ANN 



the present value of an annuity of 1. to continue certain for n years) 



5. The present value of the annuity to continue for ever from the 



death of the proposed individual is . 



n. r 1 



C. To find the present value of an annuity of 1. to be paid as long as 

 two specified individuals are both living-. 

 Find by Art. 2. the probability that they will both be alive at the end 



1 , 2, 3, &c. years to the end of the Tables, call these probabilities a, J, c, 



&c. and r the amount of 1. in one year, then -^ -f. -f. -^ -f- &c. is 

 the present value of the annuity required. 



7. To find the present value of an annuity of 1. to be paid as long as 

 either of two specified individuals is living 1 . 



Find by Art. 3. the probability that they will not both be extinct in I, 



2, 3, &c. years to the end of the tables, and call these probabilities A, B, 



ABC 



, &c, then the present value of the annuity is -f -g -f -^ -f &c, 



15 



