288 ESSAY ON PROBABILITIES. 



or less ; with this additional limitation, that the office 

 undertakes that the said accumulation shall not be less 

 than 100/. This last guarantee,, though necessary for 

 the satisfaction of the public,, is in truth so certain,, from 

 the amount of the premium demanded, that a person 

 acquainted with the subject looks upon the possibility 

 of the funds of the society suffering from it as an ex- 

 tremely remote chance. 



In order, however, to make the proceedings of such an 

 office equitable, the proportions of the premiums paid by 

 parties of different ages must be fairly regulated. On 

 the supposition that the inequality pointed out in page 

 2?0. is allowed to exist, the preceding methods of divi- 

 sion may be (I do not say are) adjusted so that every 

 interest shall be consulted. But in the present plan, it 

 is impracticable to remedy any such defect of proportion, 

 at least without dividing the establishment into as many 

 different offices as there are ages, which would not be 

 easy, and perhaps not very safe. The simple rule for 

 determining the relative premiums is to make them 

 proportional to the real premiums, with the exception 

 of a given addition to each (not premium, but) policy, 

 for expenses of management. In a large office, how- 

 ever, the expenses of management may be made a part 

 of the percentage addition to the premiums. 



The method of division in such an office is extremely 

 simple, and has been already described in page 276. 

 Subtracting the present value of all the claims, that is, 

 of all the minimum claims, reckoned as 1001. for each 

 tabular premium paid, from the sum of the present 

 values of all premiums, and of the assets of the office, 

 the proportion which this remainder is of the present 

 value of all the claims expresses the fraction of 1001. 

 which may be added to each 1001. insured. 



Let A, the assets* of the office, be 500,000/.; P, the 

 present value of all premiums, 600,000/.; and C, the 

 prseent value of all claims, 850.000/. : then A + P- C, 



* Diminished for the expenses of management, as in page 275. 



