The advances which have been made in valuation methods were brought home very forcibly to my mind when perusing the records of a valuation made many years ago.

During the past 50 or 60 years the valuation of complicated benefits has been, generally speaking, rendered a comparatively easy task, thanks to the energies of members of this and of other Actuarial Institutes—the Law of Makeham, to take one instance, has been the means of simplifying the solutions of a great number of difficult problems—and the numerous approximations to various intricate expressions, which have appeared from time to time in the pages of the Journal, have further lightened the labour of valuations.

In the discussion on Mr. Simmonds's Paper (J.I.A., vol. xlvii) allusion was made by several speakers to the omission of any reference in that Paper to Section 72 of the National Insurance Act. The omission was, I understand, intentional. Mr. Watson devoted his sixth Lecture on Friendly Society Finance to this Section and to Section 73. He dealt very fully with the position as it then existed. Any present reference to the Section can only follow the lines he laid down, and may therefore appear superfluous. As, however, there was no opportunity of discussing this subject on the Lecture, and as in the discussion following Mr. Simmonds's Paper there appeared a certain interest in this Section, it seems probable that a short demonstration of this side of the National Insurance Act may lead to an interesting and useful discussion, notwithstanding the failings in the Paper itself.

In the discussion that followed the reading of a paper before the Institute of Actuaries Students’ Society, by E. A. Woodall on the valuation of special policies, F. Bedford explained that certain classes, such as joint life endowment assurances, could be valued conveniently by assuming that all the policies will mature at the same age, and calculating the net premium on the same assumption. This method is mentioned in the Students’ Journal, vol. I, No. 2, pp. 24–26, where Mr. Woodall, in giving the method in the abstract of his paper and the discussion, explains how the method applies to certain classes, and writes : “Since the reserve for an endowment assurance maturing at “70 or 75 is practically the same as the reserve for an endowment “assurance of the same term maturing at 50, 55, 60, or 65, the “error of 10 years in the equivalent age is of little importance,” “provided the net premium is calculated on the same assumptions.” This quotation may be taken as the text for the present paper, which discusses the application of the method to ordinary endowment assurances and the errors involved in its use.

The suggestion has been made to me by Mr. George King, to write a paper upon an interesting problem which recently occupied our joint attention.

A brief statement of the case is as follows :

In a great public service there are certain well-defined ranks, the upper ones of which are exclusively recruited by promotion from the lower ones. There are limiting ages of retirement in each rank, and in the event of an officer reaching the fixed age without being promoted he is retired on a pension. The scale of pension depends mainly on length of service, varying of course with each rank, and, as the majority enter in the lowest rank between comparatively narrow limits of age, it is sufficient to deduce an average rate of pension at each age in the various ranks. The problem is to find what amount of annual contribution, uniform throughout future service, should be made in respect of each officer now in the service, of whatever age or rank, in order to provide for the ultimate charge for pensions.

In the particular case presented there were six ranks to be dealt with, and it was understood that the calculations were to be made at 3 per-cent compound interest. I trust I may be excused for this vague statement of the case, but I could hardly be more explicit without being too definite. I shall refer to these ranks throughout as first, second, third ranks, &c., where the first is understood to mean the highest.

Twenty years ago actuaries were fighting the effects of a falling rate of interest, and they did not then know that the battle would become more acute for the next few years, to be followed by a complete change of front on the side of their opponent. Life offices have, at the present time, chiefly in consequence of a rise in the rate of interest, large amounts of depreciation to face, amounts which in some cases are the equivalent of a substantial part of the quinquennial surplus. The question, therefore, of the proper treatment of this depreciation, with due regard to the enhanced rate of interest secured by the lower capital values, seems to be one that may properly occupy the attention of the Institute at a Sessional Meeting.

The subject of this Paper is Whole Life Non-Profit Assurances with uniform Premiums payable throughout life.

In choosing this subject for investigation, I have been influenced mainly by the following reasons :

(1) This type of policy represents life assurance in one of its simplest and earliest forms. The premium and the sum assured are both fixed throughout life, save for the very slight chance of insolvency of the office causing the contract to be reduced. Also nowadays it is not uncommon to find that the surrender values and equivalent paid-up policies are guaranteed from the outset.

(2) Other tables such as Whole Life by Limited Premiums, Half Premiums for first “n” years, &c., are as a rule founded on the basis of the simple whole life ordinary rates.

(3) A considerable body of data derived directly from the experience of British Offices under ordinary whole life non-profit policies is available as a result of the British Offices Mortality Investigation, 1863-93.

(4) In spite of the apparent simplicity of the contract, there are marked divergencies in the rates of premium charged by first-class offices and in the surrender values and equivalent paid-up policies offered by them.