Question

The difference between CI and SI for a loan is \rupee114 when invested for 2 years at the rate of 6\% per annum. Find the loan amount.

• A. \rupee31,667
• B. \rupee41,667
• C. \rupee51,667
• D. None of the above

Hint:

For two years, the extra compound interest over simple interest comes only from “interest on interest,” which is \(P \times (R/100)^2\). This is a fast shortcut to solve such problems.

Answer 1

The Correct Option is A

Step 1: Recall the formula.
The difference between compound interest (CI) and simple interest (SI) for 2 years is given by \[ \text{Difference} = P \times \left(\frac{R}{100}\right)^2 \] where \(P\) is the principal (loan amount), and \(R\) is the rate of interest per annum. Step 2: Substitute the known values.
Here, Difference \(=114\), \(R=6\%\). \[ 114 = P \times \left(\frac{6}{100}\right)^2 \] Step 3: Simplify.
\[ 114 = P \times \frac{36}{10000} \] \[ 114 = \frac{36P}{10000} \] \[ P = \frac{114 \times 10000}{36} \] Step 4: Calculate.
\[ P = \frac{1,140,000}{36} = 31,666.6\ldots \] Rounding to nearest integer gives \[ P \approx \rupee 31,667 \] \[ \boxed{\rupee 31,667} \]