STATISTICS

Course Credits: 3 Units

Prerequisites: Math 54(Calculus II)

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MATH 162 - Theory of Interest

Course Description

Math 162 is a course designed for applied math students to have a strong grounding in, and understanding of the basics of actuarial math. Even though the topics from this course maybe theoretical and might overwhelm you, this will be of great help in building a strong foundation in your basic financial skills. Topics for this course include the measurement of interest; solutions of problems in interest; basic annuities; more general annuities; amortization schedules and sinking fund; bonds and other securities.

After completing this course, you will broaden and deepen your knowledge and perspective of the theory of interest and its applications. This course also aims for the students to acquire fundamental knowledge of the concepts and methods in the theory of finance that can be applied in higher mathematical finance subjects and can prepare them for the Financial Mathematics (FM) exam given by the Society of Actuaries.

Course Learning Outcomes

After completion of the course, the student should be able to:

  1. Explain the underlying concepts and methods in the theory of interest.
  2. Apply discrete and continuous compounding of interest.
  3. Apply valuation principles in valuing lump sum amount and series of cash flows.
  4. Compute the values of general annuities, price and yield rate of financial instruments.
  5. Track the growth and diminution of an investment or a loan.
  6. Engage in problem-solving skills using appropriate concepts and tools learned.
Course Outline

UNIT 1. The Measurement of Interest

  1. Introduction
  2. The Accumulation and Amount Functions
  3. The Effective Rate of Interest
  4. Simple Interest and Compound Interest
  5. Present Value and Future Value
  6. Effective Rates of Discount
  7. Nominal Rates of Interest and Discount
  8. Forces of Varying Interest and Discount

UNIT 2. Solutions of Problems in Interest

  1. The Basic Problem
  2. Equations of Value
  3. Unknown Time and Unknown Rate of Interest
  4. Determining Time Periods
  5. Practical Examples

UNIT 3. Basic Annuities

  1. Annuity – Immediate
  2. Annuity – Due
  3. Annuity Values on Any Date
  4. Perpetuities
  5. Unknown Time and Rate of Interest
  6. Varying Interest

UNIT 4. More General Annuities

  1. Differing Payment and Interest Conversion Periods
  2. Annuities Payable Less Frequently than Interest is Convertible
  3. Annuities Payable More Frequently than Interest is Convertible
  4. Continuous Annuities
  5. Basic Varying Annuities

UNIT 5. Amortization Scheduled and Skinking Fund

  1. Finding Outstanding Loan Balance
  2. Amortization Schedules
  3. Sinking Funds
  4. Differing Payment Periods and Interest Conversion Periods
  5. Varying Series of Payments

UNIT 6. Bonds and Other Securities

  1. Types of Securities
  2. Price of a Bond
  3. Premium and Discount
  4. Valuation Between Coupon Payment Dates
  5. Determination of Yield Rates
  6. Callable and Putable Bonds
  7. Serial Bonds
  8. Valuation of Other Securities