The purpose of this paper is to discuss the actuarial principles on which the investment policy of life assurance offices should be founded. The policy considered relates, firstly, to the principles on which the selection of investments should be made and secondly, to the basis of their subsequent valuation.

Twice in the past forty years war has abruptly changed economic conditions in the country and the new economic conditions have in their turn affected the circumstances of all pension funds. Before the war of 1914–18, the great majority of pension funds provided pensions based on the average salary through the period of service for a low contribution rate, The inflation of salaries and wages between 1914 and 1919 disclosed the weakness of the system since the pensions provided proved to be small in comparison with the new level of remuneration and to be inadequate to support the member during retirement. The experiences of this period led to the adoption of the system of basing the pension on the remuneration of the final year of service or of the average remuneration of the years immediately prior to retirement, The financing of the additional pensions to members for whom pensions on the pre-1914 basis had been provided and the establishment of the new system for members currently contributing was materially assisted by the high yield obtainable on investments. It should be added that for a scheme with funds invested before 1914 the depreciation of assets due to the high interest rates which had been obtaining immediately after the war increased the cost of reorganization of the scheme.

The actuary employed in life office work is very closely concerned with the methods by which the valuation and other records of a life office are built up. It is surprising, therefore, that there are very few references in the pages of the Journal of the Institute to the use of punched-card equipment for life office work. The use of the equipment for calculations of interest to the actuary, such as the construction of tables, has also been largely ignored. Actuaries employed in work outside life oflices so often rely on punched-card equipment for their statistical data that the authors feel that no apology is needed to either class of actuary for presenting a paper on the subject. Punchedcard equipment has received much more attention in the Transactions of the Actuarial Society of America, most recent volumes containing a paper or note on its application.

The measurement of the rate of population growth has attracted considerable attention in scientific literature of recent years. This is, no doubt, a result of the continual decline in the birth-rate which has formed the topic of innumerable articles in the popular press and elsewhere. Several attempts have been made to obtain a simple statistical measure of the reproductivity of a population at a particular time—that is, a measure of the extent to which a population will be replacing itself if current fertility and mortality continue indefinitely. It is the aim of this paper,

• in section 1, to discuss the simple approximate formulae that have been suggested;

• in section 2, to discuss some more elaborate and more efficient formulae;

• in section 3, to analyse the effect on the formulae of section 2 of a change in the proportions married at a given age;

• in section 4, to outline the male versus female rate anomaly;

• in section 5, to suggest a formula which avoids the anomaly; and finally,

• in section 6, to discuss the application of these formulae to Australian population statistics.