Mijcellanea Curiofa, 293 



Reverfions. And as A D to A G, or r T, foare 

 all the Chances, to thofe that the elder furvives 

 the younger. I have been the more particular, 

 and perhaps tedious, in this Matter, becaufe it 

 is the Key to the Cafe of Three Live?, which 

 of it (elf would not have been fo eafie to com- 

 prehend. 



VJI. If Three Lives are propofed, to find 

 the Value of an Annuity during che cominu- 

 ance of any of thofe three Lives ; the Rule 

 is, As the Produci of the continual Multiplica- 

 tion of the three Numbers, in the Table, an fever- 

 ing to the Ages propofed, is to the difference of 

 that Product, and of the Produci of the Three 

 'Numbers of the Deceafed of thofe Ages, in any 

 given Term of Tears : So is the prefent Value of a 

 Sum of Money, to be paid certainly after fo many 

 Tears, to the prefent Value of the fam? Sum to be 

 paid, provided one of thofe Three Per fans be living 

 at the Expiration of that Term. Which Pro- 

 portion being yearly repeated, the Sum of all 

 thofe prefent Values will be the Value of an 

 Annuity granted for three fuch Lives. But 

 to? explain this, together with all the Cafes of 

 Survivance in Three Lives : Let N be the 

 Number in the Table for the younger Age, 

 n for the fccond, and v for the elder Age ; 

 let T be thofe dead of the younger Age in the 

 Term propofed, y thofe dead of the fecond 

 Age, and v thofe of the elder Age ; and let t\ 

 be the Remainder of the younger Age, r that 

 of the middle Age, and g the Remainder of 

 the elder Age. Then (hall ^ *fT be equal to 

 N, r H- y to n, and j -+• w to y, and the con- 

 tinual Produci: of the three Numbers N, n, v, 

 (hall be equal to the continual Produci of 



u ? X 



