A Spiral Approach to Financial Mathematics (Instructor's Solution Manual) (Solutions)

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