Let the given sum = Rs. $$100x$$ Rate of interest = 8% and time period = 2 years Compound interest = $$P [(1 + frac{R}{100})^T - 1]$$ = $$100x [(1 + frac{8}{100})^2 - 1]$$ = $$100x [(frac{108}{100})^2 - 1] = 100x (frac{11664 - 10000}{10000})$$ = $$frac{1664 x}{100}$$ Simple interest = $$frac{P imes R imes T}{100}$$ = $$frac{100x imes 8 imes 2}{100} = 16x$$ => Difference between simple and compound interests = $$frac{1664 x}{100} - 16x = 40$$ => $$frac{1664x - 1600x}{100} = 40$$ => $$64x = 40 imes 100$$ => $$x = frac{4000}{64} = frac{500}{8} = 62.5$$ $$ herefore$$ Value of given sum = $$100 imes 62.5 = Rs. 6250$$