Question

Equal amounts of each \(₹ 1,000\) is lent to two persons for \(3\) years one @ \(30%\) simple interest and second at \(30%\) compound interest annually. By how much percent is the compound interest greater than the simple interest received in this \(3\) years duration.

• A. \(23%\)
• B. \(33%\)
• C. \(33.33%\)
• D. \(30%\)

Hint:

If the principal is common, the ratio of Interests depends only on $R$ and $T$.
SI rate over 3 years = $30 \times 3 = 90%$.
CI rate over 3 years = $(1.3^3 - 1) \times 100 = 119.7%$.
$% \text{ Greater} = \frac{119.7 - 90}{90} \times 100 = \frac{29.7}{0.9} = 33%$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Simple Interest (SI) is calculated on the principal only, while Compound Interest (CI) is calculated on the principal plus any interest already earned. We need to find the percentage increase of CI over SI.
Step 2: Key Formula or Approach:
\[ SI = \frac{P \times R \times T}{100} \] \[ CI = P \left(1 + \frac{R}{100}\right)^T - P \] Step 3: Detailed Explanation:
1. Calculation for Simple Interest (SI):
\(P = 1000\), \(R = 30%\), \(T = 3\) years.
\[ SI = \frac{1000 \times 30 \times 3}{100} = ₹ 900 \] 2. Calculation for Compound Interest (CI):
\[ CI = 1000 \left(1 + 0.3\right)^3 - 1000 \] \[ CI = 1000 \times (1.3)^3 - 1000 \] \[ CI = 1000 \times 2.197 - 1000 = 2197 - 1000 = ₹ 1197 \] 3. Difference in Interest = \(1197 - 900 = ₹ 297\).
4. Required Percentage = \(\frac{\text{Difference}}{SI} \times 100 = \frac{297}{900} \times 100 = \frac{297}{9} = 33%\).
Step 4: Final Answer:
The compound interest is \(33%\) greater than the simple interest.