306 ESSAY ON PROBABILITIES. 



ADDITION TO CHAPTER X. 



The following formulae will sometimes be found 

 useful. 



The present value of an insurance, which is to be 

 \ if the party die in the first year, 2 if in the second, 

 and so on, is 



1 + A-rI 

 1+r 



where A is the value of a common annuity ; I that of 

 an annuity which is l at the first payment, % at 

 the second, and so on; and r the interest of g@l for 

 one year. 



If an office engage to pay \ at the death of an 

 individual, and also to return all the premiums at the 

 same time, that is, if they guarantee that the interest of 

 his investments shall amount to <!, the premium which 

 should be demanded is 



E-A 



1+A + I 



where A and I are as before, and E is the value of a 

 perpetuity of 



