Actuarial Science Program
DEPARTMENT OF MATHEMATICS
Math 210
Theory of Interest
|
Fall,
2008 |
|
|
|
319
Gregory Hall |
|
374 Altgeld Hall |
|
|
|
Phone: 244-1739 |
|
|
|
Office
Hours: or by appointment |
|
|
|
E-mail: |
Required Text: Mathematics of Investment and Credit by Broverman
(2004, 3rd Edition)
Course web page: http://www.math.uiuc.edu/~gorvett/m210f08/home.html
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 the mortgage payment of
a homeowner 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 material in the Broverman
text, in the process thoroughly exploring 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,
loan 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 understand and 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.
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.
Course
Schedule
Some key dates for the
class are noted below:
|
August 26 (Tuesday) |
First day of class:
Introduction and Motivation |
|
September 25
(Thursday) |
Exam # 1 |
|
October 30 (Thursday) |
Exam # 2 |
|
December 9 (Thursday) |
Last day of class |
|
December 17
(Wednesday, |
Exam # 3 |
In most non-exam weeks,
there will be a homework assignment and one or more short in-class or other
assignments. In addition, practicing actuaries will be invited to give guest
presentations to the class on several occasions 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) |
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 two worst
in-class/other assignment scores will be dropped. 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.
|
September 18 |
Registration deadline
for CAS Exam 3L (for Nov 2008) |
|
September 24 |
Registration deadline
for Exams 2/FM, MLC, 3F/MFE, 4/C (for Nov 2008) |
|
October 2 |
Registration deadline
for Exam 1/P (for Nov 2008) |
|
October 28 |
CAS Exam 3L |
|
November 3 |
Exam 4/C |
|
November 4 |
Exams MLC and 3F/MFE |
|
November 4-10 |
Computer-based Exam
2/FM |
|
November 18-24 |
Computer-based Exam
1/P |
Class Summaries
|
Date |
Class Topic |
Class Session Summary |
Assignments |
Textbook |
Other Items / Links |
|
Aug. 26 |
Introduction and
motivation. |
Review of syllabus. Motivation via
historical and financial context. |
|
|
|
|
Aug. 28 |
Basics of the Theory
of Interest. |
Accumulation and
amount functions. Simple versus compound
interest. Effective versus
nominal interest. |
Chapter 1.1, 1.4 |
|
|
|
Sep. 2 |
Basics of the Theory
of Interest (cont.). |
More on simple versus
compound interest. Nominal interest
rates. |
Chapter 1.3 |
|
|
|
Sep. 4 |
Basics of the Theory
of Interest (cont.). |
Force of interest. Present value. |
Chapter 1.2, 1.5 |
|
|
|
Sep. 9 |
Basics of the Theory
of Interest (cont.). |
Rate of discount. Variable rates of
interest. |
Chapter 1.4 |
||
|
Sep. 11 |
Basic Annuities |
Annuities immediate
and due. Present and
accumulated values of annuities. |
Chapter 2.1 |
||
|
Sep. 16 |
Basic Annuities
(cont.) |
Finding annuity values
at any point in time. |
Chapter 2.2 |
|
|
|
Sep. 18 |
Basic Annuities
(cont.) |
Perpetuities. Non-annual annuities. Varying interest. |
|
||
|
Sep. 23 |
Review for Exam 1 |
Went over exam from
last year. |
|
|
|
|
Sep. 25 |
Exam # 1 |
In 106 and 192 Begins at One 3-inch by 5-inch notecard allowed. Any type of calculator
allowed. |
|
|
|
|
Sep. 30 |
Advanced annuities |
Handed back and
reviewed Exam 1. Different interest
convertibility and payment periods. |
|
Chapter 2.2 |
|
|
Oct. 2 |
Advanced annuities
(cont.) |
Continuous annuities. Arithmetically varying
annuities. |
Chapter 2.3 |
|
|
|
Oct. 7 |
Advanced annuities
(cont.) |
Arithmetically and
geometrically varying annuities. Continuously varying
continuous annuities. |
|
Chapter 2.3 |
|
|
Oct. 9 |
Rate of return
measurement |
Time-weighted rates of
return. Dollar-weighted rates
of return. |
Chapter 5.2 |
||
|
Oct. 14 |
Rate of return
measurement (cont.) |
Net present value. Internal rate of
return. |
Chapter 5.1 |
|
|
|
Oct. 16 |
Rate of return
measurement (cont.) |
Reinvestment rates. |
Chapter 2.4.1 |
||
|
Oct. 21 |
Loans |
Principal versus
interest. Amortization
schedules. |
Chapter 3.1 and 3.2 |
||
|
Oct. 23 |
Loans (cont.) |