Q.At an annual interest rate of 4%, what principal amount will yield at least ₹80 difference between simple interest and compound interest over 2 years?

Let the principal amount be ₹\(x\). \[ \therefore \text{Simple interest for 2 years at 4% per annum} = \frac{x \times 4 \times 2}{100} = \frac{2x}{25} \] Compound amount after 2 years at 4% per annum: \[ x\left(1 + \frac{4}{100}\right)^2 = x\left(\frac{104}{100}\right)^2 = x \times \frac{26}{25} \times \frac{26}{25} = \frac{676x}{625} \] \[ \therefore \text{Compound interest} = \left(\frac{676x}{625} - x\right) = \frac{51x}{625} \] According to the condition: \[ \frac{51x}{625} - \frac{2x}{25} = 80 \Rightarrow \frac{51x - 50x}{625} = 80 \Rightarrow x = 80 \times 625 = 50000 \] Therefore, the principal amount is ₹50,000.
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