Q.If the compound interest on ₹5,000 for 2 years is ₹408, what is the annual rate of interest?

Let the annual rate of interest be \(x\%\). ∴ The total amount after 2 years on ₹5000 with compound interest = ₹\(5000 + 408 = 5408\) According to the condition: \[ 5000 \times \left(1 + \frac{x}{100}\right)^2 = 5408 \Rightarrow \left(1 + \frac{x}{100}\right)^2 = \frac{5408}{5000} = \frac{676}{625} \Rightarrow 1 + \frac{x}{100} = \sqrt{\frac{676}{625}} \Rightarrow \frac{x}{100} = \frac{26}{25} - 1 = \frac{1}{25} \Rightarrow x = \frac{1}{25} \times 100 = 4 \] ∴ The annual rate of interest was 4%.
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