Question

Kamal invested ₹5,500 at compound interest at the rate of R% per annum for 3 years. If the interest received by Kamal after 3 years is equal to 33.1% of the amount invested, then find the value of R.

• A. 11.3
• B. 7.2
• C. 10
• D. 15

Hint:

Standard percentages for Compound Interest at 10% p.a.: 2 years \(\to\) 21%, 3 years \(\to\) 33.1%, 4 years \(\to\) 46.41%. Recognizing 33.1% immediately points to \(R=10%\).

Answer 1

The Correct Option is C

Step 1: Understanding the Formula:
Let \(P\) be the principal amount. The Compound Interest (CI) earned is given as 33.1% of \(P\). Thus, the total amount \(A\) after 3 years is: \[ A = P + CI = P + 0.331P = 1.331P \] The formula for amount in compound interest is: \[ A = P\left(1 + \frac{R}{100}\right)^T \] Step 2: Substitute Values:
Given \(T = 3\) years. Substitute \(A = 1.331P\): \[ 1.331P = P\left(1 + \frac{R}{100}\right)^3 \] Cancel \(P\) from both sides: \[ 1.331 = \left(1 + \frac{R}{100}\right)^3 \] Step 3: Solve for R:
We know that \(11^3 = 1331\), so \(1.1^3 = 1.331\). \[ (1.1)^3 = \left(1 + \frac{R}{100}\right)^3 \] Taking the cube root on both sides: \[ 1.1 = 1 + \frac{R}{100} \] \[ 0.1 = \frac{R}{100} \] \[ R = 10% \]