ILLUSTRATING SIMPLE AND COMPOUND INTEREST || GRADE 11 GENERAL MATHEMATICS Q2

Introduction

This tutorial is designed to help you understand and illustrate the concepts of simple and compound interest as part of your Grade 11 General Mathematics curriculum. Mastering these topics is essential for both academic success and practical financial literacy.

Step 1: Understanding Simple Interest

Simple interest is calculated using the following formula:

[ \text{Simple Interest (SI)} = P \times r \times t ]

Where:

• P = Principal amount (initial investment)
• r = Annual interest rate (in decimal)
• t = Time (in years)

Example Calculation

1. Identify the principal amount (P), for example, $1,000.
2. Determine the interest rate (r), such as 5% (0.05 in decimal).
3. Decide the time period (t), for instance, 3 years.
4. Plug in the values:

[ SI = 1000 \times 0.05 \times 3 = 150 ]

Practical Tip

For quick calculations, remember that the interest earned each year is simply the principal multiplied by the rate.

Step 2: Understanding Compound Interest

Compound interest differs from simple interest as it is calculated on the principal amount and also on the accumulated interest from previous periods. The formula for compound interest is:

[ A = P \left(1 + \frac{r}{n}\right)^{nt} ]

Where:

• A = Amount of money accumulated after n years, including interest.
• P = Principal amount.
• r = Annual interest rate (in decimal).
• n = Number of times that interest is compounded per year.
• t = Time (in years).

Example Calculation

1. Let’s say the principal (P) is $1,000, the annual interest rate (r) is 5% (0.05), compounded annually (n=1), for 3 years (t=3).
2. Calculate the total amount:

[ A = 1000 \left(1 + \frac{0.05}{1}\right)^{1 \times 3} ]

[ A = 1000 \left(1 + 0.05\right)^{3} ]

[ A = 1000 \times (1.05)^{3} \approx 1157.63 ]

Common Pitfall

Many students forget to adjust the interest rate and time period correctly for different compounding frequencies. Always check the value of n to ensure your calculations are accurate.

Step 3: Comparing Simple and Compound Interest

To illustrate the difference between simple and compound interest:

• Calculate both types of interest over the same period and principal amount.
• For example, using the previous examples with $1,000 at 5% for 3 years:
  • Simple interest resulted in $150.
  • Compound interest resulted in approximately $157.63.

Key Observation

Compound interest generates more returns over time compared to simple interest due to the effect of interest on interest.

Conclusion

Understanding simple and compound interest is crucial for making informed financial decisions. This tutorial covered the formulas, example calculations, and practical tips for both concepts. To deepen your knowledge, practice with different principal amounts, interest rates, and time periods. Consider exploring how these principles apply to savings accounts, loans, and investment opportunities.