**Course co-ordinator(s):** Dr Karamjeet Singh (Malaysia), Peter Ridges (Edinburgh), Dr Haslifah Hasim (Dubai).

**Aims:**

To introduce the student to simple mathematical models of cashflows accumulated or discounted at interest, and to develop skill in applying these models to real financial contracts and transactions

**Summary:**

- Simple interest
- Compound interest and discount
- Time units and effective rates of interest
- Accumulations and present values of discrete-time cashflows
- Varying rates of interest
- Annuities
- Yields
- Measuring rates of return
- Loan schedules
- Fixed-interest securities
- Discounted Cash Flows

## Detailed Information

**Course Description: **Link to Official Course Descriptor.

**Pre-requisites:** none.

**Linked course(s):** F78AB Actuarial and Financial Mathematics B .

**Location: **Edinburgh, Malaysia.

**Semester: **1.

**Syllabus:**

- Simple interest
- Compound interest and discount
- Time units and effective rates of interest
- Accumulations and present values of discrete-time cashflows
- Varying rates of interest
- Annuities
- Yields
- Measuring rates of return
- Loan schedules
- Fixed-interest securities
- Discounted Cash Flows
- Stochastic interest rate models
- Inflation indexing and index-linked bond

**Learning Outcomes: Subject Mastery**

On completion of this course the student should be able to:

- Describe the basic concepts of simple and compound interest.
- Calculate the present value or accumulation of any set of discrete-time cashflows, at constant or varying rates of interest.
- Derive and use simple formulae for values of level and increasing annuities-certain.
- Explain the concept of the yield on a series of cashflows, and its limitations.
- Calculate time-weighted, money-weighted and internal linked rates of return.
- Analyse loan schedules, including simple alterations.
- Describe basic fixed-interest securities, and calculate prices and yields allowing for tax..
- Understand the discounted cash flow model and know what are internal rates of return (IRR), net present values (NPV) and break-even durations.
- Explain the concept of a stochastic interest rate model.
- Calculate the mean value and the variance of the accumulated amount of a single premium for a stochastic interest rate model in which the annual rates of return are independently and identically distributed (and also do this for other simple models).
- Calculate the mean value and the variance of the accumulated amount of a level annual premium for a stochastic interest rate model in which the annual rates of return are independently and identically distributed.
- Understand how an appropriate inflation index (such as the RPI) may be used to measure changes in the value of money with time.
- Understand how an appropriate index may be used to increase the monetary amounts of the future cash flows associated with a given `index-linked' investment and, in particular, how the RPI is used to determine the future payments of interest and capital associated with index-linked government securities.
- Know, in relation to a given inflation index, what is meant by the `real yield' for a particular investment and be able to calculate such yields.
- Use an appropriate computer package to apply the methods introduced in this course.

**Learning Outcomes: Personal Abilities**

- Interpreting problems from commercial practice in terms of relevant mathematical models
- Independently recognizing and applying appropriate mathematical techniques to solve problems
- Interpreting solutions expressed mathematically in terms of the original problem
- Communicating the solutions to complex problems in the financial services sector

**Reading list:**

- Garrett, S.J. (2013). An Introduction to the Mathematics of Finance (second edition). Butterworth-Heinemann.
- Zima, P. & Brown, R.L. (1996).
*Schaumâ€™s Outline: Mathematics of Finance (Second Edition)*, McGraw Hill.

**Assessment Methods:** Due to covid, assessment methods for Academic Year 2021/22 may vary from those noted on the official course descriptor. Please see:

- Maths (F1) Course Weightings 2021/22

- Computer Science (F2) Course Weightings 2021/22

- AMS (F7) Course Weightings 2021/22

**SCQF Level: **8.

**Credits:** 15.

## Other Information

**Help:** If you have any problems or questions
regarding the course, you are encouraged to contact the course leader.

**Canvas:** further information and course materials
are available on Canvas