Maths Literacy Matric Revision: Simple and compound interest

Revision Notes for CAPS Grade 12 Mathematical Literacy: Finance (Simple and Compound Interest)

Introduction

In Mathematical Literacy, understanding finance, especially topics like simple and compound interest, is essential. This knowledge helps in financial planning, investments, and loans management. The key learning objectives include distinguishing between simple and compound interest, using their formulas, and applying these concepts to solve real-life problems.

Key Points

  1. Simple Interest:
  2. Formula: ( A = P(1 + in) )
  3. Where:

    • ( A ) = Total amount at the end of the investment period
    • ( P ) = Principal (initial amount)
    • ( i ) = Annual interest rate
    • ( n ) = Number of years
  4. Compound Interest:

  5. Formula: ( A = P(1 + i)^n )
  6. Where:
    • ( A ) = Total amount at the end of the investment period
    • ( P ) = Principal
    • ( i ) = Annual interest rate
    • ( n ) = Number of years
  7. Compound interest can also be calculated for different compounding periods:
    • Annually: ( A = P(1 + i)^n )
    • Bi-annually: ( A = P\left(1 + \frac{i}{2}\right)^{2n} )
    • Quarterly: ( A = P\left(1 + \frac{i}{4}\right)^{4n} )
    • Monthly: ( A = P\left(1 + \frac{i}{12}\right)^{12n} )

Real-World Applications

Example 1: Simple Interest Calculation

Scenario: John invests R5,000 at an annual simple interest rate of 5% for 3 years.

Solution:
[
\text{A} = 5,000 \times (1 + 0.05 \times 3)
]
[
\text{A} = 5,000 \times 1.15
]
[
\text{A} = 5,750
]
John will have R5,750 after 3 years.

Example 2: Compound Interest Calculation

Scenario: Mary invests R5,000 at an annual interest rate of 5% compounded monthly for 3 years.

Solution:
[
\text{A} = 5,000 \times \left(1 + \frac{0.05}{12}\right)^{12 \times 3}
]
[
\text{A} = 5,000 \times (1 + 0.004167)^{36}
]
[
\text{A} = 5,000 \times 1.161184
]
[
\text{A} = 5,805.92
]
Mary will have R5,805.92 after 3 years.

Common Misconceptions and Errors

  1. Confusing Simple and Compound Interest:
  2. Simple Interest is calculated only on the principal.
  3. Compound Interest is calculated on the principal plus any interest earned.

  4. Misunderstanding Compounding Periods:

  5. Ensure correct use of formulas for different compounding periods.
  6. Always adjust the interest rate and the number of periods accordingly.

Practice and Review

Practice Questions

  1. What is the amount accumulated after 5 years if R2,000 is invested at an annual simple interest rate of 6%?
  2. Calculate the future value of R3,000 invested for 4 years at an annual interest rate of 8% compounded quarterly.
  3. If the interest rate of 10% is compounded bi-annually, what will be the amount after 6 years on an investment of R4,500?

Solutions

  1. ( \text{A} = 2,000 \times (1 + 0.06 \times 5) = 2,000 \times 1.3 = 2,600 )
  2. ( \text{A} = 3,000 \times \left(1 + \frac{0.08}{4}\right)^{4 \times 4} = 3,000 \times (1 + 0.02)^{16} = 3,000 \times 1.3686 = 4,105.80 )
  3. ( \text{A} = 4,500 \times \left(1 + \frac{0.10}{2}\right)^{2 \times 6} = 4,500 \times (1 + 0.05)^{12} = 4,500 \times 1.7959 = 8,081.55 )

Examination Tips

  • Always identify which type of interest is applicable: simple or compound.
  • Carefully read the problem to determine the compounding frequency.
  • Use the correct formula and double-check your calculations for accuracy.

Connections and Extensions

  • Relationship with Algebra: Using algebraic methods to isolate variables and solve equations.
  • Real-World Implications: Understanding how banks calculate interest on savings and loans helps make informed financial decisions.

Summary and Quick Review

  • Simple Interest: ( A = P(1 + in) )
  • Compound Interest: ( A = P(1 + i)^n ) and variations for different compounding periods.

Additional Resources

  • Khan Academy for video tutorials on simple and compound interest.
  • YouTube educational channels like ‘Math Antics’ for easy-to-understand content.

For further details, refer to the specific Mathematical Literacy resource materials included in your curriculum【4:1†source】【4:2†source】【4:3†source】【4:4†source】【4:5†source】【4:6†source】【4:7†source】.

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