University of Illinois at Urbana-Champaign
Department of Mathematics - Actuarial Science Program

MATH 210 - Theory of Interest

Spring 2008

319 Gregory Hall
10:30-11:50 AM Tuesday and Thursday
Course Web Site: http://www.math.uiuc.edu/~rhubsch2/m210s08/

Instructor: Ryan J. Hubscher
Email: rhubsch2! at !uiuc dot eduDeleteTheExtraCharactersAndExclamationMarksFromMyEmailAddress
Office Hours: Time: Wednesday 1-2:50 PM or by appointment
Location: The basement of Coble Hall

Required Text: Broverman, Samuel A. Mathematics of Investment and Credit (2004, 3rd Edition).

Course Overview

What is an interest rate? How is the value of a corporate bond or a share of common stock determined? How big will a mortgage payment be each month, and how is that affected by differing interest rates, or different frequencies of payments? What are the financial calculations underlying retirement plans and annuities? These and other questions can be straight-forwardly answered with a basic understanding of an important financial and actuarial topic: the theory of interest. In essence, you can think of Math 210 as a first course in financial mathematics; as such, you will find this course to be a mathematical gateway for all your future actuarial science and finance courses.

We will cover most of the first 5 chapters of the Boverman text and limited sections from chapters 6-8, comprising a thorough exploration of the mathematical theory of interest. Some of the specific topics and concepts covered will include: interest and discount rates, simple versus compound interest, nominal versus effective rates, present value, annuities and perpetuities of many types, yield rates, amortization schedules and sinking funds, the pricing of financial instruments such as stocks and bonds, duration and convexity, and short sales. Other topics may be covered, depending upon time constraints. Emphasis will be placed on the ability to solve problems dealing with these concepts. We will also discuss the broader financial and actuarial contexts and implications of this material.

This course will help you prepare for the interest theory material on the Exam 2/FM national actuarial examination, co-sponsored by the Casualty Actuarial Society and the Society of Actuaries. In addition to this course, you should also study derivative markets on your own or in a different class and take Math 370 Section Z to prepare for Exam 2/FM.

Accessibility Statement

To insure that disability-related concerns are properly addressed throughout the semester, students with disabilities who require reasonable accommodations to participate in this class are asked to contact me within the first two weeks of class.

Key Dates

January 15 (Tuesday) First day of class: Introduction and Motivation
February 26 Exam # 1 (approximately textbook Chs. 1-2)
April 3 Exam # 2 (approx. Chs. 3-4)
April 29 (Tuesday) Last day of class
May 2 (Friday 8:00-11:00 AM) Comprehensive Final Exam (mostly from chapters 5-8)

In most non-exam weeks, there will be a homework assignment and one or more short in-class assignments. In addition, practicing actuaries may be invited to give guest presentations to the class during the semester.

Grading

Course grades will be determined based on the following weights:

Homework assignments 20 %
In-class/other assignments 5 %
Exams 75 % (25% each)

Final letter grades will be assigned as follows:

A+ [97, 100]
A [93, 97)
A- [90, 93)
B+ [87, 90)
B [83, 87)
B- [80, 83)
C+ [77, 80)
C [73, 77)
C- [70, 73)
D+ [67, 60)
D [63, 67)
D- [60, 63)

Exams may not be made up or taken at different times, except in extremis. In general, the grade weight for a missed exam (provided there is a valid excuse) will accrue equally to any remaining exams. A missed in-class or homework assignment may not be made up. However, in calculating your course score and grade, your worst homework assignment score will be dropped. Thus, if you miss one homework assignment, it will count as your drop. Similarly, your lowest two in-class assignment scores will be dropped in determining your overall grade. Class attendance is expected; serious attendance problems may result in a grade lower than that indicated by the weighting system above.

Please note that the final exam schedule is prescribed by the university; in general, instructors are not permitted to change the final exam timing of their courses.

Calculators

On exams, you may use a TI-89 or any calculator inferior to the TI-89. Computers may not be used. Students preparing for exam 2/FM are strongly encouraged to use SOA approved calculators for Exam 2/FM. Students may use more than one calculator on the exam. I recommend using both the Texas Instrument's BA II Plus and the TI-30 II (IIS solar or IIB battery) simultaneously. This will give you the best preparation for Exam FM.

Calendar

Date Topic Summary Reading Assignments Other
Jan 15 Introduction Syllabus, Interest rate history, CAS vs SOA   HW1 Due Jan 24 Day 1 Presentation
Interest rate history (3-month T-bills)
Bean Actuary
SOA website
CAS website
Jan 17 Interest Basics Accumulation and amount functions. Simple and compound interest. 1.1    
Jan 22 Interest Basics Present value. Equations of value. 1.2    
Jan 24 Interest Basics Nominal rates of interest. Effective and nominal rates of discount. 1.3-1.4 HW2 Due Jan 31 HW1 Solution
Jan 29 Interest Basics Rates of discount. Force of interest. Inflation 1.4-1.6    
Jan 31 Annuities Accumulated value of annuities. 2.1.1 HW3 Due Feb 7 HW2 Solution
February 5 Annuities PV of annuities. Annuitie-immediate vs annuity-due. 2.1.2-2.1.3    
February 7 Annuities Differing interest and payment period. 2.2.1 HW4 Due Feb 14
ICA1 Solution
HW3 Solution
February 12 Annuities Continuous annuities. Unknown time. Unknown interest. 2.2.2-2.2.4    
February 14 Annuities Varying annuities. Annuities in Excell. 2.3   HW4 Solution
February 19 Review Chapter 1.   ICA2 Solution  
February 21 Annuities Varying annuities. 2.3    
February 26 Exam 1   Sections 1.1-2.3   Exam 1a Solution
Exam 1b Solution
February 28 Annuities Varying annuities. 2.3 HW5 Due Mar 6 Examples 1
March 4 Loans Amortization Schedules 3.1-3.2   Examples 2 (Excel)
March 6 Loans Amortization 3.1-3.2 HW6 Due Mar 13 HW5 Solution
HW5 Solution (Excel)
March 11 Loans Sinking Funds 3.3   Examples 3 (Excel)
Examples 4 (Sinking Fund Schedule)
March 13 Yield Rates Net present value. Internal rate of return. 5.1, 2.4.1   HW6 Solution
HW6 Solution (Excel)
March 18   Spring Break. No Class.   HW7 Due Apr 1  
March 20   Spring Break. No Class.      
March 25 Yield Rates Dollar-weighted rate of return. Reinvestment rates. 5.2, 2.4.1    
March 27 Yield Rates Book value vs market value. Time-weighted rate of return. 5.2, 2.4.4 HW8 Due Apr 10
ICA3 Solution
Examples 5 (TWRR)
April 1 Bonds Price of a bond on a coupon date and between coupon dates. Premium/Discount. Accrued coupon. 4.1 ICA4 Solution Examples 6 (Bond pricing)
HW7 Solution
April 3 Exam 2 HW 5-7, ICA 3-4     Exam 2a Solution
Exam 2b Solution
April 8 Bonds Bond/Premium Amortization. 4.2    
April 10   Guest Speakers: Tamara Johnson, Scott Christenson, Tim Ellison.   HW9 Due Apr 22 HW8 Solution
April 15 Bonds Callable bonds. 4.3.1   Examples 7 (Callable bonds)
April 17 More Yield Rates Investment Year and Portfolio Year methods. Yield curve. Spot rates. Foward rates. 5.3.1, 6.1, 6.3   Examples 8
April 22 Financial Mathematics Macaulay Duration. Modified Duration. 7.1 HW10 Due Apr 29  HW9 Solution
April 24 Financial Mathematics Exact asset liability matching. Immunization. 7.2    
April 29 Financial Mathematics Last Day of Class. Immunization. 7.2 ICA5 Solution HW10 Solution
May 1   Reading Day. No Class.      
May 2
(Friday)
Exam 3 Bring one double sided 8.5x11 note sheet. Questions will be on HW8, HW9, HW10, ICA5, and some reading from chapter 8.