## Syllabus: M329F

THEORY OF INTEREST

**Text: Vaaler & Daniel, Mathematical Interest Theory, Mathematical Association, Second Edition**

**Responsible Parties:** Shinko Harper, Milica Cudina, Alisa Havens, Jennifer Mann, January 2013

**Prerequisite and degree relevance:** M408D, M308L, M408L, or M408S with a grade of at least C-, or consent of instructor. This course covers the interest theory portion of the SOA/CAS Financial Mathematics exam (FM/2); this should be about 75-80% of the material on this professional exam, with the balance of the exam testing knowledge of elementary financial derivatives. Topics include nominal and effective interest and discount rates, general accumulation functions and force of interest, yield rates, annuities including those with non-level payment patterns, amortization of loans, sinking funds, bonds, duration, and immunization.

**Chapter 0 An Introduction to the Texas Instruments BA II Plus **(optional)

**Chapter 1 The Growth of Money (7 days)**

· 1.1 Introduction (optional)

· 1.2 What is interest?

· 1.3 Accumulation and Amount Functions

· 1.4 Simple Interest/Linear Accumulation Functions

· 1.5 Compound Interest (The usual case!)

· 1.6 Interest in Advance/The Effective Discount Rate

· 1.7 Discount Functions/The Time Value of Money

· 1.8 Simple Discount

· 1.9 Compound Discount

· 1.10 Nominal Rates of Interest and Discount

· 1.11 A Friendly Competition (Constant Force of Interest)

· 1.12 Force of Interest

· 1.14 Inflation

**Chapter 2 Equations of Value and Yield Rates (4-5 days)**

- 2.1 Introduction (optional)
- 2.2 Equations of Value for Investments Involving a Single Deposit made under Compound Interest
- 2.3 Equations of Value for Investments with Multiple Contributions
- 2.4 Investment Return
- 2.5 Reinvestment Considerations
- 2.6 Approximate Dollar Weighted Yield Rates (optional)
- 2.7 Fund Performance

**Chapter 3 Annuities (Annuities Certain) (11-12 days)**

- 3.1 Introduction (optional)
- 3.2 Annuities Immediate
- 3.3 Annuities Due
- 3.4 Perpetuities & 7.1 Common and Preferred Stock
- 3.5 Deferred Annuities and Values on any Date
- 3.6 Outstanding Loan Balances
- 3.7 Nonlevel Annuities
- 3.8 Annuities with Payments in Geometric Progression
- 3.9 Annuities with Payments in Arithmetic Progression
- 3.10 Yield Rate Examples Involving Annuities (optional)
- 3.11 Annuity Symbols for Nonintegral Terms (optional)
- 3.12 Annuities Governed by General Accumulation Functions (optional)
- 3.13 The Investment Year Method

**Chapter 4 Annuities with Different Payment and Conversion Periods (1-2 days)**

- 4.1 Introduction (optional)
- 4.2 Level Annuities with Payments Less Frequent Than Each Interest Period (optional)
- 4.3 Level Annuities with Payments More Frequent Than Each Interest Period (optional)
- 4.4 Annuities with Payments Less Frequent Than Each Interest Period and Payments in Arithmetic Progression (optional)
- 4.5 Annuities with Payments More Frequent Than Each Interest Period and Payments in Arithmetic Progression (optional)
- 4.6 Continuously Paying Annuities

**Chapter 5 Loan Repayment (2-3 days)**

- 5.1 Introduction (optional)
- 5.2 Amortized Loans and Amortization Schedules
- 5.3 The Sinking Fund Method
- 5.4 Loans with Other Repayment Patterns (optional)
- 5.5 Yield Rate Examples and Replacement of Capital (optional)

**Chapter 6 Bonds (5-6 days)**

- 6.1 Introduction (optional)
- 6.2 Bond Alphabet Soup and the Basic Price Formula
- 6.3 The Premium-Discount Formula
- 6.4 Other Pricing Formulas for Bonds
- 6.5 Bond Amortization Schedules
- 6.6 Valuing a Bond After Its Date of Issue (optional)
- 6.9 Callable Bonds

**Chapter 7 Stocks and Financial Markets (1 day)**

- 7.1 Common and Preferred Stock (cover dividend discount model with §3.4)
- 7.4 Selling Short; Selling Borrowed Stocks (optional)

**Chapter 8 Arbitrage, Term Structure of Interest Rates, and Derivatives (1-2 days)**

- 8.1 Introduction (optional)
- 8.3 The Term Structure of Interest Rates

**Chapter 9 Interest Rate Sensitivity (4-5 days)**

- 9.1 Overview
- 9.2 Duration
- 9.3 Convexity
- 9.4 Immunization (optional)
- 9.5 Other Types of Duration (optional)