The subject I have chosen for my paper is one which needs no apology for its introduction to this Institute, closely connected as it is with one of the most pressing problems which those responsible for the management of a life assurance office have to deal with at the present time. It is, no doubt, difficult, in the face of the eager competition which has to be encountered, to increase the business of an office; but it is scarcely less difficult to satisfactorily invest the surplus arising from the premiums when they are obtained. One is reminded of the picture which appeared a few years ago in Punch, in which a Dean, importuned for alms by a beggar, exclaims, “Ah, my good “woman, it is not the poor only who have their troubles; you, “for instance, have probably never experienced the difficulty of “finding investments, combining adequate security with a “remunerative rate of interest”! It is probable that she had not, but it is equally probable that the actuary of every assurance company in this country has already experienced the difficulty, and is likely to experience it increasingly in the future. The investments which, in the past, have found favour with life assurance companies, have not increased in proportion to the increase of the funds to be invested.

“The rate of interest has fallen.” “The rate of interest is falling.” “The rate of interest will probably continue to fall.” These sentences, and others of a similar nature, we have read so often, that I fear it is quite possible “familiarity” may, to some extent, have had its usual effect. The fact remains, however, that any further fall in the interest yield is of vital importance to insurance companies with large funds to invest, and bound by contracts, the fulfilment of which depends, to a large extent, on the rate of interest obtainable.

In a paper by the present writer, entitled Some Remarks on the Valuation of Endowment Assurances in Groups, which appears in the current volume of the Journal, pp. 61–84, a new method of valuing Endowment Assurances, based on Makeham's formula for μx and lx, was described, and it was shewn that very good results were obtained by the use of the method in the case of a fairly large Endowment Assurance business, particulars of which were summarized in the paper.

There appears to be a very general belief that every life may be accepted under the Double Endowment Assurance Table at the same rate, provided the term is fixed. One office, at least, grants such assurances without medical examination; another has accepted publicans under this table without the usual trade extra; and medical officers have been known to recommend acceptance at tabular rates for a Double Endowment after having declined the life out-right for an ordinary Endowment Assurance. It may be useful, perhaps, to ascertain how far this practice is justified by theory; and it is hoped, therefore, that a short note on the subject may not be without interest.