Mathematics and Financial Concepts Breakdown

Aug 1, 2024

Lecture Notes on Mathematics and Financial Concepts

1. Introduction to Mathematics Section

  • Transition from logical reasoning to mathematics.
  • Importance of calculations for mathematics and statistics.

2. Mathematics Syllabus

  • Total Chapters: 8
  • Weightage: 40 marks (objective)
  • Chapter Weightage:
    • Ratio, Proportion, Indices, Logarithms: 4-5 marks
    • Equations: 3-4 marks
    • Linear Inequalities: 1-2 marks
    • Time Value of Money: 12-16 marks
    • Permutations and Combinations: 3-4 marks
    • Sequences and Series: 3-4 marks
    • Sets, Relations and Functions: 3-4 marks
    • Differential and Integral Calculus: 4-5 marks

3. Importance of Calculations

  • Calculation is key to solving problems in mathematics and statistics.
  • Memory calculation: Using the calculator effectively to save time.

4. Memory Calculations

  • Use the memory function of the calculator (M+ for storing, M- for negative values, MRC for recalling).
  • Example of complex calculations and how to simplify using memory functions.

5. Syllabus Overview

  • Mathematics Syllabus Breakdown:
    • Focus on shortcut methods and efficient problem-solving techniques.

6. Time Value of Money

  • Concept: The idea that the value of money changes over time due to factors like inflation.
  • Key Terms:
    • Present Value (PV): The current value of money.
    • Future Value (FV): The value of money at a future date.

7. Interest Calculations

  • Simple Interest (SI): Calculated on the principal amount only.
  • Compound Interest (CI): Calculated on the principal plus previously earned interest.
  • Understanding how to calculate both SI and CI effectively using formulas.

8. Annuities and Their Applications

  • Annuity: A fixed amount paid regularly for a specified time.
  • Types of Annuities:
    • Ordinary Annuity: Payments made at the end of each period.
    • Annuity Due: Payments made at the beginning of each period.
  • Future Value of Annuity: Formula to calculate future value of regular payments.
  • Present Value of Annuity: Formula to calculate the present value of future annuity payments.

9. Effective Rate of Interest

  • The effective rate of interest takes compounding into account and is generally higher than the nominal rate when compounding occurs more than once per year.
  • Formula:
    • For effective rate: E = (1 + i/n)^(nt) - 1
    • Where i = nominal rate, n = number of compounding periods per year, t = number of years.

10. Depreciation

  • Concept: Value of assets decreases over time.
  • How to calculate depreciation using different formulas based on the method of depreciation chosen (straight-line, reducing balance etc.).

11. Valuation of Bonds

  • Bond: A debt security indicating a loan made by an investor to a borrower.
  • How to calculate the present value of a bond based on its future cash flows.

12. Investment Decision Making

  • How to decide between leasing and purchasing based on present value calculations.
  • Importance of comparing present value of cash inflows against cash outflows.

13. Exercises and Practice Questions

  • Go through previous years' papers to practice problems related to the above concepts.
  • Focus on understanding types of questions and applying the appropriate methods for solving them.