146 Mr W. Fraser on the History arid Constitution of 



The method adopted in the foregoing table, however, would not altogether 

 answer for societies who admitted members at all ages without an equalizing en- 

 try-money, but merely upon payment of an increased annual contribution. In 

 that case, one way of calculating the stock of each individual in the sickness 

 scheme, for example, is as follows : — 



It is wished to be known what stock a society should be possessed of for a 



member who entered at 21 years of age, who is now 30, and who has paid the 



standard annual contribution of L. 1, in the interval of these ages. 



The value of the future distributions to a member aged 30, (by the table, 



p. 136. col. 16.) is - - - L. 21.3011 



If he entered at 21, and is paying an annual contribution of 1„ 1, 



the value at .30, (col. 16.) of his whole future contributions, is 16.6944 



And the difference (col. 14.) is his stock ar interest in that fund, of L 4.^67 



Again, it is wi^ed to be known what should be the stock for a member who 

 entered at 30 years of age, who is now 40, and who has paid the increased an- 

 nual contribution of L. 1.27594 (col. 17) in the interval of these ages* 

 The value of the future distributions (col. 16.) to a member 



aged 40, is - - - - L. 26.5806 



The value at 40 of a future payment of L. 1, (col. 15.) is L. 14.5993 

 The annual contribution payable by a member enter- 

 ing at 30, (coL 17.) is - - - 1.27594 



The one being multiplied by the other gives the value 

 of this member's future contribution at the age of 40, 

 which is - - - - - 18.6278 



And this last being subtracted from the value of his future allow- 

 ances at that age, the difference, or his interest in the Capital at 

 the age of 40, is - - - - L. 7.9528 



Having, in this way, ascertained the estimated stock of each member at 

 every age in the society, and added the whole sums together, the total amount 

 would of course be the capital required. 



But it is very probable that neither of the above methods may be entirely 

 applicable to every society, as the requisite amount of capital must always de- 

 pend, more or less, upon a variety of circumstances, with regard to the valiie of 

 the future contributions and allowances, which it is impossible here to enume- 

 rate or foresee, but which must be taken into account at the time of balancing. 

 Our object at present is not so much to give rules for performing these ope- 

 rations as to shew their expediency ; and if societies once become convinced 

 of the necessity of entering into periodical investigations of their affairs, they 

 will have recourse for directions to some of the works on annuities •, or to per- 

 sons practically acquainted with the subject. It is to be particularly observed, 

 however, that, in performing such operations, it will not do to take the average 

 age of all the members of a society, and hence conclude that the sickness ahd 

 consequently the demands, will be the same as if each member were of that 

 age. For example, take owe member at 26 years of j^e, <m6 at 35, one at 45, 



* See the works of Price, Bailey, Milne, &c. 



