+--------+-------------+--------+-------------+--------+-------------+ | Years. | Pres. Value | Years. | Pres. Value | Years. | Pres. Value | | | of 1 _l._ | | of 1 _l._ | | of 1 _l._ | +--------+-------------+--------+-------------+--------+-------------+ | 1 | 0,9434 | 19 | 0,3305 | 37 | 0,1158 | | 2 | 0,8900 | 20 | 0,3118 | 38 | 0,1092 | | 3 | 0,8396 | 21 | 0,2941 | 39 | 0,1031 | | 4 | 0,7921 | 22 | 0,2775 | 40 | 0,0972 | | 5 | 0,7473 | 23 | 0,2618 | 45 | 0,0726 | | 6 | 0,7050 | 24 | 0,2470 | 50 | 0,0543 | +--------+-------------+--------+-------------+--------+-------------+ | 7 | 0,6650 | 25 | 0,2330 | 55 | 0,0406 | | 8 | 0,6274 | 26 | 0,2198 | 60 | 0,0303 | | 9 | 0,5919 | 27 | 0,2074 | 65 | 0,0227 | | 10 | 0,5584 | 28 | 0,1956 | 70 | 0,0169 | | 11 | 0,5268 | 29 | 0,1845 | 75 | 0,0126 | | 12 | 0,4970 | 30 | 0,1741 | 80 | 0,0094 | +--------+-------------+--------+-------------+--------+-------------+ | 13 | 0,4688 | 31 | 0,1643 | 85 | 0,0071 | | 14 | 0,4423 | 32 | 0,1550 | 90 | 0,0053 | | 15 | 0,4173 | 33 | 0,1462 | 95 | 0,0039 | | 16 | 0,3936 | 34 | 0,1379 | 100 | 0,0029 | | 17 | 0,3714 | 35 | 0,1301 | | | | 18 | 0,3503 | 36 | 0,1227 | | | +--------+-------------+--------+-------------+--------+-------------+ It were needless to advertise, that the great trouble of working so many Proportions will be very much alleviated by using Logarithms; and that instead of using _Nnν - Yyυ_ for the second Term of the Proportion in finding the Value of Three Lives, it may suffice to use only _Yyυ_, and then deducting the fourth Term so found out of the third, the Remainder shall be the present Value sought; or all these fourth Terms being added together, and deducted out of the Value of the certain Annuity for so many Years, will leave the Value of the contingent Annuity upon the Chance of Mortality of all those Three Lives. For Example; Let there be Three Lives of 10, 30, and 40 Years of Age proposed, and the Proportions will be thus; As 661 in 531 in 445 or 156190995, or _Nnν_ to 8 in 8 in 9, or 576, or _Yyυ_ for the first Year, so 0,9434. to 0,00000348. To 15 in 16 in 18, or 4320, for the second Year, so 0,8900. to 0,00002462. To 21 in 24 in 28, or 14112 for the third Year, so 0,8396. to 0,00008128. To 27 in 32 in 38, for the fourth Year, so 0,7921. to 0,00016650. To 33 in 41 in 48, for the fifth Year, so 0,7473. to 0,00031071.