Mathematical Interest Theory 3rd edition

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Leslie Jane Federer Vaaler, Shinko Kojima Harper, and James W. Daniel
Publisher: Mathematical Association of America

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  • Chapter 0: An introduction to the Texas Instruments BA II Plus
    • 0.0: Chapter 0 Writing Problems
    • 0.1: Choosing a calculator
    • 0.2: Font convention
    • 0.3: BA II Plus basics

  • Chapter 1: The growth of money
    • 1.0: Chapter 1 Writing Problems (7)
    • 1.1: Introduction
    • 1.2: What is interest?
    • 1.3: Accumulation and amount functions (6)
    • 1.4: Simple interest / Linear accumulation functions (7)
    • 1.5: Compound interest (The usual case!) (10)
    • 1.6: Interest in advance / The effective discount rate (5)
    • 1.7: Discount functions / The time value of money (7)
    • 1.8: Simple discount (5)
    • 1.9: Compound discount (7)
    • 1.10: Nominal rates of interest and discount (7)
    • 1.11: A friendly competition (Constant force of interest) (3)
    • 1.12: Force of interest (10)
    • 1.13: Note for those who skipped Sections (1.11) and (1.12) (2)
    • 1.14: Quoted rates for Treasury bills (5)
    • 1.15: Inflation (6)
    • 1.16: Choice of quotation base for interest rates (3)
    • 1: Review Problems (10)

  • Chapter 2: Equations of value and yield rates
    • 2.0: Chapter 2 Writing Problems (4)
    • 2.1: Introduction
    • 2.2: Equations of value for investments involving a single deposit made under compound interest (5)
    • 2.3: Equations of value for investments with multiple contributions (10)
    • 2.4: Investment return (8)
    • 2.5: Reinvestment considerations (3)
    • 2.6: Dollar-weighted yield rates (4)
    • 2.7: Fund performance (3)
    • 2: Review Problems (5)

  • Chapter 3: Annuities (annuities certain)
    • 3.0: Chapter 3 Writing Problems (4)
    • 3.1: Introduction
    • 3.2: Annuities - immediate (8)
    • 3.3: Annuities - due (6)
    • 3.4: Perpetuities (6)
    • 3.5: Deferred annuities and values on any date (5)
    • 3.6: Outstanding loan balances (7)
    • 3.7: Nonlevel annuities (6)
    • 3.8: Annuities with payments in geometric progression (5)
    • 3.9: Annuities with payments in arithmetic progression (6)
    • 3.10: Yield rate examples involving annuities (9)
    • 3.11: Annuity symbols for nonintegral terms (3)
    • 3.12: Annuities governed by general accumulation functions (3)
    • 3.13: The investment year method (2)
    • 3: Review Problems (6)

  • Chapter 4: Annuities with different payment and conversion periods
    • 4.0: Chapter 4 Writing Problems (2)
    • 4.1: Introduction
    • 4.2: Level annuities with payments less frequent than each interest period (6)
    • 4.3: Level annuities with payments more frequent than each interest period (4)
    • 4.4: Annuities with payments less frequent than each interest period and payments in arithmetic progression (3)
    • 4.5: Annuities with payments more frequent than each interest period and payments in arithmetic progression (7)
    • 4.6: Continuously paying annuities (6)
    • 4.7: A yield rate example (3)
    • 4: Review Problems (5)

  • Chapter 5: Loan repayment
    • 5.0: Chapter 5 Writing Problems (3)
    • 5.1: Introduction
    • 5.2: Amortized loans and amortization schedules (6)
    • 5.3: The Sinking Fund method (5)
    • 5.4: Amortized loans with other repayment patterns (6)
    • 5.5: Yield rate examples and replacement of capital (6)
    • 5: Review Problems (10)

  • Chapter 6: Bonds
    • 6.0: Chapter 6 Writing Problems (3)
    • 6.1: Introduction
    • 6.2: Bond alphabet soup and the basic price formula (7)
    • 6.3: The premium-discount formula (3)
    • 6.4: Other pricing formulas for bonds (3)
    • 6.5: Bond amortization schedules (5)
    • 6.6: Valuing a bond after its date of issue (3)
    • 6.7: Selling a bond after its date of issue (5)
    • 6.8: Yield rate examples (7)
    • 6.9: Callable bonds (4)
    • 6.10: Floating-rate bonds (2)
    • 6.11: The BA II Plus calculator Bond worksheet (3)
    • 6: Review Problems (7)

  • Chapter 7: Stocks and financial markets
    • 7.0: Chapter 7 Writing Problems (4)
    • 7.1: Common and preferred stock (2)
    • 7.2: Brokerage accounts (3)
    • 7.3: Going long: buying stock with borrowed money (2)
    • 7.4: Selling short: selling borrowed stocks (6)
    • 7: Review Problems (4)

  • Chapter 8: Arbitrage, term structure of interest rates, and derivatives
    • 8.0: Chapter 8 Writing Problems (7)
    • 8.1: Introduction
    • 8.2: Arbitrage (3)
    • 8.3: The term structure of interest rates (10)
    • 8.4: Loans with floating rate of interest (3)
    • 8.5: Interest rate swaps: the basics (5)
    • 8.6: Formulas for interest rate swaps (4)
    • 8.7: Market value of an interest rate swap (2)
    • 8.8: More swaps (2)
    • 8.9: Forward contracts (2)
    • 8.10: Commodity futures held until delivery (4)
    • 8.11: Offsetting positions and liquidity of futures contracts (4)
    • 8.12: Price discovery and more kinds of futures (2)
    • 8.13: Options (4)
    • 8.14: Using replicating portfolios to price options (4)
    • 8.15: Using weighted averages to price options (5)
    • 8: Review Problems (6)

  • Chapter 9: Interest rate sensitivity
    • 9.0: Chapter 9 Writing Problems (2)
    • 9.1: Overview (1)
    • 9.2: Duration (11)
    • 9.3: Convexity (5)
    • 9.4: Using duration to approximate price (5)
    • 9.5: Using duration and convexity to approximate price (2)
    • 9.6: Immunization (3)
    • 9.7: Other types of duration (5)
    • 9: Review Problems (7)

  • Chapter 10: Determinants of interest rates
    • 10.0: Chapter 10 Writing Problems
    • 10.1: Introduction
    • 10.2: Supply and demand of loans (1)
    • 10.3: Default risk (3)
    • 10.4: Inflation risk (2)
    • 10.5: Banks and other financial intermediaries in the retail sector
    • 10.6: Savings and lending interest rates in the retail sector
    • 10.7: Bonds issued by governments and corporations (3)
    • 10.8: The role of central banks
    • 10: Review Problems


Mathematical Interest Theory, Third Edition, by Leslie Jane Federer Vaaler, Shinko Kojima Harper, and James W. Daniel, gives students an introduction of how investments grow over time. This textbook is written for anyone who has a strong high school algebra background and is interested in being an informed borrower or investor. The content is suitable for a mid-level or upper-level undergraduate course or a beginner graduate course, and provides a solid foundation for readers embarking on actuarial careers. This book has been suggested by the Society of Actuaries for people preparing for the Financial Mathematics exam, and updates the previous edition to cover the material in the SOA study notes FM-24-17, FM-25-17, and FM-26-17.

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Group Quantity Questions
Chapter 1: The growth of money
1.0 7 001 002 003 004 005 006 007
1.R 10 001 002 003 004 005 006 007 008 009 010
1.3 6 001 002 003 004 005 006
1.4 7 001 002 003 004 005 006 007
1.5 10 001 002 003 004 005 006 007 008 009 010
1.6 5 001 002 003 004 005
1.7 7 001 002 003 004 005 007 008
1.8 5 001 002 003 004 005
1.9 7 001 002 003 004 005 006 007
1.10 7 001 002 003 004 005 006 007
1.11 3 001 002 003
1.12 10 001 002 003 004 005 006 007 008 009 010
1.13 2 001 002
1.14 5 001 002 003 004 005
1.15 6 001 002 003 004 005 006
1.16 3 001 002 003
Chapter 2: Equations of value and yield rates
2.0 4 001 002 003 004
2.R 5 001 003 004 005 006
2.2 5 001 002 003 004 005
2.3 10 001 002 003 004 005 006 009 010 011 012
2.4 8 003 004 005 007 008 009 010 011
2.5 3 001 002 003
2.6 4 001 002 003 004
2.7 3 001 002 003
Chapter 3: Annuities (annuities certain)
3.0 4 001 002 003 004
3.R 6 001 002 003 005 006 007
3.2 8 001 002 003 004 005 006 007 008
3.3 6 002 003 005 006 007 008
3.4 6 001 002 003 004 005 006
3.5 5 001 002 003 004 005
3.6 7 001 002 003 004 005 006 007
3.7 6 001 002 003 004 006 008
3.8 5 001 002 003 004 005
3.9 6 001 002 003 004 005 006
3.10 9 001 002 003 004 005 006 007 008 009
3.11 3 001 002 003
3.12 3 001 002 003
3.13 2 001 002
Chapter 4: Annuities with different payment and conversion periods
4.0 2 001 002
4.R 5 001 002 003 006 008
4.2 6 001 002 003 004 005 007
4.3 4 001 002 004 007
4.4 3 001 003 004
4.5 7 001 002 003 004 005 006 007
4.6 6 001 002 003 004 005 006
4.7 3 001 002 003
Chapter 5: Loan repayment
5.0 3 001 002 003
5.R 10 001 002 003 004 005 006 007 008 009 010
5.2 6 001 002 003 004 005 007
5.3 5 001 002 003 004 005
5.4 6 001 002 003 004 005 006
5.5 6 001 002 003 004 005 006
Chapter 6: Bonds
6.0 3 001 002 003
6.R 7 001 002 003 004 005 006 007
6.2 7 001 002 003 004 005 006 007
6.3 3 001 002 003
6.4 3 001 002 003
6.5 5 001 002 003 004 005
6.6 3 001 002 003
6.7 5 001 002 003 004 005
6.8 7 001 002 003 004 005 006 007
6.9 4 001 002 003 004
6.10 2 001 002
6.11 3 001 002 003
Chapter 7: Stocks and financial markets
7.0 4 001 002 003 004
7.R 4 001 002 003 004
7.1 2 001 002
7.2 3 001 002 003
7.3 2 001 002
7.4 6 001 002 003 004 005 006
Chapter 8: Arbitrage, term structure of interest rates, and derivatives
8.0 7 001 002 007 009 010 011 012
8.R 6 001 003 004 006 007 008
8.2 3 001 002 003
8.3 10 001 002 003 004 005 006 007 008 009 010
8.4 3 001 002 003
8.5 5 001 002 003 004 005
8.6 4 001 002 003 004
8.7 2 001 002
8.8 2 001 002
8.9 2 001 002
8.10 4 001 002 003 004
8.11 4 001 002 003 004
8.12 2 001 002
8.13 4 001 002 003 004
8.14 4 001 002 003 004
8.15 5 001 002 003 004 005
Chapter 9: Interest rate sensitivity
9.0 2 001 002
9.R 7 001 002 003 004 005 006 007
9.1 1 001
9.2 11 001 002 003 004 005 006 007 008 009 010 501.XP
9.3 5 001 002 003 004 005
9.4 5 001 002 003 004 005
9.5 2 001 002
9.6 3 001 002 003
9.7 5 001 002 003 004 005
Chapter 10: Determinants of interest rates
10.2 1 001
10.3 3 001 002 003
10.4 2 001 002
10.7 3 001 002 003
Total 480