Explaining the Difference Between Simple and Compound Interest Using Real-Life Examples

Understanding the difference between simple and compound interest is crucial in managing personal finances, making investments, and planning long-term goals.

Introduction to Simple Interest

Simple interest is a straightforward type of interest calculation where the interest is calculated only on the principal amount over a certain period. It does not consider the accumulated interest from previous periods. The formula to calculate simple interest is:

Simple Interest (SI) P × R × T / 100

Where:

P Principal amount (initial investment) R Rate of interest per year (as a percentage) T Time period (in years)

Introduction to Compound Interest

Compound interest, on the other hand, involves interest being added to the principal amount of a loan or deposit, thus increasing the base amount for further calculation of interest. It is calculated on the initial principal and also on the accumulated interest of previous periods.

Example Problem

The difference between simple and compound interest on a sum of money for 2 years at 10% per annum is Rs. 65. What is the sum?

Let the principal amount (P) be Rs. 100. Time (T) 2 years. Rate (R) 10%.

Calculate Simple Interest (SI)

Simple Interest (SI) P × R × T / 100

100 × 10 × 2 / 100

Calculate Compound Interest (CI)

Compound Interest (CI) P × (1 R/100)^T - P

100 × (1 10/100)^2 - 100

100 × (1.1)^2 - 100

100 × 1.21 - 100

Difference Between CI and SI

Difference CI - SI 21 - 10 11

To find the principal amount when the difference is Rs. 65:

11 65 * P / 100

P (11 * 100) / 65 17.31

Solving for the Principal Amount

Let the principal be Rs. 10. For 2 years at 10% interest:

Simple Interest (SI) P × R × T / 100 10 × 10 × 2 / 100 2 Compound Interest (CI) P × (1 R/100)^T - P 10 × (1 10/100)^2 - 10 10 × (1.1)^2 - 10 10 × 1.21 - 10 2.1

Difference CI - SI 2.1 - 2 0.1

Using the relationship:

1.08^2 - 1.08^2 96

Solving, P 15000

Another Real-Life Example

Let the principal Rs. 100. For 2 years:

Simple Interest (SI) 100 × 10 × 2 / 100 20 Compound Interest (CI) 100 × (1 10/100)^2 - 100 100 × 1.21 - 100 21

Difference CI - SI 21 - 20 1

Therefore, for every Rs. 1 of difference, the principal amount is Rs. 100. So, for Rs. 65 difference, the principal amount is:

Principal (65 × 100) / 1 6500

Conclusion

Simple interest and compound interest are two different ways of calculating interest. Understanding their differences is vital for making informed financial decisions. By using these formulas and real-life examples, one can easily solve problems related to interest and plan for financial growth.