391 13665 71330 0 61 62 4 6 6 7 8 0 1 2 4 5 6 18 9 80 81 82 3 4 85 86 87 88 89 0 21 92 3 4 5 6 97 8 99 100 69875 67824 55552 63335 60880 58335 55655 52874 50001 47012 43928 40856 37568 34457 31192 27975 24820 21766 18852 16113 13580 11277 213 7412 5857 4546 3462 2586 1893 1357 953 101 100 103 104 105 106 107 108 100 10 11 600 400 200 100 50 30 15 7 3 1 0