Since the 1939–45 war, successive Governments have attempted by various political and ideological processes to provide this country with built-in prosperity combined with almost complete security. The measure of their success has been the reduction in the risks that attend economic enterprises of every type and the concomitant increase in the security of the incomes arising from them. No doubt from the standpoint of the owners of these incomes this has been exceedingly beneficial, but the reverse of the coin shows a progressively increasing distaste for incomes which are limited or reduced by further provisions of security and priority.

In 1944 the Royal Commission on Population was set up in order to determine the probable consequences of population trends then current. In order to do this they prepared a range of sixteen separate population projections for Great Britain based on various combinations of assumptions as to mortality, fertility (and marriage), and migration. The method used, in which each component of population change i.e. birth, death and migration receives separate treatment, is generally known as the component method. This distinguishes it from cruder methods based on the assumption that the total numbers in a population follow some mathematical formula.

Since the Royal Commission reported, this method has continued to be used in preparing what may perhaps be described as the ‘official’ projections of the population of England and Wales.

The course of reading for the examination does no more than touch on the way in which the business of purchasing, or granting loans on, reversions is influenced by legislation. The object of this paper is to peel a second layer off the fruit of reversionary knowledge, rather than to bite too deeply at one point on its circumference. The standard work by Withers, running to 480 pages, gives evidence of the number of layers left undisturbed.

Whilst most of the matters mentioned on the following pages fall primarily within the province of the solicitor, the partnership between solicitor and actuary will be more efficient and beneficial to the client if each partner has a rudimentary grasp of the affairs of the other.

The costing technique known variously as Controlled Funding, Stabilized Costing and Aggregate Costing, is a comparatively recent development in the field of Life Office group pension schemes. Before explaining and discussing the methods used, it may be helpful to outline the principal types of Life Office group pension scheme, and to examine the more traditional methods of costing employed. It should be made clear at the outset that the term ‘group pension scheme’ relates to schemes insured by means of group deferred annuity contracts and approved under section 388(1) or section 379(3) of the Income Tax Act, 1952—endowment assurance schemes and group life assurance schemes are not within the scope of this paper.

The following method of solving a certain type of problem in permutations and combinations, and in probability, is so simple that it must have been used before. On the other hand, the writer has never seen it expounded in the following form, and it does not seem to be well known to students. Whilst, therefore, no originality is claimed, this note may be found of interest to readers; and they may care to compare the length of the solutions to the examples below with those to be found in the text-books employing more conventional methods.