MANAGEMENT OP AN INSURANCE OFFICE. 29# 



fraction which a year's interest on C is of c, otherwise 

 the fund would increase without limit. 



2. Neither can there he such a fund unless the sum 

 of m and c should fall short of the sum of p, and of a 

 year's interest on the excess of C over P. But, when 

 this is the case, the limiting surplus capital is found 

 by dividing the excess of the second total just men- 

 tioned over the first,, by a divisor obtained as follows : 

 multiply together t and c, divide the product by C, 

 and subtract r from the quotient. To this surplus 

 capital, add the excess of C over P, and the limiting 

 capital is obtained. 



3. If it should happen that the limiting surplus 

 capital is less than the actually existing surplus, it is a 

 sign that the action of the preceding plan would 

 diminish the surplus towards that limit instead of 

 increasing it. In such a case, the surplus is already 

 too large for the value of t to increase it; and if t be 

 not diminished, that is, if less of the tabular surplus 

 be not taken into the computation of the dividend, the 

 fund will diminish. 



It is not to be supposed that any office will ever 

 reach a stationary state ; but the approach may be near 

 enough to make the preceding process of some use, in 

 the determination of the dividends due to the insured. 

 If, following the plan which the preceding problem 

 supposes, we were to inquire what value should be 

 given to the fraction t, the answer to the question must 

 depend on the reduction of interest which is supposed 

 within the bounds of probability. Suppose the present 

 rate of interest to be 3-J per cent, and that the extreme 

 limit is supposed to be 2j per cent, in such a case 

 the value of P and C must be calculated at 2J- per 

 cent., and such a limiting surplus must be fixed upon 

 as will, at that rate of interest, enable the office to pay 

 at least its guaranteed claims But it is impossible to 

 lay down an entire system of rules for the regulation of 

 a species of undertaking which depends on the fluc- 

 tuations of the state of society. Whatever maxims 

 u 3 



