Generations of actuarial students have been confronted at an early stage of their careers with Woolhouse's formula, important for its well-known application to annuities payable several times per year. However, it is probably fair to say that most of the derivations of the formula presented to students have been in some respects unsatisfactory, since they have usually relied on “ the separation of symbols ”, manipulations of the finite difference operators D, Δ, Σ and Σ(m), and have involved arguments somewhat lacking in rigour. This is not a severe criticism of the relevant textbooks, which were after all written from a practical actuarial viewpoint and which understandably enough wished to avoid the relatively difficult analysis required to derive Woolhouse's formula in its complete generality.