Course Code: MATH 2211
Course Title: Mathematics of Finance I
Course Type: Core
Level: 2
Semester: 1
No. of Credits: 3
Prerequisite(s): MATH 1141, MATH 1142,
MATH 1151, MATH 1152
Course Rationale
The aim of this course is to provide an understanding of the fundamental concepts of financial mathematics, and how those concepts are applied in calculating present and accumulated values for various streams of cash flows. These cash flows are viewed as a basis for future use in reserving, valuation, pricing, asset/liability management, investment income, capital budgeting and valuing contingent cash flows. The candidate will also be given an introduction to financial instruments.
Course Description
This course covers topics relevant in financial mathematics that include measurement of interest, accumulation and discount, forces of interest and discount, equations of value, annuities, perpetuities, amortization and sinking funds, yield rates, bonds and securities, depreciation, depletion, and capitalized costs.
Assessment is designed to encourage students to work continuously with the course materials. Active learning will be achieved through marked assignments supplemented by problem papers, allowing continuous feedback and guidance on problem solving techniques in tutorials and lectures. Assessment will be based on the marked assignments and incourse tests followed by a final examination based on the whole course. Software used in the actuarial field will be incorporated in the course so that students develop practical skills.
Content
 Introduction to actuarial science;
 Measurement of interest;
 Accumulation and discount
 Forces of interest and discount;
 Equations of value
 Basic annuities;
 Perpetuities
 Yield rates.
 Amortization schedule and sinking funds:
 Bonds
 Common stocks, preferred stocks and other securities Practical applications.
Learning Outcomes
On completion of these modules the student should be able to:
A. Introduction to Actuarial Science
 Apply the basic techniques of actuarial mathematics and its application to insurance, pensions, banking etc.
 Explain the role of actuarial mathematics in the world of finance.
B. Measurement of Interest
 Define the following terms: interest rate (rate of interest), simple interest, compound interest, accumulation function, future value, present value/net present value, discount factor, discount rate (rate of discount), convertible mthly, nominal rate, effective rate, force of interest and equation of value
 Given any two of interest rate, present value, or future value, students will be able to calculate the third based on simple or compound interest.
 Given any one of the effective interest rate, the nominal interest rate convertible mthly, the effective discount rate, the nominal discount rate convertible mthly, or the force of interest, students will be able to calculate all of the other items.
 Write the equation of value given a set of cash flows and an interest rate.
C. Annuities
 Define the following terms: annuityimmediate, annuitydue, perpetuity, payable mthly, level payment annuity, arithmetic increasing/decreasing payment annuity, geometric increasing/decreasing payment annuity, and term of annuity
 Given an annuity with level payments, immediate (or due), payable mthly, and any three of present value, future value, interest rate, payment, and term, calculate the remaining two items.
 Given an annuity with nonlevel payments, immediate (or due), payable mthly, the pattern of payment amounts, and any three of present value, future value, interest rate, payment amounts, and term of annuity, calculate the remaining two items. .
D. Loans
 Define the following terms: principal, interest, term of loan, outstanding balance, final payment (drop payment, balloon payment), amortization, and sinking fund
 Given any four of term of loan, interest rate, payment amount, payment period, principal, calculate the remaining items.
 Calculate:
 The outstanding balance at any point in time.
 The amount of interest and principal repayment in a given payment.
 Given the quantities, except one, in a sinking fund arrangement calculate the missing quantity.
E. Bonds and other Securities
 Define the following terms: price, redemption value, par value/face value, coupon, coupon rate, term of bond, yield rate, callable/noncallable, book value, and accumulation of discount
 Given any four of price, redemption value, yield rate, coupon rate, and term of bond, calculate the remaining item.
F. Yield Rates
 Define the following terms: yield rate/rate of return, dollarweighted rate of return/timeweighted rate of return, current value, duration (Macaulay and modified) , convexity, portfolio, spot rate, forward rate, yield curve, stock price, and stock dividend
 Calculate the following:
 Current value of a set of cash flows.
 Portfolio yield rate.
 Dollarweighted and timeweighted rate of return.
 Duration and convexity of a set of cash flows.
 Either Macaulay or modified duration given the other
 Price of a stock using the dividend discount model.
G. Practical Applications
 Calculate installments for:
 Consumer loans;
 Real estate mortgages;
 Depreciation costs.
Cognitive skills, Core skills and Professional Awareness
 Awareness of the principal statistical methods and models used in assessing problems in interest theory for actuarial work
 Possession of the knowledge required to work in the area of finance in the actuarial context
 Application of the appropriate and rigorous use of mathematical modeling to formulate workable solutions to important financial problems
Teaching Methodology
Lectures: Three lectures per week (50 minutes each)
Tutorial: One weekly tutorial session (50 minutes), based on material covered during lectures.
Assessment Criteria
Mathematics of Finance is assessed by combination of coursework (50%) and a single 2hour written exam at the end of the semester (50%).
Assessment: Incourse Tests 30%
Assignments and Quizzes 20%
Final Exam 50%
Incourse Tests: Two 50minute written papers (15% each) consisting of compulsory questions of varying length
Assignments: Two papers to be submitted: One paper on the first part of the course and the other on the second part of the course. Each assignment is worth 4%. Tutorial practice papers will be given every week to be handed in the next week. Tutorial papers are not graded as part of the course work.
QUIZZES: Six quizzes worth 2% each.
Exam Format: One twohour written paper with compulsory questions.
Course Calendar
Week 
Topic to be taught 
Assessment

1 
Introduction /Course Overview Introduction to actuarial science, measurement of interest 
Tutorial #1 is given 
2 
Accumulation and discount 
Tutorial #2 is given and Tutorial #1 is corrected 
3 
Forces of interest and discount 
Tutorial #3 is given and Tutorial #2 is corrected 
4 
Equations of value, basic annuities 
Tutorial #4 is given and Tutorial #3 is corrected 
5 
Basic annuities, Perpetuities 
First coursework test is given 
6 
Yield rates 
Tutorial #5 is given and Tutorial #4 is corrected. Assignment #1 is given 
7 
Amortization schedules and sinking funds 
Tutorial #6 is given and Tutorial #5 is corrected 
8 
Bonds 
Tutorial #7 is given and Tutorial #6 is corrected 
9 
Duration 
Tutorial #8 is given and Tutorial #7 is corrected 
10 
Immunization 
Second coursework test is given 
11 
Common stocks, preferred stocks and other securities 
Tutorial #9 is given and Tutorial #8 is corrected. Assignment #2 is given. 
12 
Practical applications 
Tutorial #10 is given and Tutorial #9 is corrected 
13 
Revision 
Revision 
Required Readings
The prescribed text is “The Theory of Interest” by Stephen G. Kellison 3^{rd} Edition 2008.
Additional Readings
Other recommended texts that students may find useful are:
 Mathematics of Investment and Credit – Samuel A. Broverman 4^{th} Edition 2008
 Mathematical Interest Theory – Daniel & Vaaler 2009
 Schaum’s Outline:Mathematics of Finance –Petr Zima, Robert L. Brown 2^{nd} Edition 1996.