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A sum of money lent at compound interest for 2 years at 20% per annum would fetch ₹96.4 more interest if compounded half-yearly. Find the sum.

1. ₹4,000
2. ₹2,500
3. ₹3,750
4. ₹4,250

Correct answer: ₹4,000

Solution

Let the principal be $P$. Annual compounding for 2 years gives interest $P(1.2^2-1)=0.44P$. Half-yearly compounding gives interest $P(1.1^4-1)=0.4641P$. Their difference is $0.0241P=96.4$, so $P=4000$.

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