Approximations to the Values of Certain Actuarial Functions leading to Suggested Check Methods of Valuation of Endowment Assurances

Abstract

It is demonstrated, with particular reference to the OM, OM(5) and A1924–29 Tables, that over the range age 20 to age 65 of a normal mortality table, μx can, with a close degree of approximation to the tabular values, be expressed in the formleading to the following analogous expressions:—Generally, all functions involving mortality within the stipulated range can be expressed in a similar form as purely mathematical and easily evaluated functions of the initial age and interest in combination.It is claimed that the evaluation of such temporary functions at any rate of interest is thereby greatly facilitated.The retrospective and prospective values of an endowment assurance policy in terms of the formula are investigated, and check methods of valuation, continuous in process and independent of the working principles and practice of the principal method, are put forward.Numerical results and examples of the procedure are given in the paper.