In venturing to submit a paper on the subject of bonuses to the Institute, I feel that a word of explanation is necessary as to the reasons that led me to take up this investigation, and as a preliminary to this, I would first call attention to some results presented by previous writers.

In 1887 the late Mr. Sunderland read a paper (J.I.A., vol. xxvi) dealing with Whole-Life Assurances, and he followed this up by a further paper (J.I.A., vol. xxviii) dealing with Endowment Assurances. A valuable set of tables was given with each paper, based on a HM 3 per-cent valuation, showing, among other things, the bonus arising from surplus interest margins of ½, 1, 1½, and 2 per-cent for whole-life, and 1 and 1½ per-cent for endowment assurances.

He also gave the bonuses arising from an annual surplus margin of premium of 10s. at the various experience rates of interest, and showed that bonus from surplus premium in any year is proportional to the amount of such surplus premium. Dealing with mortality, he showed the results of experiencing Sprague's Select Mortality under whole life policies, and gave an illustration of the effect of experiencing a favourable mortality under a 25-year endowment assurance. The papers were practically independent, and did not aim at comparing bonuses under the two classes, although so far as interest and loading profits were concerned, they gave the means of doing so.