It is now widely recognized that the future must see far-reaching changes in our monetary system, and that these changes must be in the direction of a conscious and planned management, as distinct from leaving the system to be regulated in a more or less automatic manner by factors which reflect and are governed by international conditions; that the monetary system should in fact be made to serve and not govern the requirements of the economic system.

This changed view of the function of the monetary system is probably mainly the result of two economic phenomena which were witnessed in the ten years preceding the war.

A Number of papers have been submitted to the International Congresses of Actuaries on the subject of life reassurance and full discussions have taken place at the Seventh, Eighth and Eleventh Congresses. Very little has been contributed to the Journal, and many years have elapsed since a paper was prepared on this subject.

This paper is devoted mainly to the extension of the ‘n-ages method’ of approximation for product-sums to summations in respect of two variables; some uses in valuation work of the formulae developed are indicated and illustrated arithmetically. Hitherto, apart from a special formula devised for the particular purpose of illustrating the possibilities of valuing whole-life assurances by limited payments grouped by years of entry (J.I.A. Vol. LXIV, p. 325), the n-ages method has been confined to one variable.

There are in existence numerous charitable funds which provide financial assistance to members or their dependants in the form of either grants or annuities and of which the principal characteristics are usually:

(1) that the benefits are neither legally claimable nor clearly defined,

(2) that membership is voluntary,

(3) that the members' contributions are usually inadequate to support the benefits, and

(4) that donations, voluntary subscriptions and legacies frequently form a large part of the income.

Interpolation and other formulae involving advancing differences are frequently developed, or at least conveniently reproduced from memory, from the familiar operational identities

where

W. Perks in his recent paper (see p. 377 of this issue of the Journal) has shown how we may avoid tabulating net premiums or other special functions applicable to a particular valuation basis on individual valuation cards, and how a change may thus be made easily and rapidly from one valuation basis to another. The primary purpose of the present note is to develop Perks's principles and to test the methods on the actual valuation of the whole-life assurances of a life office.