A Spiral Approach to Financial Mathematics 0128015802, 9780128015803

Table of contents :
Front-matter_2018_A-Spiral-Approach-to-Financial-Mathematics
A Spiral Approach to Financial Mathematics
Copyright_2018_A-Spiral-Approach-to-Financial-Mathematics
Copyright
Preface_2018_A-Spiral-Approach-to-Financial-Mathematics
Preface
Why the Changes in Content Sequencing?
What About Changes in Pedagogy?
Student Audience and How to Utilize the Materials
Students Hoping to Gain a Solid Understanding of Financial Mathematics Concepts
Students Hoping to Pass Actuarial Certification Exam FM
To All Students
To the Actuary Student
Chapter-One---Savings--Fundamentals-o_2018_A-Spiral-Approach-to-Financial-Ma
One Savings: Fundamentals of Interest
Section 1.1. Simple and compound interest
Learning objectives
Example 1.1. Saving Money to Study Abroad
Interest over longer periods
Exploration 1.1. Saving for Your First Car
Interest over longer periods
Turning to technology: Excel
Summary
Homework Questions: Section 1.1
Conceptual questions
Practice questions
Application questions
Looking ahead
Section 1.2. Changing the Compounding Period: Nominal vs Effective Interest Rates
Learning objectives
Example 1.2. Saving Money to Study Abroad (Revisited)
Nominal versus effective interest rates
Back to the saving for study abroad example
Exploration 1.2. Saving for Your First Car (Revisited)
Changing the period over which interest Is computed
Nominal versus effective interest rates
Back to the car example
Summary
Homework Questions: Section 1.2
Conceptual questions
Practice questions
Application questions
Looking ahead
Section 1.3. Valuing Accounts with Multiple Transactions
Learning objectives
Example 1.3. Saving for a Down Payment on a House
Basic account chart
Creating a dynamic account chart using Excel
What if you saved $900/month instead?
How much would you need to save each month to reach your goal within 18 months?
What about an extra deposit?
Exploration 1.3. Saving for College
Getting started
Basic account chart for college savings
Begin filling in the account chart
Revisiting nominal rates of interest
Creating a dynamic account chart using Excel
Summary
Homework Questions: Section 1.3
Conceptual questions
Practice questions
Application questions
Looking ahead
Section 1.4. Tips and Tricks for Solving Cash Flow Problems
Learning objectives
Example 1.4. Saving for a Down Payment (Revisited)
Nonrecursive approach
Evaluating the impact of a withdrawal
Irregular payments and withdrawals
Problems involving an unknown interest rate
Problems involving an unknown time period
Exploration 1.4. Saving for College (Revisited)
Recursive approach
Nonrecursive approach
Irregular payments and withdrawals
Problems involving an unknown interest rate
Problems involving an unknown time period
Summary
Homework Questions: Section 1.4
Conceptual questions
Practice questions
Application questions
Looking ahead
End of chapter summary
End of chapter review problems
Chapter-Two---Loans--Fundamentals-of-Borr_2018_A-Spiral-Approach-to-Financia
Two Loans: Fundamentals of Borrowing and Lending
Section 2.1. Introduction to Loans
Learning Objectives
Example 2.1. Paying Back a Student Loan
Loan Terminology
Paying Off the Interest Over Time
Amortization
How Much Does Your $3,500 Actually Cost You?
Exploration 2.1. So, You Want to Buy a Car…
What is a Loan and How Does It Work?
Paying Off the Interest Over Time
Amortization
Using Excel Functions and Online Loan Calculators to Simplify Loan Computations
Summary
Homework Questions: Section 2.1
Conceptual Questions
Practice Questions
Application Questions
Looking Ahead
Section 2.2. Refinancing a Loan
Learning Objectives
Example 2.2. Paying Back a Student Loan (Revisited)
Refinancing
Exploration 2.2. So, You Want to Buy a Car… (Revisited)
Understanding Amortization
Refinancing
Summary
Homework Questions: Section 2.2
Conceptual Questions
Practice Questions
Application Questions
Look Ahead
Section 2.3. Sinking Funds
Learning Objectives
Example 2.3. Paying Back a Personal Loan
Interest Rate Comparisons Between Sinking Funds and Amortized Loans
A Direct (Shortcut) Formula to Compute Sinking Fund Payment Sizes
Exploration 2.3. Buying a House With an Interest-Only Loan
A Sinking Fund Savings Account
Sinking Funds With Different Terms
A Direct (Shortcut) Formula to Compute Sinking Fund Payment Sizes
Summary
Homework Questions: Section 2.3
Conceptual Questions
Practice Questions
Application Questions
Prove It! Questions
End of Chapter Summary
End of Chapter Review Problems
Chapter-Three---Annuities--Fundamentals-o_2018_A-Spiral-Approach-to-Financia
Three Annuities: Fundamentals of Regular Payments
Section 3.1. Perpetuities
Learning Objectives
Example 3.1. Living on the Interest: Perpetuities in Retirement
Exploration 3.1. Living on the Interest: Perpetuities at College
Summary
Homework Questions: Section 3.1
Conceptual Questions
Practice Questions
Application Questions
Looking Ahead
Section 3.2. Basic Annuities
Learning Objectives
Example 3.2. Planning for Retirement
A Direct (Shortcut) Formula to Compute Account Balances and Payment Sizes for Annuities
Discount Factor
Exploration 3.2. Using a Life Insurance Payout as a Basic Annuity
A Direct (Shortcut) Formula to Compute Account Balances and Payment Sizes for Annuities
Discount Factor
Summary
Homework Questions: Section 3.2
Conceptual Exercises
Practice Exercises
Application Exercises
Prove It!
End of Chapter Summary
End of Chapter Exercises
Chapter-Four---Stocks-and-Bonds--Fundamental_2018_A-Spiral-Approach-to-Finan
Four Stocks and Bonds: Fundamentals of Investment Strategies
Section 4.1. Bonds
Learning objectives
Example 4.1. Investing $1 Million
Zero-coupon bonds
A bond with coupons
Coupon rate
A formula for bond pricing
What size bond can you actually afford?
Exploration 4.1. Launching a New Product Line
Zero-coupon bonds
A bond with coupons
Coupon rate
A formula for bond pricing
Summary
Homework Questions: Section 4.1
Conceptual questions
Practice questions
Application questions
Prove it!
Section 4.2. Buying and Selling Bonds
Learning objectives
Example 4.2. Investing $1 Million (Revisited)
Yield rate vs coupon rate
Selling at a premium, discount, and par
Bond markets and changing yield rates
Exploration 4.2. Starting a New Product Line (Revisited)
Selling bonds
Yield rate vs coupon rate
Selling at a premium, discount, and par
Bond markets and changing yield rates
Summary
Homework Questions: Section 4.2
Conceptual questions
Practice questions
Application questions
Section 4.3. Stocks
Learning objectives
Example 4.3. Investing $1 Million in the Stock Market
Stock
Exploration 4.3. Raising Money by Selling Ownership in the Company
Cash flow approach to value investments
Stock
Summary
Homework Questions: Section 4.3
Conceptual questions
Practice questions
Application questions
End of Chapter Summary
End of Chapter Exercises
Chapter-Five---Portfolios--Fundamentals-of-Col_2018_A-Spiral-Approach-to-Fin
Five Portfolios: Fundamentals of Collections of Assets and Liabilities
Section 5.1. Yield Rates on a Portfolio
Learning objectives
Example 5.1. Timing a Market Investment
1 year later
Another year later
Dollar-weighted yield rate
Time-weighted yield rate
Comparing dollar-weighted and time-weighted yield rates
Exploration 5.1. Playing the Bond Market
Investment strategy 1
What will you do now?
Dollar-weighted yield rate
What if…..?
What if…..?
Time-weighted yield rate
Time-weighted yield rate if you buy another bond
Comparing dollar-weighted and time-weighted yield rates
Summary
Homework Questions: Section 5.1
Conceptual questions
Practice questions
Application questions
Section 5.2. Changing Yield Rates on a Portfolio
Learning objectives
Example 5.2. How Risky is My Portfolio?
Summarizing price sensitivity: Macaulay duration
Computing the Macaulay duration for the entire portfolio
Exploration 5.2. Evaluating Portfolio Risk
Summarizing price sensitivity: Macaulay duration
Computing the Macaulay duration for the entire portfolio
Summary
Homework Questions: Section 5.2
Conceptual questions
Practice questions
Application questions
Looking ahead
Section 5.3. Strategies to Mitigate Portfolio Risk
Learning objectives
Example 5.3. Getting Ready to Payback a Bond Debt
Looking into investment options in the bond market
Cash-flow matching
Buying 2-year bonds
Buying 4-year bonds
Evaluating interest-rate risk
Duration matching
Concluding Remarks
Exploration 5.3: Anticipating Paying Back a Loan
Cash-flow matching
Buying bonds with different payoff times
Duration matching
Comparing all of the different scenarios
Concluding Remarks
Summary
Homework Questions: Section 5.3
Conceptual questions
Practice questions
Application questions
End of Chapter Summary
End of Chapter Exercises
Chapter-Six---Savings-Revisite_2018_A-Spiral-Approach-to-Financial-Mathemati
Six Savings Revisited
Section 6.1. Force of Interest
Learning objectives
Example 6.1. Which Investment Will You Choose?
Changing the force of interest
Generalizing the idea of force of interest (requires calculus)
Exploration 6.1. Choosing Between Investments With Different Compounding Periods
Changing the force of interest
Generalizing the idea of force of interest (requires calculus)
Summary
Homework Questions: Section 6.1
Conceptual questions
Practice questions
Application questions
Prove it! questions
Section 6.2. Discount Rate
Learning objectives
Example 6.2. Saving Money in U.S. Treasury Bills
Mini example of a $1,000 T-bill
Back to main example
Relationship between discount rate and interest rate
Discount rate vs discount factor
Discount rate over multiple periods/fractional periods
Exploration 6.2. Investing in U.S. Treasury Bills
Mini example of a $1,000 T-bill
Back to your $950,000
Relationship Between Discount Rate and Interest Rate
Discount rate vs discount factor
Discount rate over multiple periods/fractional periods
Summary
Homework Questions: Section 6.2
Conceptual questions
Practice questions
Application questions
Prove it! questions
Section 6.3. Nominal Discount Rates
Learning objectives
Example 6.3. More Savings Accounts
Trends with more compounding
Exploration 6.3. Saving With U.S. T-Bills
Summary
Homework Questions: Section 6.3
Conceptual questions
Practice questions
Application questions
End of Chapter Summary
End of Chapter Exercises
Chapter-Seven---Loans-Revisite_2018_A-Spiral-Approach-to-Financial-Mathemati
Seven Loans Revisited
Section 7.1. Loans as Annuities
Learning objectives
Example 7.1. Paying Back a Student Loan
Drop payments
Prospective Method of Loan Valuation
Amount of principal and interest in any future payment
Exploration 7.1. Taking Out a Car Loan
Drop payments
Prospective method of loan valuation
Amount of principal and interest in any future payment
Summary
Homework Questions: Section 7.1
Conceptual questions
Practice questions
Application questions
Prove It! questions
Section 7.2. More About Loans as Annuities
Learning objectives
Example 7.2. Paying Back a Student Loan (Revisited)
Finding an outstanding loan balance using the retrospective method
Finding amount of interest and principal in a payment
Computing the exact value of the drop payment
Exploration 7.2. Paying Back a Car Loan (Revisited)
Finding an outstanding loan balance using the retrospective method
Finding amount of interest and principal in a payment
Computing the exact value of the drop payment
Summary
Homework Questions: Section 7.2
Conceptual questions
Practice questions
Application questions
End of Chapter Summary
End of Chapter Exercises
Chapter-Eight---Annuities-Revisi_2018_A-Spiral-Approach-to-Financial-Mathema
Eight Annuities Revisited
Section 8.1 Geometrically Increasing and Decreasing Annuities
Learning objectives
Example 8.1 Buying a Retirement Annuity Allowing for Inflation
Inflation-adjusted annuity
Equations for inflation-adjusted annuities
What about an increasing perpetuity?
Exploration 8.1 Life Insurance Payout as an Annuity Allowing for Inflation
Inflation-adjusted annuity
Equations for inflation-adjusted annuities
What about an increasing perpetuity?
Summary
Homework Questions: Section 8.1
Conceptual questions
Practice questions
Application questions
Prove it! questions
Section 8.2 Arithmetically Increasing and Decreasing Annuities
Learning objectives
Example 8.2 Buying a Retirement Annuity (Revisited)
Calculating initial payment size for an arithmetically increasing annuity that grows by $20/month
Arithmetically increasing perpetuity
Concluding remarks
Exploration 8.2. Life Insurance Payout as an Annuity Allowing for Inflation (Revisited)
Equations for arithmetically increasing annuity
Arithmetically increasing perpetuity
Summary
Homework Questions: Section 8.2
Conceptual questions
Practice questions
Application questions
Prove it! questions
Section 8.3 Annuities With Payments at the Beginning of the Period (Annuities-due)
Learning objectives
Example 8.3 Buying a Retirement Annuity (Revisited)
Perpetuity-due
Another shortcut formula for an annuity-due
Computing the present value of an annuity-due using the discount rate
Concluding remarks
Exploration 8.3 Leaving Money for a New Scholarship
Perpetuities and annuities-due
Another shortcut formula for an annuity-due
Computing the present value of an annuity-due using the discount rate
Changing the donation amount
Summary
Homework Questions: Section 8.3
Conceptual questions
Practice questions
Application questions
Prove it! questions
Looking ahead
Section 8.4 Increasing and Decreasing Annuities-due
Learning objectives
Example 8.4 Retirement Savings (Revisited)
Scenario 1—annuity-due for 30 years growing 0.1652% per month
Scenario 2—annuity-due in perpetuity growing 0.1652% per month
Scenario 3—annuity-due for 30 years growing $20 per month
Scenario 4—perpetuity-due growing $1 per month
Concluding remarks
Exploration 8.4. Donating Money for a New Scholarship
Arithmetically increasing and decreasing perpetuities and annuities
Deferring the start
Summary
Homework Questions: Section 8.4
Conceptual questions
Practice questions
Application questions
Prove it! questions
End of Chapter Summary
End of Chapter Exercises
Chapter-Nine---Bonds-Revisited_2018_A-Spiral-Approach-to-Financial-Mathemati
Nine Bonds Revisited
Section 9.1. Finding Bond Values at Any Point in Time
Learning objectives
Example 9.1. Valuing a $10 Million Bond Issue
Book value of a bond
Bond amortization schedule
Exploration 9.1. Valuing a $1 Million Bond Issue
Book value of a bond
Bond amortization schedule
Summary
Homework Questions: Section 9.1
Conceptual questions
Practice questions
Application questions
Section 9.2.Pricing Callable vs Noncallable Bonds
Learning objectives
Example 9.2. Valuing a $10 Million Bond Issue (Continued)
Bond strategies when interest rates change
Should the company exercise their European call option?
What if the company does nothing?
What if the company calls the bond?
Does refinancing always make sense?
Exploration 9.2. Valuing a $1 Million Bond Issue (Continued)
Bond strategies when interest rates change
Should the company exercise their European call option?
Summary
Homework Questions: Section 9.2
Conceptual questions
Practice questions
Application questions
Section 9.3. Spot and Forward Rates
Learning objectives
Example 9.3. Making Bond Pricing Decisions
Spot rates
Using spot rates to compute zero-coupon bond prices
Using spot rates to compute yield rates
Forward rate
Important notes
Exploration 9.3. Understanding Bond Pricing As an Investor
Spot rates
Using spot rates to compute zero-coupon bond prices
Using spot rates to compute yield rates
Forward rate
Homework Questions: Section 9.3
Conceptual questions
Practice questions
Application questions
End of Chapter Summary
End of Chapter Exercises
Chapter-Ten---Portfolios-Revisit_2018_A-Spiral-Approach-to-Financial-Mathema
Ten Portfolios Revisited
Section 10.1. Comparing Measures of Interest Rate Risk
Learning objectives
Example 10.1 How Risky is My Portfolio?
Review: Macaulay duration
Modified duration
Calculating the modified duration
Method 1—estimating the modified duration
Method 2—computing modified duration as a function of the Macaulay duration
Slightly different answers?
Finding the modified duration for each bond
Finding the modified duration for the portfolio
Method 1
Method 2
Exploration 10.1 Evaluating Portfolio Risk
Review: Macaulay duration
Modified duration
Method 1
Method 2
Finding the modified duration for Bond 2
Finding the modified duration for the portfolio
Summary
Homework Questions: Section 10.1
Conceptual questions
Practice questions
Application questions
Section 10.2. Convexity
Learning objectives
Example 10.2. How Risky is My Portfolio? (Revisited)
Convexity
Macaulay convexity
Modified convexity
Final comments
Exploration 10.2 Evaluating Portfolio Risk (Continued)
Convexity
Macaulay convexity
Modified convexity
Summary
Homework Questions: Section 10.2
Conceptual questions
Practice questions
Application questions
Section 10.3. Redington Immunization
Learning objectives
Example 10.3. Getting Ready to Pay Back a Bond Debt
Immunizing the liability by buying a mix of bonds
Redington immunization
Confirming Redington Immunization Works
Full immunization
Concluding Remarks
Exploration 10.3. Revisiting Anticipating Paying Back Bonds
Buying bonds with different payoff times
Buying a 1-year coupon bond
Buying a 3-year coupon bond
Immunizing the liability by buying a mix of bonds
Redington immunization
Confirming redington immunization works
Full immunization
Summary
Homework Questions: Section 10.3
Conceptual questions
Practice questions
Application questions
End of Chapter Summary
End of Chapter Exercises
Glossary_2018_A-Spiral-Approach-to-Financial-Mathematics
Glossary
Formulas_2018_A-Spiral-Approach-to-Financial-Mathematics
Formulas
Chapter One Saving: Fundamentals of Interest
Chapter Two Loans: Fundamentals of Borrowing and Lending
Chapter Three Annuities: Fundamentals of Regular Payments
Chapter Four Stocks and Bonds: Fundamentals of Investment Strategies
Chapter Five Portfolios: Fundamentals of Collections of Assets and Liabilities
Chapter Six Savings Revisited
Chapter Seven Loans Revisited
Chapter Eight Annuities Revisited
Chapter Nine Bonds Revisited
Chapter Ten Portfolios Revisited
Appendix_2018_A-Spiral-Approach-to-Financial-Mathematics
Appendix
Chapter 1
Section 1.1
Section 1.2
Section 1.3
Section 1.4
End of Chapter 1
Chapter 2
Section 2.1
Section 2.2
Section 2.3
End of Chapter 2
Chapter 3
Section 3.1
Section 3.2
End of Chapter 3
Chapter 4
Section 4.1
Section 4.2
Section 4.3
End of Chapter 4
Chapter 5
Section 5.1
Section 5.2
Section 5.3
End of Chapter 5
Chapter 6
Section 6.1
Section 6.2
Section 6.3
End of Chapter 6
Chapter 7
Section 7.1
Section 7.2
End of Chapter 7
Chapter 8
Section 8.1
Section 8.2
Section 8.3
Section 8.4
End of chapter 8
Chapter 9
Section 9.1
Section 9.2
Section 9.3
End of Chapter 9
Chapter 10
Section 10.1
Section 10.2
Section 10.3
End of Chapter 10
Index_2018_A-Spiral-Approach-to-Financial-Mathematics
Index