# BSc Actuarial Science and Mathematics

Year of entry: 2022

## Course unit details:Financial Mathematics for Actuarial Science 1

Unit code MATH10951 10 Level 1 Semester 1 Department of Mathematics No

### Overview

This unit explores various simple financial topics from a mathematical point of view.

### Pre/co-requisites

For students on the Actuarial Science and Mathematics programme only.

### Aims

Provide an introduction to simple financial transactions as used in actuarial science and the mathematics involved.

### Learning outcomes

On successful completion of this module students will be able to:

• given monthly income and outlay figures, write down a cash flow vector;
• carry out calculations involving simple interest, compound interest, nominal rate of interest,  force of interest and accumulation factors;
• apply discounting  and accumulation to calculate the present and future value of money;
• calculate discounted and accumulated values of cash flow;
• carry out calculations involving continuously payable, p-thly payable, deferred and varying annuities;
• schedule loan repayments and calculate the APR of a repayment scheme; compute the yield of a cash flow.

### Syllabus

1. Brief reminder of underlying mathematics. Geometric Series and Sum, derivatives and integrals, Maclaurin Series for exponential.
2. Brief introduction to role of finance in actuarial science
3. Generalised cashflow model. Inflow and outflow. Examples of simple models
4. Simple and compound interest and discount. The time value of money
5. Interest Rates. The force of interest and nominal rate of interest. Compound interest applied at various time intervals
6. The value of a cashflow at a given time
7. Nomenclature for compound interest functions as applied to annuities certain, deferred annuities and varying annuities
8. Equations of Value
9. Loan Schedules. Calculating Repayments. Flat Rates and APRs

### Assessment methods

Method Weight
Other 20%
Written exam 80%

One in-class test;  Weighting within unit 20%
End of semester examination; Weighting within unit  80%

### Feedback methods

Feedback seminars will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

• Core Reading : Subject CT1, Financial Mathematics. Produced by the Actuarial Profession
• JJ McCutcheon and WF Scott, An Introduction to the Mathematics of Finance, Heinemann, 1986

### Study hours

Scheduled activity hours
Lectures 11
Tutorials 11
Independent study hours
Independent study 78

### Teaching staff

Staff member Role
Jonathan Bagley Unit coordinator

The independent study hours will normally comprise the following. During each week of the taught part of the semester:

·         You will normally have approximately 60-75 minutes of video content. Normally you would spend approximately 2-2.5 hrs per week studying this content independently

·         You will normally have exercise or problem sheets, on which you might spend approximately 1.5hrs per week

·         There may be other tasks assigned to you on Blackboard, for example short quizzes or short-answer formative exercises

·         In some weeks you may be preparing coursework or revising for mid-semester tests

Together with the timetabled classes, you should be spending approximately 6 hours per week on this course unit.

The remaining independent study time comprises revision for and taking the end-of-semester assessment.