# School of Mathematical and Computer Sciences

## F78AA Actuarial and Financial Mathematics A

Lecturer:G. Reid

#### Aims

This course aims to provide students with an introduction to the basic concepts and models of financial mathematics.

#### 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
• Inflation indexing
• Discounted Cash Flows
• Nominal rates of interest

#### Learning outcomes

At the end of studying this course, students 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 how an appropriate inflation index (such as the Retail Price Index) may be used to measure changes in the value of money with the passage of 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 what, in relation to a given inflation index, is meant by the `real yield' for a particular investment and be able to calculate such yields.
• Understand, the discounted cash flow model and know what internal rates of return (IRR), net present values (NPV) and break-even durations are
• Describe and calculate nominal rates of interest

McCutcheon & Scott is a required text. It is available from the Faculty and Institute of Actuaries at a discounted price. Zima & Brown is an American book and uses slightly different terminology in places, but is a source of hundreds of exercises and examples.

• McCutcheon, J.J. & Scott, W.F. (1986). An Introduction to the Mathematics of Finance, Heinemann.
• Zima, P. & Brown, R.L. (1996). Schaum's Outline: Mathematics of Finance (Second Edition), McGraw Hill.

#### Assessment

There will be a two-hour end-of-course examination, contributing 90\% of the total mark. During the second half of the semester there will be an Excel-based assignment counting for 10\% of the total mark.

#### Help

If you have any problems or questions regarding the course, you are encouraged to contact the lecturer, Gavin Reid, in CM S19

#### Course web page

Further information and course materials are available on Vision.
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