Interest Growth Comparison: Simple vs. Compound

This question asks us to evaluate an Assertion (A) and a Reason (R) about how different types of interest affect investment growth. Let's break down the concepts of simple and compound interest.

Simple Interest Explained

Simple Interest is calculated only on the initial amount of money invested, which is called the principal (P). The interest earned does not get added back to the principal for future interest calculations. The formula for calculating Simple Interest (SI) is:

$ SI = \frac{P \times R \times T}{100} $

Where:

• P = Principal amount
• R = Rate of interest per year
• T = Time period in years

With simple interest, the amount of interest earned each year is constant.

Compound Interest Explained

Compound Interest is calculated on the initial principal amount and also on the accumulated interest from previous periods. Essentially, you earn "interest on interest." This causes the investment to grow at a faster rate over time compared to simple interest. The formula for the final amount (A) with compound interest is:

$ A = P \left(1 + \frac{R}{100}\right)^T $

The compound interest earned is $CI = A - P$.

Assertion (A) Truthfulness

Assertion (A): Compounding interest allows an investment to grow faster over time compared to simple interest.

This assertion is true. Because compound interest includes interest earned on previously earned interest, the total amount grows exponentially. In contrast, simple interest grows linearly because it's always based only on the original principal.

Example: Invest $1000 at 10% per year.

• Simple Interest: Earns $100 each year (10% of $1000). After 3 years, total interest is $300, and the total amount is $1300.
• Compound Interest:
  • Year 1: Interest = $100. Total = $1100.
  • Year 2: Interest = $110 (10% of $1100). Total = $1210.
  • Year 3: Interest = $121 (10% of $1210). Total = $1331.
  After 3 years, the total amount is $1331, which is more than with simple interest.

Reason (R) Accuracy

Reason (R): Simple interest earns interest on Previously earned interest.

This reason is false. This description accurately defines *compound* interest, not simple interest. Simple interest is calculated *only* on the principal amount. It does not take into account any interest that may have been earned previously.

Conclusion on Assertion and Reason

Based on the analysis:

• Assertion (A) is factually correct. Compounding does lead to faster growth.
• Reason (R) is factually incorrect. It misrepresents how simple interest works.

Therefore, the correct option is the one stating that Assertion (A) is true, but Reason (R) is false.