**Mathematics for Finance, Business and Economics**

**Table of Contents**

Introduction

1 Elementary Mathematical Concepts and Operations

. Simple Operations on Positive and Negative Numbers

. Fractions and Square Roots

. BEDMAS

. Algebraic Expressions

. Expanding Brackets

. Factorizing Algebraic Expressions

. The Cartesian Plane

Summary

Exercises

2 Linear Equations

. Equations and Linear Equations

. Linear Equations (LE) of One Variable

. The Equation of a Line

. Graphing a Linear Function

. Slope of a Line

. Economic Application of Linear Equations: Supply and Demand Models

. Simultaneous Linear Equations

. Solving a Set of Linear Equations

. The Equation of a Line Revisited

Summary

Exercises

3 Non-Linear Functions and Equations

. Quadratic Equations

. Solving a Quadratic Equation Using the Perfect Square

. Graphing the Quadratic

. Powers

. Roots

. Exponential Functions

. Logarithms

Summary

Exercises

4 Functions and Differentiation

. Functions

. Definition of the Derivative

. Calculating the Derivatives

. Minima and Maxima

. Price Elasticity of Demand

Summary

Exercises

5 Economic Application of Functions and

Differentiation

. Cost Concepts

. Revenue, Cost, Profit and Break-Even Point

. Maximizing Profit and Minimizing Cost

. Marginal Revenue and Cost

. Opportunity Cost

Summary

Exercises

6 Σummation, Percentages and Interest

. Óummation Sign Ó 113

. Percentages

. Interest

. Time Value of Money

. Depreciation of an Asset

. Nominal and Effective Interest

. The Future Value of a Sequence of Payments

Summary

Exercises

7 Arithmetic and Geometric Series

. Series

. Arithmetic Series

. Geometric Series

Summary

Exercises

8 Annuity and Amortization

. Savings account

. Present Value of an Annuity

. Amortization

Summary

Exercises

9 Matrices and Markov Chains

. What is a Matrix

. Matrices and Operations on Matrices

. Determinant and the Cramer’s rule

. Markov Chains

Summary

Exercises

Solutions

Bibliography

Picture credits

Glossary

Index

About the authors

**Preface**

Welcome to your new

**Mathematics book**. Our desire to write this book was borne out of our experience of lecturing Mathematics, Economics and Marketing courses for five years at The Hague University of applied Science. The motivation arose when a couple of our students approached us and suggested writing a simplified Mathematics syllabus because the notes we gave in class were more comprehensive and easier to understand than the textbook.

It occurred to us that some students with an intermediate or advanced level of Mathematics were strongly motivated to tackle the course, whilst some with no background or a very poor knowledge of Mathematics tended to be daunted by the complex text, and this demotivated them. In order toimprove students’ knowledge of Mathematics, we decided to write a book that would be simple to understand, and make the subject more appealing and less off-putting to them.

This book is written informally, in order to be easy to read and understand. It’s not just a lot of text, and then lots of exercises, such as you might find in traditional textbooks but a combination of explanations, explorations, and real-life applications of major concepts.

**Introduction**

For a long time, Mathematics has been seen as subject for highly skilled and specialized students. Business students are often not able to understand the benefits of Mathematics beyond simple everyday calculations. Mathematics develops the imagination. It requires clear and logical thought. Mathematics is a science of patterns and structures that provides students with a uniquely powerful set of tools for understanding and solving real-life problems. Math studies non-tangible objects like numbers, circles and functions.

However, we can profit greatly from this science because it has a big impact on our daily lives. For example, Math is essential in medicine, for analysing data on the causes of illness and the use of new drugs. Travel by aeroplane would not be possible without the Mathematics of airflow and control systems. Furthermore, Math is very useful in Finance, Economics and Accounting. For example, in exercise .: suppose you have € in a savings account with a yearly interest rate of %; how long would you have to wait until your money has doubled? Or exercise .: can we build a model of the behaviour of customers in order to predict the market for the next few years? These and many other questions will be answered in this book.

All Business students need to master the basic concepts of Mathematics, as this is the key to understanding other courses, such as Economics, Finance, Statistics, and Accounting. Therefore, this book follows a logical order (from easy topics to challenging topics) so that students can stay focused. Because this book is mainly dedicated to Business and Economics students, we have tried to relate it to subjects such as Economics, Marketing and Finance through real-life problems and situations.

In this book you will find theory, examples and exercises in each chapter. Solutions to the exercises can be found at the back of the book.