If the compound interest on a sum for 2 years at 5% per annum is ₹102.50, what is the sum?
₹1,000
For 2 years the compound interest on principal \(P\) at rate \(R\%\) is \(CI = P\left[\left(1+\frac{R}{100}\right)^2 - 1\right]\).
With \(R = 5\%\), the factor is \(\left(1+\frac{5}{100}\right)^2 = \left(\frac{21}{20}\right)^2 = \frac{441}{400}\).
So \(CI = P\left(\frac{441}{400}-1\right) = P \times \frac{41}{400}\).
Setting this equal to 102.50: \(P \times \frac{41}{400} = 102.5\).
Therefore \(P = \frac{102.5 \times 400}{41} = 1000\).
Hence, the sum is ₹1,000.
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