1. The methods of analysis leading to the usual formulae for the value of the benefits provided by a pension fund are contained in the historic papers of H. W. Manly, J.I.A. Vol. XXXVII, p. 193 and G. King, J.I.A. Vol. XXXIX, p. 129. The purpose of this paper is to set forth certain developments of the formulae of G. King from which the balance of forces within the fund may be investigated. It is emphasized that the formulae themselves are but algebraic shorthand for processes of calculation, and the deductions do not arise from the formulae but from the numerical results obtained. These results will vary from fund to fund according to the relative financial importance of the various portions of the benefits granted. Within the limits of this paper it is not possible to deal either with the financial situation of an existing fund or with the varying contributions and benefits met in current practice, and in order to produce results for discussion, calculations have been made on the basis of the benefits and contributions of a standard type of fund.