The object of these Notes is to obtain for the valuation of pension funds a method in which commutation functions operating over groups of ages are calculated directly from the decremental rates applicable to the groups. By this means the labour involved in the construction of a full service table and commutation functions at each age can be avoided. Valuations have been effected by various methods, and it is shown that the results brought out by the short methods are as reliable as those obtained by using functions at individual ages. In proceeding to the particular short method advocated, other possible lines of attack have been suggested, and it is not disputed that formulae based on similar assumptions, but different from those in the Notes, might give equally satisfactory results.

In a note to his paper on "the Approximate Valuation of Endowment Assurances" (J.I.A. Vol.XLVIII, p. 32) Mr Elderton suggested that it might be possible to approximate to the true net premium reserves by accumulating the premium at interest only without having any direct regard to mortality, and I have made an attempt in this paper to arrive at a suitable method of approximation.