INTRODUCTION TO BUSINESS MATHEMATICS

1 I INTRODUCTION TO BUSINESS MATHEMATICS Code: 1349 Units: 1 9 DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCES ALLAMA IQBAL OPEN UNIVERSITY ii (All Rights are Reserved with the Publisher) Year of 2020 5000 Price .. Rs. Printing Incharge .. Shakil Ahmad Khan Printer .. AIOU-Printing Press, H-8, Islamabad. Publisher .. Allama Iqbal Open University, Islamabad iii COURSE DEVELOPMENT TEAM Dean Faculty of Sciences: Prof. Dr. Syed Zafar Ilyas Development Coordinator: Dr. Nasir Rehman Writers: 1. Dr. Nasir Rehman 2. Ms. Fouzia Rehman 3. Ms. Mubashra Hafeez Reviewers: 1. Dr. Nasir Rehman 2. Dr. Babar Ahmad 3. Ms. Fouzia Rehman Editor: Mr. Fazal Karim Course Coordinator: Ms. Fouzia Rehman Composed by: Ms. Mubashra Hafeez iv CONTENTS Page No. Foreword ..v Message from the Dean .. vi vi i Course INTRODUCTION .

2 Vi ii Unit-1: BUSINESS Arithmetic-I ..01 Unit-2: BUSINESS Arithmetic-II ..15 Unit-3 MATHEMATICS of Finance-I ..29 Unit-4 MATHEMATICS of Finance-II ..39 Unit-5 Linear, Quadratic and Simultaneous Equations ..51 Unit-6 Functions and Their Graphs ..67 Unit-7 Elements of Matrix Algebra-I ..93 Unit-8 Elements of Matrix Algebra-II ..120 Unit-9 Binary Number System and Its Operations ..140 Bibliography ..152 v FOREWORD MATHEMATICS plays a vital role in the logical development of any society. That is why it serves as an essential subject during the early ages of all students. To make the best use of our available resources, we must have a better understanding, knowledge and practice of MATHEMATICS . This is very vast subject and ranges from some abstract ideas to purely applied concepts.

3 The present book has been written to understand the basic concepts of MATHEMATICS and its applications in issues related to BUSINESS , Economics, Commerce and many other Social Sciences. This book with its simple text style serves as the first step for students who aim to get an INTRODUCTION of the subject. Keeping in mind the objectives of the book, I am sure it will provide an insight into the subject along with enhancing the mathematical abilities of the students. Moreover, it is especially written to help students learn the applications of relevant mathematical concepts. In the end I would like to congratulate the course team, chairman, course development coordinator, writers, reviewers and editor for developing a very useful textbook. Prof. Dr.

4 Zia Ul-Qayyum (Vice-Chancellor) vi MESSAGE FROM THE DEAN MATHEMATICS is the branch of science which develops a relationship and fills the gaps between the natural sciences. Naturally MATHEMATICS looks a bit abstract, but when we use it in other sciences. Its applications come across to us at once. This course is much needed for our students to inculcate the first-level concepts. The basic MATHEMATICS needed for BUSINESS and other social sciences subjects is beautifully covered in this book. I wish to express my sincere thanks, appreciation and congratulations to all those persons who have contributed in the development of this book. I am sure this will be very beneficial to our students to groom their BUSINESS ideas mathematically. (Prof. Dr. Syed Zafar Ilyas) Dean Faculty of Sciences vii ACKNOWLEDGFMENTS First and foremost, I would like to thank Allah that I have been able to present this book.

5 I deeply indebted to all who have contributed either directly or indirectly in producing this book. My deep and sincere thanks to Chairman, Department of MATHEMATICS , AIOU, Dr. Nasir Rehman who encouraged and directed me. It is with his direction that this work came into existence. I would like to thank my colleagues Dr. Irfan Mustafa, Dr. Muhammad Nazam, Mr. Faisal Iqbal, Mr. Muhammad Aatif and Ms. Mubashra for their constant support and encouragement. I am especially grateful to Dr. Babar for his extremely detailed reviews and suggestions of the manuscript many times till the finalization of this book. Many extraordinary talented are responsible for helping to create this text. I would like to thank Ms. Mubashara for typing and editing this course on priority basis. I am highly grateful to Prof.

6 Dr. Zia ul Qayyum, Vice-Chancellor AIOU and Prof. Dr. Syed Zafar Ilyas, Dean Faculty of Sciences AIOU for giving creative ideas of writing difficult mathematical concepts in a simple way and provided all facilities to complete this course in the shortest possible time. Suggestions and criticism to improve the text will be highly appreciated. (Ms. Fouzia Rehman) Course Coordinator viii COURSEINTRODUCTION Basic idea is to develop and inculcate the important concepts needed for the study of BUSINESS MATHEMATICS in our students at undergraduate level. An effort has been made to make these contents self-explanatory and understandable. It is the need of hour to understand the applications of MATHEMATICS in studying different subjects of social sciences and other fields too.

7 OBJECTIVES The course aims to teach students, the basic concepts of MATHEMATICS and also create value for their applications and uses in practical situations. The objectives of the course are: To develop an understanding and desire of MATHEMATICS in students To present the material in a way which is helpful in motivating the students to study these subjects at a higher level To develop an approach of application of Maths in BUSINESS subjects How the course is organized? The text is divided into nine units in one volume. An attempt has been made to present the material in an informal way. Only those topics of MATHEMATICS are covered which are thought to be useful for everyone. we started studying MATHEMATICS when we were in class one and we continue its studies. In spite of this, most of us do not have full command on every day arithmetics.

8 Unit-1 Unit 1 covers the idea of Rate with Ratio and how they can be expressed in percentage form also applied these concepts on BUSINESS related problems. Unit-2 Unit 2 explains the concept of Profit, Revenue, Cost and Depreciation. Two different methods to charge depreciation are also discussed in this chapter. Unit-3 Unit 3 is concerned with interest rates and their effects on the value of money. Unit-4 Unit 4 discusses the concept of annuity and its types. Apply this concept on various BUSINESS related problems. Unit-5 In Unit 5, is about the INTRODUCTION of equations and their uses in the solution of different practical problems. Nature of solution of First degree, second degree and simultaneous linear equations are also discussed in this unit. Unit-6 In this unit the concept of a function is discussed which is the fundamental mathematical object which is used to describe relationship between variable quantities.

9 Different types of functions and their graphs are also explained in this unit. Unit-7 Unit 7 explains the term matrix and its different types with and without taking change in the matrix. Unit-8 This unit explains the different operation on matrices and its application in BUSINESS . Unit-9 Unit 9 This unit explains the binary number system. This is the language that most of the electronic devices understand. Arithmetic operation on Binary number and relationship between binary and decimal number system are also explained in this unit. 1 Unit 1 BUSINESS ATHMETIC I Written By: Mubashara Hafeez Reviewed By: Ms Fouzia Rehman 2 CONTENTS Page # INTRODUCTION .. 3 Objectives .. 3 Ratio .. 4 Rate .. 4 Use of Ratio .. 5 Proportion .. 7 Types of 7 (i) Direct Proportion.

10 7 (ii) Inverse Proportion .. 8 (iii) Compound Proportion .. 9 (iv) Continued Proportion .. 9 Percentage .. 10 Conversion of a Percentage into a Fraction .. 10 Conversion of a Percentage into Decimal .. 11 BUSINESS Applications of Percentage .. 11 Self-Assessment 12 3 INTRODUCTION The word arithmetic is from the Greek word arithmos it is a branch of MATHEMATICS which deal with the study of numbers. MATHEMATICS used in marketing, accounting, sales forecasting, inventory management and financial analysis. MATHEMATICS typically used in commerce includes arithmetic. Arithmetic is not only frequently use in statistics and MATHEMATICS but also use in various fields such as history, sociology and economics. For example, per capita income is the arithmetic mean income of a nation's population.