Calculation of Life Insurance Gross Premiums: A Suggested Modification of the Traditional Textbook Approach

Abstract

The purpose of this paper is to describe an approach to gross premium calculations that has been used by the author in an attempt to provide students with a clearer understanding of the nature of the process. The system is designed primarily as a teaching device rather than as a description of the way in which life insurance companies actually calculate gross premiums. Assumptions are made about interest, mortality, lapsation, expenses, cash surrender values, dividends, and profit. Then the gross premium is calculated by solving a linear equation in one unknown. Collegiate life insurance textbooks attempt to describe the manner in which life insurance companies develop gross premiums. Some authors have been more successful than others in communicating the essentials while avoiding such a high degree of complexity that students become discouraged. From time to time, textbook revisions incorporate certain new Joseph M. Beith, Ph.D., C.L.U., C.P.C.U., is Associate Professor of Insurance in the Graduate School of Business at Indiana University. He is author of Participating Insurance Sold by Stock Companies (1965), for which he received the 1966 Elizur Wright Award of the American Risk and Insurance Association, and The Retail Price Structure in American Insurance (1966). Dr. Belth is a frequent contributor to this Journal and serves as its Communications Editor. He has received four N.A.I.I. awards for papers published in this Journal. The author wishes to acknowledge the assistance of Norman L. Chervany, a doctoral candidate in Indiana University's Graduate School of Business. From the author's detailed instructions Mr. Chervany wrote the computer program used in the preparation of this paper. The author alone, however, assumes full responsibility for any errors that may remain. The computer used was the CDC 3600 in Indiana University's Research Computing Center. This paper was submitted in January, 1967. techniques, and occasionally a summary of current procedures is published.' Although the materials generally made available for students seem to achieve some success in describing the procedures involved in the calculation of life insurance gross premiums, such materials seem to be deficient in helping the student gain a real understanding of the meaning of those procedures. The purpose of this paper is to describe an approach to gross premium calculations that has been used by the author in an attempt to provide students with a clearer understanding of the nature of the process. Several points should be noted at the outset. First, the procedure described in this paper is intended solely to help students understand the essentials of gross premium calculations. The paper is not intended to suggest that the system is or should be in actual use by companies, although some companies are apparently using such an approach or modifications of it. Second, a number of hallowed terms I See, e.g., Alfred N. Guertin, Life Insurance Premiums, Journal of Risk and Insurance, Vol. XXXII, No. 1 (March, 1965), pp. 23-49.