J.I.A. Vol. LXVII, Part I. Page 13, line 18.

For “T.F.A. Vol. XIII, p. 149”

read “T.F.A. Vol. XIII, p. 419”.

(1) In a paper read before the Institute in November 1933 (J.I.A. Vol. LXV, p. 38), Mr C. D. Rich showed how to calculate the inherent rate of growth of a population by combining in a single index the current data regarding mortality and fertility. Valuable though this index is in showing the true underlying trend at a particular point of time, it cannot be adapted (nor is it intended) to show the actual future populations at any particular time.

(2) It is the purpose of the present paper to make estimates of the population of Great Britain, according to age and sex, for certain future years, and in order to do this an attempt is made to forecast the probable future course of mortality and fertility in Great Britain, in the light of the experience of the past, and such indications as there may be regarding the factors which will influence the future.

Mortality of Assured Lives 1924–29 (Monetary Tables, Vol. I), p. 182. For ·01557 read ·01547 where P[33]:42 with 3½% interest is shown.

The subject of this paper is essentially a practical one, and although it has been before the Institute on various occasions it is some considerable time since there has been a discussion on the actual methods employed in classifying and valuing industrial assurance contracts.

Forty years ago a paper was read before the Institute by the late Frederick Schooling “On some Methods of Grouping Policies for the Purpose of Valuation“ (J.I.A. Vol. XXXII, p. 301). It dealt with the classification and method of valuation of industrial assurance policies. Since the paper was written many changes have taken place, and it will be useful as an introduction to consider the developments which have occurred during that period.

The term “family annuities” appears to have been coined by George King, who used it in a paper read before the Institute on 19th December, 1892 (J.I.A. Vol. xxx, p. 291), to describe that form of orphans' benefit in which a small annuity is paid to each child of a deceased father until the child attains a specified age, such as 14 years. King gave a formula for the evaluation of the benefit and discussed a suitable basis, but though he worked out commutation columns he did not give any results in the form of specimen premiums. He was mainly concerned with the problem as an element in the schemes of State insurance which were then under discussion; indeed, as he revealed in a letter to the Insurance Record in 1920 (see J.I.A. Vol. LII, p. 35), he had been asked to make estimates in this connexion in 1890 by Mr Joseph Chamberlain.

The objects of this paper are (1) to set out for members of the profession some account of the further investigations that have been made into the statistics that formed the basis of the A 1924-29 Table, (2) to correct certain errors that have been discovered, (3) to explain the possible weaknesses in the statistics, (4) to discuss the variations in mortality shown by individual offices, and (5) to give some idea of the range in mortality above and below the combined result of all the offices. There is necessarily some overlapping in the treatment of these objects and it is difficult to draw hard and fast lines between them, but we hope that by bearing these general objects in mind the reader will not be disturbed by what is, we fear, a somewhat discursive paper.

The subject of annuities is one which has rarely been discussed by this Institute and the two classic papers of modern times on the subject (Oakley, J.I.A. Vol. XLIII, p. 281 and Elderton and Oakley, J.I.A. Vol. LV, p. 211) deal very largely with the mortality aspect of the problem. Income Tax is also a subject which has received but scant attention in our literature, the most modern paper in the Journal being that by Faulks written in 1903 (J.I.A. Vol. xxxvIII, p. 297); a later paper was read in Edinburgh in 1922 (Barnett, T.F.A. Vol. IX, p. 65) but even this is quite out of date as regards annuities because the Finance Act of 1923, following the recommendations of the Colwyn Committee, introduced important new factors into the taxation of the annuity fund. Recknell's paper in J.S.S. (Vol. 11, p. 93) suffers from the same disadvantage, having been written in 1921.

On various occasions when mortality tables have been prepared in select form difficulty has been experienced in running the select rates into those of an aggregate or ultimate table. The difficulty has been ascribed to various special circumstances, such as further elimination of duplicates at the end of the select period; class selection; and heterogeneity of the data due to the length of the period covered. It seems always to have been taken for granted that, at the end of some period of years, the select rates ought to run into those of an ultimate table.

In November 1927 I submitted to this Institute a paper on the place of ordinary stocks and shares in the investment of life assurance funds. The conclusions were drawn from an investigation of hypothetical investments made in 1912 of uniform amount in the equities of nine groups of companies and followed out during a period of fifteen years. A comparison was made with similar investments made in the fixed interest securities of the same groups of companies. The records showed clearly in favour of the equities both as to income during the fifteen years and as to capital values at the end of the term. It has been on my conscience for some time that the record is incomplete without the inclusion of the period of the world depression in industry and trade which followed soon after the close of the period selected.