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(B) Step $1$: Find the principal $P$ using the annual compounding condition.For $2$ years at $10 \%$ p.a.:$C.I. = P[(1 + 0.1)^2 - 1] = P[1.21 - 1] = 0

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$31.01$

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(B) Step $1$: Find the principal $P$ using the annual compounding condition.For $2$ years at $10 \%$ p.a.:$C.I. = P[(1 + 0.1)^2 - 1] = P[1.21 - 1] = 0.21P$$S.I. = (P 	imes 2 	imes 10) / 100 = 0.2P$Given $C.I. - S.I. = 20$,so $0.21P - 0.2P = 20 \Rightarrow 0.01P = 20 \Rightarrow P = 2000$.Step $2$: Calculate the difference if interest is compounded half-yearly.For half-yearly compounding,rate $r = 5 \%$ per half-year,and time $n = 4$ half-years.$C.I. = P[(1 + 0.05)^4 - 1] = 2000[(1.05)^4 - 1]$$(1.05)^4 = 1.21550625$$C.I. = 2000[0.21550625] = 431.0125$$S.I. = (P 	imes 2 	imes 10) / 100 = 2000 	imes 0.2 = 400$Difference $= 431.0125 - 400 = 31.0125 \approx ₹ 31.01$.

The difference between compound interest and simple interest on a sum for $2$ years at $10 \%$ per annum,when the interest is compounded annually,is ₹ $20$. If the interest were compounded half-yearly,the difference in the two interests (in ₹) will be:

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