Book description
An introduction to the mathematical skills needed to understand finance and make better financial decisions
Mathematical Finance enables readers to develop the mathematical skills needed to better understand and solve financial problems that arise in business, from small entrepreneurial operations to large corporations, and to also make better personal financial decisions. Despite the availability of automated tools to perform financial calculations, the author demonstrates that a basic grasp of the underlying mathematical formulas and tables is essential to truly understand finance.
The book begins with an introduction to the most fundamental mathematical concepts, including numbers, exponents, and logarithms; mathematical progressions; and statistical measures. Next, the author explores the mathematics of the time value of money through a discussion of simple interest, bank discount, compound interest, and annuities. Subsequent chapters explore the mathematical aspects of various financial scenarios, including:
Mortgage debt, leasing, and credit and loans
Capital budgeting, depreciation, and depletion
Breakeven analysis and leverage
Investing, with coverage of stocks, bonds, mutual funds, options, cost of capital, and ratio analysis
Return and risk, along with a discussion of the Capital Asset Pricing Model (CAPM)
Life annuities as well as life, property, and casualty insurance
Throughout the book, numerous examples and exercises present realistic financial scenarios that aid readers in applying their newfound mathematical skills to devise solutions. The author does not promote the use of financial calculators and computers, but rather guides readers through problem solving using formulas and tables with little emphasis on derivations and proofs.
Extensively classtested to ensure an easytofollow presentation, Mathematical Finance is an excellent book for courses in business, economics, and mathematics of finance at the upperundergraduate and graduate levels. The book is also appropriate for consumers and entrepreneurs who need to build their mathematical skills in order to better understand financial problems and make better financial choices.
Table of contents
 Coverpage
 Titlepage
 Copyright
 Dedication
 Contents
 Preface

UNIT I MATHEMATICAL INTRODUCTION

1 Numbers, Exponents, and Logarithms
 1.1. Numbers
 1.2. Fractions
 1.3. Decimals
 1.4. Repetends
 1.5. Percentages
 1.6. Base Amount, Percentage Rate, and Percentage Amount
 1.7. Ratios
 1.8. Proportions
 1.9. Aliquots
 1.10. Exponents
 1.11. Laws of Exponents
 1.12. Exponential Function
 1.13. Natural Exponential Function
 1.14. Laws of Natural Exponents
 1.15. Scientific Notation
 1.16. Logarithms
 1.17. Laws of Logarithms
 1.18. Characteristic, Mantissa, and Antilogarithm
 1.19. Logarithmic Function
 2 Mathematical Progressions
 3 Statistical Measures
 Unit I Summary
 List of Formulas
 Exercises for Unit I

1 Numbers, Exponents, and Logarithms

UNIT II MATHEMATICS OF THE TIME VALUE OF MONEY
 Introduction

1 Simple Interest
 1.1. Total Interest
 1.2. Rate of Interest
 1.3. Term of Maturity
 1.4. Current Value
 1.5. Future Value
 1.6. Finding n and r When the Current and Future Values are Both Known
 1.7. Simple Discount
 1.8. Calculating the Term in Days
 1.9. Ordinary Interest and Exact Interest
 1.10. Obtaining Ordinary Interest and Exact Interest in Terms of Each Other
 1.11. Focal Date and Equation of Value
 1.12. Equivalent Time: Finding an Average due Date
 1.13. Partial Payments
 1.14. Finding the Simple Interest Rate by the DollarWeighted Method
 2 Bank Discount

3 Compound Interest
 3.1. The Compounding Formula
 3.2. Finding the Current Value
 3.3. Discount Factor
 3.4. Finding the Rate of Compound Interest
 3.5. Finding the Compounding Term
 3.6. The Rule of 72 and Other Rules
 3.7. Effective Interest Rate
 3.8. Types of Compounding
 3.9. Continuous Compounding
 3.10. Equations of Value for a Compound Interest
 3.11. Equated Time For a Compound Interest

4 Annuities
 4.1. Types of Annuities
 4.2. Future Value of an Ordinary Annuity
 4.3. Current Value of an Ordinary Annuity
 4.4. Finding the Payment of an Ordinary Annuity
 4.5. Finding the Term of an Ordinary Annuity
 4.6. Finding the Interest Rate of an Ordinary Annuity
 4.7. Annuity Due: Future and Current Values
 4.8. Finding the Payment of an Annuity Due
 4.9. Finding the Term of an Annuity Due
 4.10. Deferred Annuity
 4.11. Future and Current Values of a Deferred Annuity
 4.12. Perpetuities
 Unit II Summary
 List of Formulas
 Exercises for Unit II

UNIT III MATHEMATICS OF DEBT AND LEASING
 1 Credit and Loans

2 Mortgage Debt
 2.1. Analysis of Amortization
 2.2. Effects of Interest Rate, Term, and Down Payment on the Monthly Payment
 2.3. Graduated Payment Mortgage
 2.4. Mortgage Points and the Effective Rate
 2.5. Assuming a Mortgage Loan
 2.6. Prepayment Penalty on a Mortgage Loan
 2.7. Refinancing a Mortgage Loan
 2.8. Wraparound and Balloon Payment Loans
 2.9. Sinking Funds
 2.10. Comparing Amortization to Sinking Fund Methods
 3 Leasing
 Unit III Summary
 List of Formulas
 Exercises for Unit III
 UNIT IV MATHEMATICS OF CAPITAL BUDGETING AND DEPRECIATION

UNIT V MATHEMATICS OF THE BREAKEVEN POINT AND LEVERAGE

1 BreakEven Analysis
 1.1. Deriving BEQ and BER
 1.2. BEQ and BER Variables
 1.3. Cash BreakEven Technique
 1.4. The Breakeven Point and the Target Profit
 1.5. Algebraic Approach to the BreakEven Point
 1.6. The BreakEven Point When Borrowing
 1.7. Dual BreakEven Points
 1.8. Other Applications of the BreakEven Point
 1.9. BEQ and BER Sensitivity to their Variables
 1.10. Uses and Limitations of BreakEven Analysis
 2 Leverage
 Unit V Summary
 List of Formulas
 Exercises for Unit V

1 BreakEven Analysis
 UNIT VI MATHEMATICS OF INVESTMENT
 UNIT VII MATHEMATICS OF RETURN AND RISK

UNIT VIII MATHEMATICS OF INSURANCE
 1 Life Annuities

2 Life Insurance
 2.1. Whole Life Insurance Policy
 2.2. Annual Premium: Whole Life Basis
 2.3. Annual Premium: mPayment Basis
 2.4. Deferred Whole Life Policy
 2.5. Deferred Annual Premium: Whole Life Basis
 2.6. Deferred Annual Premium: mPayment Basis
 2.7. Term Life Insurance Policy
 2.8. Endowment Insurance Policy
 2.9. Annual Premium for the Endowment Policy
 2.10. Less than Annual Premiums
 2.11. Natural Premium vs. the Level Premium
 2.12. Reserve and Terminal Reserve Funds
 2.13. Benefits of the Terminal Reserve
 2.14. How Much Life Insurance Should You Buy?
 3 Property and Casualty Insurance
 Unit VIII Summary
 List of Formulas
 Exercises for Unit VIII
 References
 Appendix
 Index
Product information
 Title: Mathematical Finance
 Author(s):
 Release date: July 2012
 Publisher(s): Wiley
 ISBN: 9780470641842
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