BY ERNEST BROWN SKINNER ASSOCIATE PROFESSOR OF MATHEMATICS IN THE UNIVERSITY OF WISCONSIN
GINN AND COMPANY BOSTON NEW YOBK CHICAGO LONDON ATLANTA DALLAS COLUMBUS SAN FBANCISCO COPYRIGHT, 1913, BY ERNEST BROWN SKINNER
ALL BIGHTS BBSBRVKD B21.1
Cfte gttienitam gte«« GINN AND COMPANY PRO- PRIETORS BOSTON U.S.A. PEEFACE This book has been written for the use of students of business and public affairs. The fact that, with a few notable exceptions, colleges and universities have hitherto made no provision for courses in mathematics adapted to meet the needs of students trained for commercial careers and for the public service, is due in no small measure to the lack of a suitable textbook. In recent years the closer study of business methods and the extension of governmental control over many forms of industrial and financial activity have greatly emphasized the value, to students of finance, of a knowledge of what the Germans call " political arithmetic." In an attempt to meet the need for a book covering this field, some of the more important topics relating to the theory of interest and its application to the larger affairs of modern every- day life have been brought together. The following pages con- tain, in somewhat elaborated form, the substance of a course of lectures given annually for the last five years to the students in the course in commerce in the .University of Wisconsin. While I have tried to make the book practical throughout, I have sought to make it a book of first principles rather than a guide to detailed practice. I trust that the reader will find the treatment adapted to present-day conditions and heeds. I shall be gratified if I have in any way contributed to the more efficient training, in principles of sound finance, of the splendid body of young men who are going out from our courses in commerce to become leaders in the business world. In selecting topics for consideration, an effort has been made to avoid those that are still the subject of controversy. If this rule has been departed from in devoting some space to deprecia- tion, it is on account of the great importance of the subject. The public-utility commission seeking to make an equitable ad- justment of rates must make some sort of quantitative deter- mination of depreciation, even though neither the exact meaning iv MATHEMATICAL THEORY OF INVESTMENT of the term nor the method of treating the subject has been agreed upon. It is believed that the discussion in §§ 56-58 fol- lows logically from the definitions therein proposed. It might be added that it is in substantial agreement with the practice of the Wisconsin Railroad Commission. Much of the inspiration for the book has come from M. Cantor's admirable "Politische Arithmetik," while most of the material may be found in some form in Todhunter and King's " Institute of Actuaries' Text-Book." I have consulted freely Fuzet and Reclus, " Precis de mathematiques commerciales et financieres "; Martini, "Aritmetica commerciale e politica"; Schlimbach, " Poli- tische Arithmetik "; Wolff, "Inheritance Tax Computations"; Broggi, " Matematica attuariale " ; Lowy, " Versicherungsmathe- matik"; Dawson, "Practical Lessons in Actuarial Science"; and Willey, " Principles and Practice of Life Insurance," revised by Moir. Tables III-VII are based upon Spitzer's " Tabellen fur Zinses- Zinsen- und Rentenrechnung," and have been carefully compared with Vintejoux's " Nouvelles tables d'interets composes et an- nuites." Tables XI and XII have been taken, with the kind per- mission of The Spectator Company, from the books of Dawson and Willey. In preparing the manuscript, I have had the benefit of the valued criticism of my colleagues, Professors E. B. Van Vieck and L. W. Bowling, and of Mr. L. A. Anderson, Actuary for the Wisconsin Insurance Department. Professor Arnold Dresden, Dr. Florence Alien, Dr. G. R. Clements, and Mr. T. M. Simpson, who have tried out a large part of the material in the class- room, have made many helpful suggestions in the selection of material and examples, and have rendered valuable assistance in verifying worked-out examples and in correcting proofs. I am also under obligations to Professor D. F. Campbell, of Armour Institute, for placing at my disposal notes and other material relating to the elements of the theory of life insurance.