The purpose of this paper is to indicate some of the points which arise during the currency of transactions in reversions and life interests; the selections of appropriate bases for mortality, interest, valuation of funds and estate duties do not fall within the scope of the paper. References to strictly legal aspects are no more than incidental.

As in many other matters with which actuaries are concerned, mistakes (including errors of judgment) sometimes only become apparent many years after they were made. It follows, therefore, that no hard and fast distinctions can be drawn between the preliminaries necessary to a transaction and what comes after. For this reason I feel obliged to refer to my earlier paper entitled ‘Notes on transacting new business in reversions and life interests’ which appeared in this Journal (10, 1); it is hoped, however, that the present paper will be found to be complete in itself.

Since my own experience of the cycle of monetary operations I shall describe is concerned with banking, it would seem natural to commence by discussing the functions of a bank. There is no legal definition of a bank, but the term is generally understood to apply to an institution which accepts from depositors money withdrawable on demand, in practice generally by cheque. The cardinal point to bear in mind is that a bank is a trustee of other people's money which, apart from deposit accounts at 14 days' notice, is all repayable on demand. The fundamental consideration is that it is customers' money, apart, of course, from the comparatively small proportion of resources represented by shareholders' capital.

A bank's first duty, therefore, is to its depositors (not to its borrowers!), and the exercise of that trust requires that any depositor shall be free to come to his bank and withdraw all or part of the funds he has entrusted to it. Hence liquidity is of prime importance and a bank must arrange its structure of assets so as to comply with this requirement. But like other commercial concerns a bank must have earning power to cover its outgoings, reward its shareholders and try to satisfy its staff! So, consistent with liquidity, a bank's ‘quick’ assets are arranged to bring in as large a return as possible subject to this overriding limitation.

Measures of marriage based on the data for one sex only do not give a fair comparison between two communities unless the relative numbers and ages of the sexes available for marriage are the same in both. Such a similarity is unlikely to exist; in 1921, for example, at ages 15–54 the number of marriageable women was 87% of the number of marriageable men in New Zealand but the corresponding ratio in England and Wales was 119%, and this fell to 113% by 1931.

W. S. Hocking discussed the balance of the sexes in Great Britain in J.I.A. (74, 340) and showed the extent of variations in the relative numbers available for marriage in England and Wales in this Journal (10, 24). It is desirable in a number of problems to be able to make some allowance for such variations, particularly in connexion with the measurement of reproduction, depending as it does on marriage intensity.

The contracts discussed in this note are annuities certain provided by Life Offices. A schedule for income-tax purposes dividing payments into capital and interest determines the variable net sum paid by the office from year to year to the payee under each contract; it is the effect of this arrangement on the office to which attention will be drawn.

To comply with the Assurance Companies Acts, 1909–46, and the Finance Act, 1938, section 27, the office must pay the considerations for such contracts into a fund which is separate from the life assurance and life annuity funds, and which must not relate to business effected before 1 January 1938. This fund is taxed on an interest less expenses basis (subject to certain limitations), and the full standard rate of tax is applied. However, the office is permitted to withhold tax on the interest portion of each annuity payment from the payee, and to retain this tax provided its amount is exceeded by the tax suffered on interest credited to the fund, adjusted for the relief on expenses. Profits tax will be ignored in this note; the tax position of the office as a whole has such an intimate bearing on the problem that further discussion would be outside the intended scope of the present analysis.

The volume of group life and pension scheme business transacted by life offices in this country is considerable, and is increasing steadily. A great deal of work is being spent in the preparation of quotations for such schemes. Readers may, therefore, be interested in a method of reducing to a minimum an especially uninteresting part of the work arising in connexion with quotations for schemes in which the cost of pension benefits for future service or of life assurance benefits is calculated on the ‘single-premium’ basis.

In these schemes it is customary for the amount of life assurance cover provided during any Scheme Year, and the amount of pension earned in respect of that year, to depend only on the salary of the member and not on his age. The employee normally contributes an amount, also fixed in relation to his salary, to purchase part of the pension by means of a deferred annuity providing a return of premiums without interest in the event of his death. The employer in each year pays the single premium required to purchase the balance of the pension accruing in respect of that year's service (usually by a deferred annuity without return of premiums in the event of the employee's death), and also to purchase the whole of the temporary life assurance granted during that year. The employer's premiums are recalculated each year on the basis of the ages attained in that year and thus for any individual employee the cost to the employer increases from year to year. Considering the scheme as a whole, this rise is partly or wholly compensated by deaths, withdrawals and retirements, and it may be quite reasonable to expect that the cost in the future will only rise by a small amount, or even decline.