MATH 2620

Financial Mathematics

This is an introductory course to financial mathematics, please see the course syllabus for details. Main topics include interest rates, annuities, loans, financial instruments, etc.; most, if not all, of them are test topics of the SOA FM Exam.

The required textbook is: Chris Ruckman and Joe Francis. Financial Mathematics: A Practical Guide for Actuaries and other Business Professionals (Second Edition), 2005.

The materials in this site are being updated on a regular (weekly) basis in Fall 2020.

Chapter 1 Interest Rates

Lecture Slides & Annotated Version

1.1 Interest and 1.2 Simple Interest (video1 & notes)
1.2 Sub-content Decreasing Impatience (video2 & notes)
1.3 Compound Interest (video3 & notes)
1.4 Accumulated Value and 1.5 Present Value (video4 & notes)
1.6 Rate of Discount (video5 & notes)
1.7/1.8 Constant/Varying Force of Interest Rate (video6 & notes)
1.9 Discrete Changes in Interest Rates and 1.10 Summary (video7 & notes)
Chapter 1 Practice Questions (video8 & notes)
Chapter 1 Review (video9 & notes)
Chapter 1 SOA Questions (video10, video11 & notes)

Chapter 2 Preliminaries: Sequences

Lecture slides & Annotated Version & video12

Chapter 2 Level Annuities

Lecture slides

2.1 Introduce: definitions of all kinds of annuities (video13 & notes)
2.2 Pricing Annuities: Annuity-Immediate and Annuity-Due (video14 & notes)
2.2 Pricing Annuities: Deferred Annuity (video15 & notes)
Quick Summary of 2.1-2.3 (video16 & notes)
2.4 Continuously payable annuity & 2.5 Perpetuity (video17 & notes)
2.6 Equation of values (video18 & notes)
Chapter 2 Practice Questions (video19, video20 & notes)
Chapter 2 SOA Questions (video21 & notes)

Exam 1 (Ch1 & Ch2)

Practice Exam 1 (video22 & notes)
Exam 1 (Exam & Solutions)

Chapter 3 Varying Annuities

Lecture slides

3.1 Increasing Annuity-Immediate (video23 & notes)
3.2 Increasing Annuity-Due (video24 & notes)
3.3/3.4 Decreasing Annuity-Immediate/Due (video25 & notes)
3.5 Continuously Payable Varying Annuities (video26 & notes)
3.6 Compound Increasing Annuities (video27 & notes)
3.7 Continuously Varying Annuities (video28 & notes)
3.8/3.9 Continuously Increasing/Decreasing Annuities (video29 & notes)
Chapter 3 Practice Questions (video30 & notes)
Chapter 3 SOA Questions (video31 & notes)

Chapter 4 Non-Annual Interest Rates and Annuities

4.1 Non-Annual Interest Rate and Discount Rate (video32 & notes)
4.2 Nominal pthly Interest Rate (video33 & notes)
4.3 Nominal pthly Discount Rate (video34 & notes)
4.4 Annuity-Immediate Payable pthly (video35, video36 & notes)
4.5 Annuity-Due Payable pthly (video37 & notes)
4.6 Increasing pthly Annuities (video38 & notes)
4.7 pthly Increasing pthly Annuities (video39 & notes)
Chapter 4 Practice Questions (video40 & notes)

Exam 2 (Ch3 & Ch4)

Exam 2 Review (video41 & notes)
Exam 2 (video42 & notes, Exam & Solutions)

Chapter 5 Project Appraisal and Loans

5.1 Discounted Cash Flow Analysis (video43, video44 & notes)
5.2 Nominal and Real Interest Rates (video45 & notes)
5.3 Investment Funds (video46, video47 & notes)
5.4 Allocating Investment Income (video48 & notes)
5.5 Loan Amortization (video49 & notes & Ex.5.15 Excel)
5.6 Sinking Fund Method (video50 & notes)
Chapter 5 Practice Questions (notes)

Chapter 6 Financial Instruments

6.1 Types of Financial Instruments (video51 & notes)
6.2 Bond Valuation (video52 & notes; video53 & notes; video54 & notes; Ex.6.7 Excel)
6.3 Stock Valuation (video55 & notes)
Chapter 6 Practice Questions (notes)

Exam 3 (Ch5 & Ch6)

Exam 3 (Exam & Solutions)