490, or 298900 Chances; of these there are 50 × 73, or 3650, that they are both dead. And as 298900, to 298900 - 3650, or 295250: So is the present Value of a Sum of Money to be paid after 8 Years, to the present Value of a Sum to be paid, if either of the two live. And as 560 × 73, so are the Chances that the Elder is dead, leaving the Younger; and as 417 × 50, so are the Chances that the Younger is dead, leaving the Elder. Wherefore as 610 × 490 to 560 × 73, so is the present Value of a Sum to be paid at 8 Years end, to the Sum to be paid for the Chance of the Younger's Survivance; and as 610 × 490 to 417 × 50, so is the same present Value to the Sum to be paid for the Chance of the Elder's Survivance.
This possibly may be yet better explained, by expounding these Products by Rectangular Parallelograms, as in Fig. 7. wherein AB or CD represents the number of Persons of the younger Age, and DE , BH those remaining alive after a certain Term of Years; whence CE will answer the number of those dead in that time: So AC , BD may represent the number of the elder Age; AF , BI the Survivors after the same Term; and CF , DI , those of that Age that are dead at that time. Then shall the whole Parallelogram ABCD be Nn , or the Product of the two Numbers of Persons, representing such a number of Persons of the two Ages given; and by what was said before, after the Term proposed, the Rectangle HD shall be as the number of Persons of the younger Age that survive, and the Rectangle AE as the number of those that die. So likewise the Rectangles AI , FD shall be as the Numbers, living and dead, of the other Age. Hence the