Although Book-keeping has been for many years one of the subjects of examination prescribed for students of the Faculty, it is an open secret that it has been somewhat neglected by them. One reason for this is that the elementary text-books are rather discouraging, with their continual references to hogsheads of wine and bales of cloth; and another is that the writings on Insurance Book-keeping proper assume a certain amount of knowledge which, I fear, the average student does not possess.

In the notes which follow I have endeavoured to begin at the beginning, and to impart as much information as will enable the student to understand the books of an office and the entries made in them. I have made no attempt to teach the art of Bookkeeping or to describe the numerous auxiliary books in use. The forms of these vary very much in different offices and have been fully treated of elsewhere.

My paper divides itself roughly into three parts. The first is rudimentary; the second describes the principal books in use, dwelling specially on those which are common to all offices; and in the third I have given specimens and explanations of such entries in the books as a beginner is apt to find difficulty in understanding.

The improvement in vitality is a subject of interest alike to the actuary and to the public statistician. It formed one of the topics for discussion at the Fourth International Congress of Actuaries held in New York in 1903, and papers were submitted by actuaries of different countries dealing with the subject mainly from the point of view of population statistics. The results of most direct interest to us were embodied in a paper by Mr. S. G. Warner On the Improvement in Longevity in the Nineteenth Century. They were based on the summarised returns of the Registrar-General's Reports for England and Wales for the years 1875 and 1900; and, while admitting the defects inherent in the data, Mr. Warner held that the statistics showed “a distinct decrease in the rate of “mortality as the century progresses; a decrease, on the whole, “so steady and symmetrical that it might fairly be looked on as a “settled and permanent tendency.

Reference has frequently been made to the fact that Life Assurance Companies are daily in the habit of undertaking liabilities which, in most cases, will not mature for a great number of years to come. As a rule, such deferment of the liability is welcomed by the offices as being in their view advantageous rather than otherwise. In most cases, however, it is not the office alone that undertakes liability. The policyholder on his part agrees to pay to the office a premium, it may be for a fixed number of years, should he live so long, or even during the remainder of his lifetime, no matter how long that may endure. It has been pointed out that, while the policyholder may at any time bring the engagement entered into between himself and the Assurance Office to an end without the latter's consent, the Company has usually no power to terminate the contract except with the concurrence of the policyholder.

The Valuation of a Friendly Society differs from that of a Life Assurance Company trading under modern conditions, in that the object of the Valuation is to ascertain the minimum amount required to enable the Society to meet its obligations. In other words, Valuations are made on a solvency basis, and questions such as the maintenance of a sufficient margin of security to keep up a Bonus Rate and an equitable distribution of Profits do not, as a rule, arise. This being so, it is of the greatest importance to be sure that the Tables made use of for valuation purposes conform with the Experience of the Society in regard to rates of sickness, mortality, withdrawal and interest.

Some of the more common forms of benefit involving compound interest and mortality are merely variations of one general contract, and are in their limiting cases identical. For example, a short-term policy becomes simply a whole-life assurance when the term is indefinitely extended; and limited-payment policies and endowment assurances continually approach the whole-life contract as the number of payments or the term of the endowment is increased. When more than one life is involved the benefit, if payable on the first death, is of a slightly different nature, but if payable on the death of the last survivor—in the case of either a joint or a contingent assurance—it approaches in one of its limiting cases merely a whole-life policy on a single life. The object of the present paper is to consider in a general way some features of the curves of the values under different classes of policy, and to notice how these curves are affected by Select Mortality and other factors.

So far back as 1863 the Institute of Actuaries stated, in preparing the HM Experience, that the most important question was the rate of mortality at the more advanced ages of assured lives. The information so collected has since been materially added to by the British Offices' Experience of 1893. At the same time the rates of premium charged by various life assurance offices for ages at entry 60 and upwards show large differences, which sufficiently prove that the rating of such lives does not yet rest on anything like a definite basis. The reason is clear enough, for the available facts are still necessarily scanty, and consequently the probability of fluctuation or accidental variation in the rate of mortality is considerable. As life advances the flame of vitality burns lower, the average rate of mortality increases, and frequently there are material changes from one year to another. While some lives of from 60 to 70 years of age have 30 years of life before them, a large number will certainly die within a much shorter period, even although the originally defective have been excluded. At such ages health suffers fatal impairment with greater rapidity than at younger ages, and the impairment can be less easily foreseen and provided against. Thus it is evident that if an office is to accept proposals on the lives of aged persons, exceptional care must be taken with the medical examination, that the average quality of the stock selected may be sufficiently good. It has to be recalled that the effect of variation in the average rate of mortality is greater at advanced ages than at young ages. If, for example, the premium at an advanced age at entry be 10 per cent, per annum, it makes a marked difference to the financial results whether each life contributes on the average for seven years or for eight. At young ages, with a premium of say two per cent, per annum, a variation of one year in the expectation of life is not so important.