Financial Mathematics

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FINANCIAL MATHEMATICS BY CLARENCE H. RICHARDSON, PH. D. Professor of Mathematics, Bucknell University AND ISAIAH LESLIE MILLER Late Professor of Mathematics, South Dakota State College of Agriculture and Mechanic Arts NEW YORK D. VAN NOSTRAND COMPANY, INC. 250 FOURTH AVENUE 1946 COPY RIGHT, 1946 BY D.

VAN NOSTHAND COMPANY, INC. All Rights Reserved Thin book, or any parts thereof, may not be reproduced in any form without written per mission from the authors and the publishers. Based on Business fathematics, I. L. Miller, copyright 1935 second edition copyright 1939 and Commercial Algebra and Mathematics of Finance, I.

L. Miller and C. H. Richardson, copyright 1939 by D. Van Nostrand Company, Inc. PRINTED IN THE UNITED STATES OF AMERICA PREFACE This text is designed for a three-hour, one-year course for students who desire a knowledge of the mathematics of modern business and finance. While the vocational aspects of the subject should be especially attractive to students of commerce and business administration, yet an understanding of the topics that are considered interest, discount, an nuities, bond valuation, depreciation, insurance may well be desirable information for the educated layman.

To live intelligently in this complex age requires more than a super ficial knowledge of the topics to which we have just alluded, and it is pal pably absurd to contend that the knowledge of interest, discount, bonds, and insurance that one acquires in school arithmetic is sufficient to under stand modern finance.

Try as one may, one cannot escape questions of finance. The real issue is shall we deal with them with understanding and effectiveness or with superficiality and ineffectiveness Whilethis text presupposes a knowledge of elementary algebra, we have listed for the students convenience, page x, a page of important formulas from Miller and Richardson, Algebra Commercial Statistical that should be adequate for the well-prepared student.

Although we make frequent reference to this Algebra in this text on Financial Mathematics, the necessary formulas are found in this reference list. In the writing of this text the general student and not the pure mathe matician has been kept constantly in mind. The text includes those tech niques and artifices that many years of experience in teaching the subject have proved to be pedagogically fruitful.

Some general features may be enumerated here 1 The illustrative examples are numerous and are worked out in detail, many of them having been solved by more than one method in order that the student may compare the respective methods of attack. 2 Line diagrams, valuable in the analysis and presentation of problem material, have been given emphasis. 3 Summaries of important formulas occur at strategic points. 4 The exercises and problems are nu frierous, and they are purposely selected to show the applications of the theory to the many fields of activity.

These exercises and problems are abundant, and no class will hope to do more than half of them. 5 Sets iv Preface of review problems are found at the ends of the chapters and the end of the book. A few special features have also been included 1 Interest and dis count have been treated with unusual care, the similarities and differences having been pointed out with detail. 2 The treatment of annuities is pedagogical and logical.

This treatment has been made purposely flexible so that, if itis desired, the applications may be made to depend upon two general formulas. No new formulas are developed for the solution of problems involving annuities due and deferred annuities, and these special annuities are analyzed in terms of ordinary annuities. 3 The discussion of probability and its application to insurance is more extended than that found in many texts.

In this edition we are including Answers to the exercises and problems...