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(A) Let the principal be $P$.When interest is compounded half-yearly,the rate $R = 20/2 = 10 \% \, p.a.$ and time $T = 2 	imes 2 = 4$ half-years.$CI_

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$40000$

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(A) Let the principal be $P$.When interest is compounded half-yearly,the rate $R = 20/2 = 10 \% \, p.a.$ and time $T = 2 	imes 2 = 4$ half-years.$CI_{half-yearly} = P \left[ (1 + 10/100)^4 - 1 ight] = P \left[ (1.1)^4 - 1 ight] = P (1.4641 - 1) = 0.4641 P$.When interest is compounded annually,the rate $R = 20 \% \, p.a.$ and time $T = 2$ years.$CI_{annually} = P \left[ (1 + 20/100)^2 - 1 ight] = P \left[ (1.2)^2 - 1 ight] = P (1.44 - 1) = 0.44 P$.According to the question,the difference is $Rs. 964$:$0.4641 P - 0.44 P = 964$$0.0241 P = 964$$P = 964 / 0.0241 = 40000$.Thus,the sum is $Rs. 40000$.

$A$ sum of money lent at compound interest for $2 \, yr$ at $20 \% \, p.a.$ would fetch $Rs. 964$ more,if the interest was payable half-yearly than if it was payable annually. What is the sum (in $Rs.$)?

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