MATHEMATICS OF ACCOUNTING BY ARTHUR B. CURTIS, B. C. S., C. P. A. AND JOHN H. COOPER, B. Accts., C. P. A. THIRD EDITION PRENTICE-HALL, INC. Englewood Cliffs PRENTJOT ALL ACCOUNTING SERIES . A. Finney, Editor COPYRIGHT, 1925, 1934, 1947, BY PRENTICE-HALL, INC. ENGLEWOOD CLIFFS, N J. ALL RIGHTS RESERVED. NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM, BY MIMEOGRAPH OR ANY OTHER MEANS, WITHOUT PERMISSION IN WRITING FROM THE PUBLISHERS. Nineteenth Printing. September, 1946 Thud Edition Fust Printing . January, 1047 Second Piintmg . August, 1047 Third Printing October, 1947 Fourth Printing . . June, 19J9 Fifth Printing . October, 1949 Sixth Printing September, 1952 Seventh P .... O- 1952 Eighth Pinning May, 1954 Ninth Punting November, 1954 Tenth Printing August, 1955 Eleventh Printing .... Match, 1936 Twelfth Printfnsr. Senfpmbpr. 195ft Thirteenth Printing, June, 1957 Preface It is now somewhat more than twenty years since the publica tion of the first edition of Mathematics of Accounting. Those familiar with the original edition, and the revised edition ten years later, will find that in the present revision the sequence of subjects has been considerably changed the treatment of some subjects has been amplified certain other subjects have been added. Some problems have been changed new problems and review problems have been included. Subjects new to Part 1 are Factors and Multiples, Business Insurance, and Payroll Records and Procedure. The chapter on Graphs has been expanded to include Index Numbers. Part 2 has been enlarged to include chapters on the following Permutations and Combinations, Probability, Probability and Mortality, Life Annuities, Net Premiums, and Valuation of LifeInsurance Policies. Algebraic formulas have been changed to conform to standard usage, while arithmetical substitutions and detailed solutions have been retained. Those desiring to work entirely from the tables in the appendix will find table references in the detailed solutions. Grateful recognition is here given to those who have taught from the previous editions and who have responded with sugges tions for this revision, ARTHUR B. CURTIS JOHN H. COOPER Contents PART I 2SAPTEB PAGB 1. FUNDAMENTAL PROCESSES AND SHORT METHODS FOR THE ACCOUNTANT 1 Addition Drill tables Streamline addition Drill table Combinations whose sum is 10 Drill table Adding where the same number is repeated many times Drill table Group addition Drill table Addition of two columns at a time Drill table Recording addition by columns Practical applications Subtraction Avoid errors Difference between a given minu end and several subtrahends Balancing an account Complement method Subtracting on an adding machine Practical problems Multiplication Contractions in multiplication To multiply by factors of the multiplier To multiply when a part of the multiplier is a factor or multiple of another part To multiply a number of two figures by 11 To multiply any number by 11 Multiplying by 25 Multiplying by 15 Multiplying numbers ending with ciphers Multiplication by numbers near 100, and by numbers near 1,000 Multiplication of two numbers each near 100, 1,000, and so forth Multiplying by numbers a little larger than 100 Multiplication of two numbers each a little more than 100 Cross multiplication To cross-multi ply a number of three digits by a number of two digits To cross-multiply a number of three digits by another numberof three digits Preparation of a table of multiples of a number Division To divide by 25, 50, or 125 Abbreviated division Use of tables in division Reciprocals in division. 2. CHECKING COMPUTATIONS 29 Methods Rough check Absolute check Check numbers obtained by casting out the nines Verification of addition Verification of subtraction Verification of multiplication Verification of division Verification of division where there is a remainder...