# MATH 373 Syllabus

### Theory of Interest for Actuarial Exam FM

Revised: February, 2015

## Course Description

Topics in financial mathematics on the second exam of the Actuarial Societies: interest rates, annuities, accumulation functions, amortization schedules, present values, future values, and bonds. Prerequisites: MATH 255. Three semester hours.

## Objectives

• Given any two of interest rate, present value, or future value, calculate the third based on simple or compound interest.
• Write the equation of value given a set of cash flows and an interest rate.
• Given an annuity with level or non-level payments, immediate (or due), payable m-thly, (or payable continuously), and any three of present value, future value, interest rate, payment, and term calculate the remaining two items.
• Given any four of term of loan, interest rate, payment amount, payment period, principal, calculate the remaining items.
• Given any four of price, redemption value, yield rate, coupon rate, and term of bond, calculate the remaining item.
• Calculate the current value of a set of cash flows.
• Construct an investment portfolio to fully immunize a set of liability cash flows.

## Text

Kellison, Stephen. Theory of Interest, Third Edition. McGraw-Hill/Irwin, 2008.

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

## Attendance Policy

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

## Course Outline

• Chapter 1: The Measurement of Interest (5 class days)
The accumulation and amount function. The effective rate of interest. Simple interest. Compound interest. Present value. The effective rate of discount. Nominal rates of interest and discount. Forces of interest and discount. Varying interest.
• Chapter 2: Solutions of Problems in Interest (2 days)
Equations of value. Unknown time. Unknown rate of interest. Determining time periods.
• Chapter 3: Basic Annuities (5 days)
Annuity-immediate. Annuity-due. Annuity values on any date. Perpetuities. Unknown time. Unknown rate of interest. Varying interest.
• Chapter 4: More General Annuities (4 days)
Differing payment and interest conversion periods. Annuities payable less frequently than interest is convertible. Annuities payable more frequently than interest is convertible. Continuous annuities. Payments varying in arithmetic progression. Payments varying in geometric progression. More general varying annuities. Continuous varying annuities.
• Chapter 5: Amortization Schedules and Sinking Funds (4 days)
Finding the outstanding loan balance. Amortization schedules. Sinking funds. Differing payment periods and interest conversion periods. Varying series of payments.
• Chapter 6: Bonds and Other Securities (4 days)
Types of securities. .Price of a bond. Premium and discount. Valuation between coupon payment dates. Determination of yield rates. Callable and putable bonds. Other securities.
• Chapter 7: Yield Rates (4 days)
Discounted cash flow analysis. Uniqueness of the yield rate. Reinvestment rates. Interest measurement of a fund. Time-weighted rates of interest. Portfolio methods and investment year methods.
• Chapter 9: More Advanced Financial Analysis (1 day)
Recognition of inflation.
• Chapter 10: The Term Structure of Interest Rates (3 days)
Yield curves. Spot rates. Relationship with bond yields. Forward rates.
• Chapter 11: Duration, Convexity and Immunization. (5 days)
Duration. Convexity. Interest sensitive cash flows. Analysis of portfolios. Matching assets and liabilities. Immunization. Full immunization.