Mathematical Theory of Interest
Actuaries focus on using math and statistics to evaluate risk and make strategic decisions. This course covers a range of topics relevant to actuaries, including measurement of interest rates, interest theory, and the pricing of bonds, mortgages, annuities, and other financial instruments. This course will also fully cover all content required by the Society of Actuaries Financial Mathematics (FM) Exam and its equivalents.
Syllabus
Course Topics
- Interest Fundamentals
- Accumulation of interest
- Compound, simple, and continuous interest rates
- Effective interest rates
- Present value
- Nominal interest rates
- Discount rates
- The force of interest
- Continuous investment growth
- Actuarial notation
- Annuities
- Level payment annuities
- Present and accumulated annuity value
- Annuities with non-constant payments (geometric & arithmetic progressions)
- Yield and reinvestment rates
- Sinking fund method of evaluation
- Loans
- Loan repayment
- Construction of general amortization schedules
- Level and non-level repayment schemes including:
- Interest only payments with final lump-sum balloon payments
- Sinking-fund loan repayment
- Makeham’s formula
- Bond Investments
- Bond valuation with and without coupon payments
- Premium & discount bonds
- Bond yield rates
- Bond amortization
- Exotic bonds (e.g. callable bonds)
- Pricing Cash Flows
- Rates of return on investments
- Internal rate of return (IRR)
- Modified internal rate of return (MIRR)
- Net-present-value (NPV)
- Dollar and time-weighted rates of return
- The Yield Curve
- Term structure of interest rates
- Spot rates and their arbitrage-free relation to yield rates
- Forward interest rates
- Interest rate swaps & the swap rate
- Introduction to arbitrage opportunities
- Duration, Convexity, & Immunization
- Modified and Macaulay duration of cash flows for bonds
- General cash flows
- Convexity and portfolio immunization (e.g. Redington)
Course Level
200
Disclosure
This course is delivered online through an institution of the Lower Cost Models Consortium (LCMC) that is different than your degree-granting institution that awards the academic credit for the course.
