**PAPER NO.2 FINANCIAL MATHEMATICS **

**GENERAL OBJECTIVE**

This paper is intended to equip the candidate with knowledge, skills and attitudes that will enable him/her to apply financial mathematics in decision making.

**LEARNING OUTCOMES**

A candidate who passes this paper should be able to:

- Compute present and future values of cash flows
- Apply financial forecasting techniques in business
- Apply mathematical functions in finance
- Apply statistical tools in finance
- Use of probability to solve business problems
- Compute and interpret index numbers
- Use of financial calculators to solve financial

### CONTENT

** ****Introduction to financial mathematics**

- Nature and scope of finance; financing, investment, management of working capital and profit sharing (dividend policy) decisions
- Relationship between finance and other disciplines; finance and economics, finance and accounting, finance and mathematics
- Purpose of financial modeling

### Financial algebra

- Simultaneous and quadratic equations
- Developing finance functions
- Interactive graphs; graphing financial functions
- Overview of calculator operations: Turning on and off the calculator, selecting second functions, setting calculator formulae, clearing calculator memory, mathematical operations, memory operations, using worksheets

### Time value of money and interest rate mathematics

- Concept of interest rates and inflation
- Simple interest
- Compound interest
- Continuously compounded interest
- Present values
- Basics of capital budgeting
- Loan amortisation
- Time value of money and amortisation worksheets, entering variables in amortisation worksheets, entering cash inflows and outflows, generating amortisation schedules
- Cash flow worksheets; calculator worksheet variables for both even and uneven and grouped cash flow, entering, deleting, inserting and computing results
- Bond worksheets: Bond worksheets variables and terminology, entering bond data and computing results
- Depreciation worksheets; depreciation worksheet variables, entering data and computing results
- Other worksheets: Percentage change/compound interest worksheets, interest conversion worksheets, profit margin worksheets, break-even worksheets, memory worksheets

### Financial forecasting

- Need for financial forecasting
- Techniques of forecasting: statistical and non-statistical methods
- Time-series components and analysis
- Share valuation
- Fixed income models for bonds and construction of yield curves
- Regression and correlation
- Use of financial calculators in regression and correlation models, entering data, computing the results and interpretation

### Financial calculus

- Introduction to calculus
- Differentiation; ordinary and partial derivatives
- Integration
- Application of calculus to solve financial problems relating to maximisation of returns and minimisation of costs

### Descriptive statistics

- Measures of central tendency; mean, mode, median
- Measures of relative standing; quartiles, deciles, percentiles
- Measures of dispersion; range, mean deviation, variance, standard deviation, coefficient of variation
- Statistical worksheets; statistical worksheet variables, computing statistical results and interpretation

### Probability theory

- Relevance of probability theory
- Events and probabilities
- Probability rules
- Random variables and probability distributions
- Binomial random variables
- Expected value
- Variance and standard deviation
- Probability density function
- Normal probability distribution
- Stochastic functions
- Application of probability to solve business problems

### Index numbers

- Purpose of index numbers
- Construction of index numbers
- Simple index numbers; fixed base method and chain base method
- Weighted index numbers; Laspeyre’s, Paasche’s, Fisher’s ideal and Marshall- Edgeworth’s methods
- Consumer Price Index (CPI)
- Use of Consumer Index Price (CPI); inflation, cost of living
- Limitations of index numbers

### Emerging issues and trends