On a Method of Obtaining Half-yearly and Quarterly Premiums from the Annual Premium

Abstract

SIR,—Allow me to draw the attention of your readers to a method of obtaining half-yearly and quarterly premiums from the annual premium. As it is one of much utility to the practical computer, and I do not remember to have met with it in any of the works in use among actuaries, it may not be altogether unworthy of a place in your columns. The subject has been treated by the late Mr. Orchard in his exceedingly valuable work, Single and Annual Assurance Premiums, where at p. vii. of the Introduction he gives the expression for finding cx, the quantity to be added to half the yearly premium to form the half-yearly premium. That expression is as follows:—