Endowment assurance can boast of no great antiquity, though its constituent elements, the temporary assurance and the pure endowment, both date from early times. Traces of the latter are found as long ago as the 16th century; thus, in a pamphlet by one Thomas Wilson, published in 1572, and entitled “A Discourse upon Usurie, by waie of Dialogue and oracions, for “the better varietie and more delight of all those that shall read “this treatise”, it is stated that, “Whosoever lendeth such a summe “of money (£100), and hath a childe of one yeere, shall have for “his childe, if the same childe doe live till he be full fifteene years “of age, 500li (£) of money: but if the childe die before that “time, the father to lose his principal for ever.” It is evident that the rate of mortality in those days must have been alarmingly high, either among children or among the institutions granting these benefits. A form of assurance, similar in some respects to the above, called “Apprenticeship Assurance”, was introduced towards the beginning of the 18th century. In a prospectus dated 1710 it is stated that, “Anyone who now is, or that is to be an “apprentice, may by paying 1s. entrance and 2s. 6d. per quarter, “gain, probably from £40 to £50 up to £500 or £600.” After reading this astonishing statement, one cannot but admit that the tontine and other estimates of American Companies, about which we hear so much in the present day, pale their uneffectual fire before the similar extravagant statements made by our predecessors in the reign of Queen Anne.

As there is a prospect of the Scottish Insurance Companies again collecting the statistics of their mortality experience, it is desirable to consider anew the mode in which the facts should be tabulated, in order to ascertain the rate of mortality experienced among assured lives. The previous collection was drawn from theexperience of 10 offices, and consisted of the total lives assured from the beginning of the several offices, brought down to 31 December 1863. Thirty years having elapsed, it is proposed to begin with the facts then existing—tabulating the deaths arising among these; and also to tabulate new assurances, dealing with them separately. It is proposed also to discuss whole-life assurances and endowment assurances. It is also proposed to collect the experience of male and female annuitants. With so large an undertaking in prospect, it is expedient to re-consider the modes previously adopted, and in some detail to state the manner in which these experiences should be now collected.

In a discussion I had with Professor J. J. McCutcheon and Dr W. F. Scott, the authors of the new book on compound interest, An Introduction to the Mathematics of Finance (Heinemann 1986) it was suggested that a chapter describing the theoretical economic background to the determination of interest rates might be of interest to actuarial students. I therefore drafted the substance of this note as such a chapter. In the event it was felt that the subject fitted uneasily with the mainly technical and numerical approach to compound interest appropriate for students at that particular stage of the examinations, and that the more theoretical approach in this note would in any case be of wider actuarial interest. It is therefore presented as this note in the Journal. I am grateful to Professor McCutcheon and Dr Scott for agreeing to this, and to the discussions I had with them while the note was being drafted.

The merits and demerits of the present mode of assessing the Property and Income Tax have been so frequently made the subject of popular discussion, and are in themselves questions of such national importance, that I feel no apology to be necessary for again bringing the subject under the notice of the Institute of Actuaries.

A valuable paper on the inequitable operation of this tax was, some time ago, read before the Institute by Mr. Jellicoe; and, more recently, an elaborate and important contribution on the same subject was brought by Mr. Farr under the notice of the Statistical Society of London, which paper has given rise to a lengthened and very interesting discussion. An exceedingly temperate and able pamphlet has also been recently published by Mr. John G. Hubbard, the Deputy Governor of the Bank of England, in which that gentleman has discussed, with very considerable ability, the views of Mr. Warburton, and has, in my opinion, very effectually exposed their absurdity.

In every branch of business, even in the very rudest stage of barter, men have to count. A skin is exchanged for so many cowries, a rifle for so many skins. Do what we will, go where we will, the necessity for counting meets us. Yet, though numbers be essential to all our operations, we do not easily form an idea of large numbers. Thus in no language do the separate names for numbers reach to twenty. In one, I believe, the numeration goes as far as fifteen; in the northern languages of Europe it reaches to twelve, but in most languages it stops short at ten.

All members of the Institute are more or less conversant with the “field” work of American Life Insurance Companies, but comparatively few have had the opportunity of becoming acquainted with the “inside” methods of these Institutions, which, as might be supposed, differ in many respects from the methods of British Companies. One of these differences is that Valuation Tables are much more extensively used there than in Britain, and it is not surprising, therefore, that various Valuation Tables have, from time to time, been published in America. No notice seems to have been taken of them in the Journal, so I propose, in the first place, to indicate briefly the contents of these publications, and then to refer to some of the American methods which necessitate the existence of these various Tables.

Pollard and Pollard pointed out that, while it has been conventional to refer to Ax, as ‘the present value of an assurance of one on a life aged x’, this value is a random variable (denoted by Ãx) with mean Ax.

The Friendly Societies, which are sometimes called Benefit Clubs, have for many hundred years been highly popular in England; not merely because they supplied one of the principal wants of the working classes—namely, relief in sickness or accidents which disable them from obtaining their usual wages—but because, by mutual association, they afforded some scope for the talents and sagacity of some of the members to be recognised and appreciated by others. But by the very nature of their composition they were deficient in the element of stability ; and notwithstanding the best intentions of the members, the Societies have been constantly broken up and reformed.

The history of the United Provinces, and of Holland especially, from the close of the Spanish rule down to the establishment of the modern monarchy of the Netherlands, is distinguished for its manifestation of a permanent struggle between different opposite principles. Liberty and authority, municipal principle and state principle, republic and monarchy, the spirit of federal isolation and that of centralization, appear to give battle to each other upon a territory itself with difficulty defended from the waves of the ocean by the watchful industry of its inhabitants.