Question

Indu gives Bindu a loan of Rs \(1250\) for \(2\) years at \(4%\) annual compound interest rate. How much rupee would he have lost if he had given that amount on loan for \(2\) years at \(4%\) simple interest?

• A. \(10\)
• B. \(8\)
• C. \(3\)
• D. \(2\)

Hint:

Remember: \[ \text{CI} - \text{SI} = P\left(\frac{R}{100}\right)^2 \] for \(2\) years. This shortcut saves time in competitive exams.

Answer 1

The Correct Option is D

Concept: Difference between Compound Interest (CI) and Simple Interest (SI) for \(2\) years is: \[ \text{CI} - \text{SI} = P\left(\frac{R}{100}\right)^2 \] where:

• \(P\) = Principal
• \(R\) = Rate of interest

Step 1: Write the given values. Principal: \[ P = 1250 \] Rate: \[ R = 4% \] Time: \[ T = 2 \text{ years} \]

Step 2: Use the formula for difference between CI and SI. \[ \text{Difference} = 1250\left(\frac{4}{100}\right)^2 \] \[ = 1250 \times \frac{16}{10000} \] \[ = 1250 \times 0.0016 \] \[ = 2 \] Thus, the extra amount earned in compound interest over simple interest is: \[ 2 \text{ rupees} \] Hence, if the amount had been given at simple interest, the loss would be: \[ \boxed{2} \]