The present paper has been given the title of ‘The Analysis of profits of a Life Office,’ but it is clear that it will not be possible in the time available to discuss all the points which may arise in practice under this heading, and it is therefore intended to limit the paper to a discussion of the more usual questions which arise in analysing profits where an annual valuation is made by the ordinary net premium method. Whatever be the precise method adopted in valuing the liabilities of a life office, the principles underlying an analysis of the profits will be the same, and once these principles are grasped no difficulty will be found in applying them to any particular case. In the first place, it should be appreciated that the necessity, or at any rate, desirability, of analysing profits arises only through our assuming in the valuation of the liabilities, rates of mortality and interest different from those actually realised in practice.