Recent years have seen a material growth in the annuity business of British offices and in many instances what was a relatively insignificant part of the offices' activities has now assumed considerable importance. In fact in the case of some offices, the amount of the liability in respect of annuity business exceeds that in respect of assurances.

In this paper the reader is asked to watch the heuristic development of an idea and its implications.

The subject is the way in which the working of a life office is unaffected by changes in the market rate of interest. For this purpose all other questions such as mortality, expenses, etc., will be ignored as far as possible. The idea is that actuarially a life office is qualitatively different from the sum of its individual policies; that many of the difficulties in discussing this subject occur because basic actuarial concepts and techniques, especially

(i) the idea of an average rate of interest, and

(ii) the method of discounting into a present value,

which have been designed primarily to deal with the problems of individual policies, are inappropriate to the large-scale problems of a life office, e.g. valuation, investment and bonus declarations.

The heuristic development is that of an alternative theory and technique; these do not, for instance, make use of (i) and (ii) above.