This subject was ably dealt with in 1894 by Mr. G. F. Hardy (J.I.A., xxxi, 261), who submitted suitable methods and formulas for the calculation of premiums, and dealt with other practical points, such as the treatment of these policies at a valuation. The article and the discussion constitute a most valuable contribution to the science of life assurance: accordingly in the following essay it is proposed to avoid the repetition of questions which were then fully discussed, and rather devote attention to the application of the system.

So far as I have been able to discover, very little has been written on the effect which the allowing for the lapse element has on premiums and the corresponding reserves. In Mr. T. G. Ackland's paper, reported in vol. xxxiii, part II of the Institute Journal, he treats of the “Effect of an Estimated Allowance for “Withdrawals upon the Net Premiums and Valuation Factors “computed, and upon the Reserves on Net Liability”, and shows the effect which a certain assumed lapse rate has on the premiums and reserves, but does not show what effect there is when the lapse rate is increased or diminished. The province of this paper is to show the general effect of lapse rate, and whether a larger element of lapse in the calculation increases or decreases the corresponding reserves.