Question

A simple interest on a certain sum for 3 years is Rs. 225 and the compound interest on the same sum for 2 years is Rs. 165. Find the rate percent per annum:

• A. \( \text{20%} \)
• B. \( \text{2.5%} \)
• C. \( \text{5%} \)
• D. \( \text{15%} \)

Hint:

Compound interest accumulates faster than simple interest due to interest on previously earned interest.

Answer 1

The Correct Option is A

Using the simple interest formula: \[ SI = \frac{P \times R \times T}{100} \] \[ 225 = \frac{P \times R \times 3}{100} \] \[ P \times R = \frac{225 \times 100}{3} = 7500 \] Now, using the compound interest formula: \[ CI = P \left( \left(1 + \frac{R}{100} \right)^T - 1 \right) \] Substituting the values for \( CI = 165 \) and \( T = 2 \): \[ 165 = P \left( \left(1 + \frac{R}{100} \right)^2 - 1 \right) \] Solving, we get \( R = 20% \).