+------+------------+------+------------+------+------------+ | Age. | Years Pur. | Age. | Years Pur. | Age. | Years Pur. | +------+------------+------+------------+------+------------+ | 1 | 10,28 | 25 | 12,27 | 50 | 9,21 | | 5 | 13,40 | 30 | 11,72 | 55 | 8,51 | | 10 | 13,44 | 35 | 11,12 | 60 | 7,60 | | 15 | 13,33 | 40 | 10,57 | 65 | 6,54 | | 20 | 12,78 | 45 | 9,91 | 70 | 5,32 | +------+------------+------+------------+------+------------+ This shews the great Advantage of putting Money into the present _Fund_ lately granted to Their Majesties, giving 14 _per Cent. per Annum_, or at the Rate of 7 Years Purchase for a Life; when young Lives, at the usual Rate of Interest, are worth above 13 Years Purchase. It shews likewise the Advantage of young Lives over those in Years; a Life of Ten Years being almost worth 13½ Years Purchase, whereas one of 36 is worth but 11. _Use_ VI. Two Lives are likewise valuable by the same Rule; for the number of Chances of each single Life, found in the Table, being multiplied together, become the Chances of the Two Lives. And after any certain Term of Years, the Product of the two remaining Sums is the Chances that both the Persons are living. The Product of the two Differences, being the numbers of the Dead of both Ages, are the Chances that both the Persons are dead. And the two Products of the remaining Sums of the one Age multiplied by those dead of the other, shew the Chances that there are, that each Party survives the other: Whence is derived the Rule to estimate the Value of the Remainder of one Life after another. Now as the Product of the Two Numbers in the Table for the Two Ages proposed, is to the difference between that Product, and the Product of the two numbers of Persons deceased in any space of time; so is the Value of a Sum of Money to be paid after so much time, to the Value thereof under the Contingency of Mortality. And as the aforesaid Product of the two Numbers answering to the Ages proposed, to the Product of the Deceased of one Age multiplied by those remaining alive of the other; so the Value of a Sum of Money to be paid after any time proposed, to the Value of the Chances, that the one Party has that he survives the other, whose number of Deceased you made use of, in the second Term of the Proportion. This perhaps may be better understood, by putting _N_ for the number of the younger Age, and _n_ for that of the Elder; _Y_, _y_ the Deceased of both Ages respectively, and _R_, _r_ for the Remainders; and _R + Y_ = _N_, and _r + y_ = _n_. Then shall _Nn_ be the whole Number of Chances; _Nn - Yy_ be the Chances that one of the two Persons is living, _Yy_ the Chances that they are both dead; _Ry_ the Chances that the elder Person is dead, and the younger living; and _rY_ the Chances, that the elder is living, and the younger dead. Thus