Various Tables of Annuities. 325 



the values of annuities at 0, 5, &c. may be obtained in a similar 

 manner. This value of the annuity will be a very close approxi- 

 mation, the error whatever it be, will be nearly constant for 

 different tables of mortality, and as the first correction which is 



in this case - is constant, the whole correction may be con- 

 sidered as constant. It may therefore be determined easily by 

 calculating the annuity first accurately, and afterwards by the 

 approximate method from any Table of mortality in which the 

 deaths are given for every age, the difference between the two 

 values so obtained will be the correction required. By means 

 of the Chester Table for males, I determined the correction as 

 follows, supposing the Table of mortality to give the living at 

 0, 5, 10, 20, 30, 40, 50, &c., and that the annuity commences at 

 the end of the first year. 



Age. Age. 



At Birth 2.481 30 4.109 



5 3.692 40 4.024 



10 4.167 50 3.920 



20 4.242 60 3.792 



Thus the value of an annuity at 20 is 



10 X I ^^'"' L P-^'^ .- &cl+4 242 



1(1 + ry + (1 + rf ®'^-| ^ • • 



How close an approximation this method gives may be seen 

 in Table II, where I have placed underneath the results which 



