## MATH1515 Interest Rates and Cashflow Modelling

### 15 creditsClass Size: 410

Module manager: Dr Esmaeil Babaei Khezerloo
Email: E.BabaeiKhezerloo@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2022/23

### Pre-requisite qualifications

Grade B in A-level Mathematics or equivalent.

Module replaces

MATH1510

This module is approved as a discovery module

### Module summary

This module serves as an introduction to financial mathematics, the application of mathematics to financial problems. We will look at simple financial transactions, like mortgages, annuities and government bonds, and study how to assign a value to them. Central concepts are interest rates and the time value of money (the idea that one pound now is preferable to one pound later). This theory can then be used to evaluate investment projects.

### Objectives

- Introduction to mathematical modelling of financial and insurance markets with particular emphasis on the time-value of money and interest rates.
- Introduction to simple financial instruments.
- This module covers a major part of the Faculty and Institute of Actuaries CM1 syllabus (Actuarial Mathematics 1).

Learning outcomes
On completion of this module, students should be able to:
- understand the time value of money and to calculate interest rates and discount factors
- apply these concepts to the pricing of simple, fixed-income financial instruments and the assessment of investment projects.

### Syllabus

1. Interest rates. Simple interest rates. Present value of a single future payment. Discount factors.
2. Effective and nominal interest rates. Real and money interest rates. Compound interest rates. Relation between the time periods for compound interest rates and the discount factor.
3. Term structure of interest rates.
4. Compound interest functions. Annuities and perpetuities.
5. Loans.
6. Introduction to fixed-income instruments. Generalized cashflow model.
7. Net present value of a sequence of cashflows. Equation of value. Internal rate of return. Investment project appraisal.
8. Examples of cashflow patterns and their present values.
9. Elementary compound interest problems.
10. Effective duration, convexity and portfolio immunisation.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 22 1.00 33.00 Practical 9 1.00 9.00 Private study hours 108.00 Total Contact hours 42.00 Total hours (100hr per 10 credits) 150.00

### Private study

Consolidation of course notes and background reading: J. McCutcheon, W.F. Scott "An Introduction to Mathematics of Finance".

### Opportunities for Formative Feedback

- Assessment of coursework assignments.
- Contact during tutorials.

!!! In order to pass the module, students must pass the examination. !!!

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment Assignment . 20.00 In-course Assessment Weekly Quizzes 5.00 Total percentage (Assessment Coursework) 25.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 30 mins 75.00 Total percentage (Assessment Exams) 75.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated