The object of this paper is to give a brief exposition of the different possible methods or classes of methods of equitably dividing the net profits of a Mutual Life Assurance Office among the members. By an equitable division must be understood one which is fair not only between persons of different ages entering the Office at the same time, but also between persons entering the Office at different epochs of its existence,–one from which the members of different ages will, relatively to one another, receive the same benefit from the profits during the earlier and growing years of the Office, and during years when the amount of its business is declining, as during its stationary period. I assume the premiums actually paid to be composed of the net premium calculated from a correct life table, and of a charge of 25 per cent. on the net premium added to guard against unfavourable contingencies, and that this additional charge is really the source of all the profit divisible among the members; or at least, that whatever profits arise from any other source may be fairly apportioned in the same proportions as appear equitable on the supposition that the charge is the sole source of profits. The addition to the premiums for defraying the expenses of the Office, for the sake of simplicity, I leave out of account. In consideration of the payments of the successive net premiums, the assured is guaranteed a sum at death such that the present prospective value of that sum is equal to the present value of the successive net premiums. Similarly, in consideration of the successive charges on the premiums, he should have the prospect of receiving a sum or sums either at death or at any times before that; not guaranteed, it is true, to any fixed amount, but variable with the circumstances of the Society, such that the present value of such sums or bonuses shall be equal to the present value of the successive charges. That this equation between the present values ought to subsist is as clear in the case of the charges and bonuses as in that of the net premiums and sums assured. If the system of division of profits be such that this equation always subsist, it must be fair as respects each member; and any Office adopting a system in which it does not subsist is committing as great an injustice towards its members as one which calculates the premiums on false life tables.
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