(i) The characteristic feature of Double Endowment Assurances is that for a given term of years the annual premium is almost independent of the age, provided the age at maturity does not exceed a certain limit. If we assume it to be precisely true that the annual premium is independent of the age, it follows that the premium must be identical with that for a Capital Redemption Policy for the same term of years and assuring an amount equal to the Double Endowment.

The subject of Bimetallism is not a burning question now as it was some few years ago, but it is worth while to consider the arguments used for and against, as it is possible thereby to obtain an idea of the principles underlying currency problems.

1. Alleged evils—

(a) A great fall in gold prices, causing

(1) A disturbance of the standard of value,

(2) Increased burden on debtors,

(3) Discouragement of industry.

Office Premiums should fulfil the following conditions:—

(1) They should be adequate. Whatever the method of construction, the premium must be sufficient to cover the risk and expense, and leave a reasonable margin of profit.

(2) They must be reasonable from a competitive standpoint.

(3) They must be consistent with one another.

The premiums should be based on select rates of mortality, and our decision of the table of mortality to be used for the premiums for particular classes of risk should be based on—

(1) The experience of the class of assurance.

(2) Possible variation in that experience in the future.

(3) The special conditions of the particular office.

In dealing with the general question of the valuation of special policies, it must be borne in mind that the particular circumstances of each office as regards special schemes, &c, have to be considered when the method of valuation of any class is fixed, and that, therefore, some latitude must be allowed, and hard and fast rules and unnecessary complications and refinements avoided. In those cases where exact reserves are not obtained the approximations used in practice should be simple in application, and give a reserve which does not in the aggregate fall -short of the true reserve.

The general principles on which a valuation should be made are the same for Industrial as for Ordinary Assurance policies, but the differences between the two classes of business necessitate considerable difference in the methods by which these principles are applied.

The greater number of Industrial Assurance policies are issued on the basis of the weekly payment of id. and small multiples of id., the premiums being collected weekly by agents. The average sum assured is consequently small and the expense of collection relatively great. Medical examination is not asked for except in special cases, the agents being required to form their own opinion of the eligibility for insurance of the proposer. The effects of serious errors of judgment in this matter are minimised by the usual condition that a proportion only—usually one quarter—of the sum assured shall be paid should death occur otherwise than by accident during the first three or six months of the assurance; the proportion being increased to one-half for the second period of three or six months; and the full sum assured being payable thereafter.

In connection with the financial arrangements of Insurance Offices it is sometimes of advantage to borrow money in order to make permanent investments, or for other reasons, and at other times funds are available which can conveniently be placed on deposit with Bankers or Discount Houses, or elsewhere, pending permanent investment. In the former case the Office should seek to obtain- the money at the cheapest rate, in the latter case the Office should obtain as good a rate of interest as possible for the short period during which the money is deposited.

To such money, borrowed or deposited for short periods is applied the term “Short Money.”

Insurance Offices place their money with their own Bankers, the Discount Houses, the Stock Exchange, and the Joint Stock Banks, and obtain money from their own Bankers, or from the Discount Houses.

In the discussion that followed the reading of a paper on graduation A. Henry gave the following proof which leads to the equation for the “Normal Curve of Error” (A) and to an expression for the average deviation (irrespective of sign) from the most probable result (B).

Let the probability of the happening of a certain event be p and that of its failing q. Then in n trials the most probable number of occasions on which the event will happen will be np.

Actuarial students who have passed their second examination and wish to study the more practical part of their work, frequently have difficulty in deciding the most suitable books and papers to read, and consequently do little work by themselves and rely perhaps more than is necessary on the advice given them by tutors.

Although the present suggestions of preliminary reading are not meant to eliminate the assistance of a tutor, which is in many cases indispensable, they might be sufficient from an examination point of view for those who have a considerable amount of practical experience.