Let the given sum = Rs. $$100x$$ Rate of interest = 20% and time period = 2 years Compound interest = $$P [(1 + frac{R}{100})^T - 1]$$ = $$100x [(1 + frac{20}{100})^2 - 1]$$ = $$100x [(frac{6}{5})^2 - 1] = 100x (frac{36 - 25}{25})$$ = $$100x imes frac{11}{25} = 44x$$ Simple interest = $$frac{P imes R imes T}{100}$$ = $$frac{100x imes 20 imes 2}{100} = 40x$$ => Difference between simple and compound interests = $$44x - 40x = 200$$ => $$x = frac{200}{4} = 50$$ ---------------(i) If interest is compounded half yearly, => Compound interest for 1st year = $$P[(1+frac{R}{200})^{2T}-1]$$ = $$100x[(1+frac{20}{200})^2-1]=100x[(frac{11}{10})^2-1]$$ = $$100x (frac{121-100}{100})=21x$$ Similarly, Simple interest for 1st year = $$frac{100x imes 20 imes1}{100}=20x$$ $$ herefore$$ Required difference = $$21x-20x=x=Rs.$$ $$50$$ => Ans - (A)