# F78AA Actuarial and Financial Mathematics A

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

• 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