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Mohan invested a sum at the rate of 15% simple interest per annum for two years and received a total amount of ₹9984. He invested the same amount at the rate of \(x\)% per annum at compound interest for two years and received ₹6500 more interest than the simple interest. Find the value of \(x\) approximately.

1. 46.50%
2. 30.50%
3. 25.50%
4. 35.50%

Correct answer: 46.50%

Solution

From SI, the amount after 2 years is \(P(1+0.15\times2)=1.3P=9984\), so \(P=7680\). The extra interest in CI over SI for 2 years is \(P(r/100)^2\), which is given as 6500. Solving gives \(7680(r/100)^2=6500\), so \(r\approx 46.5\%\).

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