Financial Mathematics
Unit Outlines

Financial Mathematics

AI Generated Advanced 45 hours 10 topics
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Learning Objectives

6 objectives
  • Understand and apply the concept of the time value of money in various financial contexts.
  • Calculate and analyze compound interest, annuities, perpetuities, and their implications on financial decisions.
  • Evaluate investment opportunities using Net Present Value (NPV) and Internal Rate of Return (IRR) methodologies.
  • Understand bond and stock valuation techniques and interpret their market implications.
  • Analyze risk and return measures and apply portfolio management principles to optimize investment outcomes.
  • Explore capital budgeting techniques and comprehend the use of derivatives such as options and futures in financial markets.

Content Outline

Preview

Unit 1198: Advanced Financial Concepts and Investment Analysis

1. The Time Value of Money

1.1 Introduction to Time Value of Money (TVM)

  • Definition and importance in finance
  • Conceptual basis: money today vs. money in the future

1.2 Present Value (PV) and Future Value (FV)

  • Present Value formula and applications
  • Future Value formula and applications

1.3 Compounding and Discounting

  • Compounding: concept and formulas
  • Discounting: concept and formulas
  • Relationship between compounding and discounting

2. Compound Interest

2.1 Compound Interest Principles

  • Definition and difference from simple interest
  • Formula for compound interest

2.2 Frequency of Compounding

  • Annual, semi-annual, quarterly, monthly, continuous compounding
  • Effect of compounding frequency on investment growth

2.3 Impact on Investments and Loans

  • Growth of investments over time
  • Loan amortization and interest accumulation

3. Annuities and Perpetuities

3.1 Types of Annuities

  • Ordinary annuity vs. annuity due

3.2 Annuity Calculations

  • Present value and future value of annuities
  • Formulas and examples

3.3 Perpetuities

  • Definition and characteristics
  • Valuation formula

4. Net Present Value (NPV) and Internal Rate of Return (IRR)

4.1 Investment Decision Criteria

  • Overview of capital budgeting

4.2 Net Present Value (NPV)

  • Definition and calculation
  • Interpretation and decision rules

4.3 Internal Rate of Return (IRR)

  • Definition and calculation methods
  • Comparing IRR with required rate of return

4.4 Comparing NPV and IRR

  • Advantages and limitations of each method

5. Bonds and Bond Valuation

5.1 Basics of Bonds

  • Definition, features, and types

5.2 Bond Pricing

  • Present value of coupon payments and face value

5.3 Yield to Maturity (YTM)

  • Concept and calculation

5.4 Relationship Between Interest Rates and Bond Prices

  • Inverse relationship explained

6. Stock Valuation

6.1 Dividend Discount Models (DDM)

  • Gordon Growth Model
  • Multi-stage growth models

6.2 Price-Earnings (P/E) Ratios

  • Definition and use in valuation

6.3 Discounted Cash Flow (DCF) Analysis

  • Estimating free cash flows
  • Discount rates and valuation

7. Risk and Return

7.1 Understanding Risk

  • Types of risk: systematic vs. unsystematic

7.2 Measuring Return

  • Expected return calculation

7.3 Risk Measures

  • Standard deviation
  • Beta coefficient
  • Sharpe ratio

7.4 Risk-Return Trade-off

  • Concept and practical implications

8. Portfolio Management

8.1 Principles of Portfolio Management

  • Diversification benefits
  • Asset allocation strategies

8.2 Efficient Frontier

  • Concept and graphical representation

8.3 Portfolio Optimization

  • Risk minimization and return maximization

9. Capital Budgeting

9.1 Overview of Capital Budgeting

  • Importance in long-term decisions

9.2 Payback Period

  • Calculation and limitations

9.3 Accounting Rate of Return (ARR)

  • Formula and usage

9.4 Discounted Cash Flow Techniques

  • NPV revisited
  • IRR revisited

10. Options and Futures

10.1 Introduction to Derivatives

  • Definition and types

10.2 Options

  • Call and put options
  • Option pricing basics (intrinsic and time value)

10.3 Futures

  • Contract features
  • Pricing and settlement

10.4 Hedging and Speculation Strategies

  • Using derivatives for risk management
  • Examples and case studies
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Quick Information

Unit Financial Mathematics
Difficulty Advanced
Duration45 hours
Topics10
CreatedJul 19, 2026
GeneratedJul 19, 2026 17:53

Prerequisites

  • Basic understanding of finance and accounting principles
  • Fundamental mathematics including algebra and basic statistics
  • Introductory knowledge of financial markets

Recommended Resources

  • Brealey, R. A., Myers, S. C., & Allen, F. (2020). Principles of Corporate Finance. McGraw-Hill Education.
  • Ross, S. A., Westerfield, R. W., & Jaffe, J. (2019). Corporate Finance. McGraw-Hill Education.
  • Bodie, Z., Kane, A., & Marcus, A. J. (2021). Investments. McGraw-Hill Education.
  • Investopedia (www.investopedia.com) – for supplementary articles and tutorials.
  • Financial calculator or spreadsheet software (e.g., Microsoft Excel) for computations.

Unit Topics

10
The Time Value of Money
Understanding the concept of the time value of money, including present value, future value, compoun...
Compound Interest
Exploring the calculation of compound interest, including formulas, frequency of compounding, and th...
Annuities and Perpetuities
Learning about annuities (ordinary and annuity due) and perpetuities, including calculations for reg...
Net Present Value (NPV) and Internal Rate of Return (IRR)
Analyzing investment decisions using NPV and IRR methods to evaluate the profitability of projects a...
Bonds and Bond Valuation
Understanding the basics of bonds, including bond pricing, yield to maturity, and the relationship b...
Stock Valuation
Examining different methods for valuing stocks, such as dividend discount models, price-earnings rat...
Risk and Return
Discussing the concepts of risk and return in investments, including calculating and interpreting me...
Portfolio Management
Exploring the principles of portfolio management, including diversification, asset allocation, and t...
Capital Budgeting
Evaluating long-term investment decisions using techniques like payback period, accounting rate of r...
Options and Futures
Introducing derivatives like options and futures, examining their characteristics, pricing models, a...