It is now widely recognized that the future must see far-reaching changes in our monetary system, and that these changes must be in the direction of a conscious and planned management, as distinct from leaving the system to be regulated in a more or less automatic manner by factors which reflect and are governed by international conditions; that the monetary system should in fact be made to serve and not govern the requirements of the economic system.

This changed view of the function of the monetary system is probably mainly the result of two economic phenomena which were witnessed in the ten years preceding the war.

According to the Home Office Statistics of Compensation paid during the year 1938, nearly 40% of the number of cases of compensation in the seven main groups of industries in Great Britain occurred in the mining industry, and 80% of the compensation to workers in the industry is paid by employers who insure their Workmen's Compensation risk with Mutual Indemnity Associations. As these Coal Trade Mutual Indemnity Associations deal with about one-third of the compensation paid in the seven main industrial groups, the experience of the larger associations is capable of useful analysis according to the age of the workman, the cause and effect of the accident or industrial disease, and the degree and duration of the resulting incapacity.

A Number of papers have been submitted to the International Congresses of Actuaries on the subject of life reassurance and full discussions have taken place at the Seventh, Eighth and Eleventh Congresses. Very little has been contributed to the Journal, and many years have elapsed since a paper was prepared on this subject.

The main object is to discuss principles and therefore many points of detail will be omitted, however intrinsically interesting they may be. Satisfactory consideration of principles entails reference to all classes of business which involve an actuarial valuation (viz. life assurance and annuity business, sinking fund business and permanent sickness insurance business). Reference will be made to the National Defence Contribution and the Excess Profits Tax, which are based upon income-tax legislation. The subject in mind is the relation of such taxation to insurance business and funds of the classes mentioned, as distinct from other aspects of income tax which an insurance office encounters, and it will be considered solely from the point of view of an office established in the United Kingdom which transacts business only in the United Kingdom. In view of the paper by Messrs S. J. Rowland and F. H. Wales on ‘The Taxation of the Annuity Fund’ (March 1937, J.I.A. Vol. LXVIII), only brief reference will be made to annuity business, and it will be assumed that it is unnecessary, in describing taxation processes, to include explanations or qualifying phrases on account of annuity business.

This paper falls into three parts which form a progressive study involving

I. proposals for the reform of the Income Tax system as related to personal assessments,

II. consideration of the interrelation of Income Tax and Social Security,

III. proposals for the co-ordination of the Income Tax and Social Security systems.

Part I of this progressive study is a plea for a business-like administration of the Income Tax system. Part II examines the combined effect upon the individual of the Income Tax system and the Social Security plan proposed by Sir William Beveridge. Part III sets out to co-ordinate Income Tax and Social Security and to simplify the financial relationship between the individual and the community.

An important part of the work of an actuary consists in making and testing graduations of mortality statistics. Much space has been devoted in the Journal to methods of graduation, but for many years, apart from the recent paper by H. L. Seal (J.I.A. Vol. lxxi, p. 5), little attention seems to have been paid to the testing of graduations. Although statistical methods are usually employed in making the tests, consideration has not often been given to ascertaining whether mortality statistics fulfil the conditions necessary for the tests to be strictly applicable. It is the purpose of this paper to set out some investigations into this question. Such matters may be thought to be of only theoretical interest, since, in practice, the tests work satisfactorily as a general rule; but actuaries should not employ their tools in a mechanical fashion without realizing fully their limitations and implications, and the question therefore takes on a practical as well as a theoretical aspect. It is hoped that this paper will show how far the tests of a graduation are satisfactory in theory and practice and indicate where modifications are required.

This paper is devoted mainly to the extension of the ‘n-ages method’ of approximation for product-sums to summations in respect of two variables; some uses in valuation work of the formulae developed are indicated and illustrated arithmetically. Hitherto, apart from a special formula devised for the particular purpose of illustrating the possibilities of valuing whole-life assurances by limited payments grouped by years of entry (J.I.A. Vol. LXIV, p. 325), the n-ages method has been confined to one variable.

There are in existence numerous charitable funds which provide financial assistance to members or their dependants in the form of either grants or annuities and of which the principal characteristics are usually:

(1) that the benefits are neither legally claimable nor clearly defined,

(2) that membership is voluntary,

(3) that the members' contributions are usually inadequate to support the benefits, and

(4) that donations, voluntary subscriptions and legacies frequently form a large part of the income.

I have limited this paper to the consideration of appreciation or depreciation in fixed interest-bearing securities resulting from a fall or rise in the general level of interest rates and not from any alteration in the intrinsic value of the securities, i.e. there is assumed to be no change in the probabilities that the terms of the contracts will be fulfilled. My object is to discuss how this appreciation or depreciation should be treated in order to obtain the maximum practicable degree of equity between the different generations of policyholders in an office which distributes its surplus by means of a uniform reversionary bonus.

The problem can be most easily discussed by showing the effect on a model office of adopting various methods of treating this appreciation or depreciation. I propose to limit the discussion in the first place to the question of depreciation in an office employing a bonus reserve valuation.