Let the given sum = Rs. $$100x$$ Rate of interest = 16% and time period = 2 years Compound interest = $$P [(1 + frac{R}{100})^T - 1]$$ = $$100x [(1 + frac{16}{100})^2 - 1]$$ = $$100x [(frac{29}{25})^2 - 1] = 100x (frac{841 - 625}{625})$$ = $$100x imes frac{216}{625} = frac{864 x}{25}$$ Simple interest = $$frac{P imes R imes T}{100}$$ = $$frac{100x imes 16 imes 2}{100} = 32x$$ => Difference between simple and compound interests = $$frac{864 x}{25} - 32x = 320$$ => $$frac{864x - 800x}{25} = 320$$ => $$64x = 320 imes 25$$ => $$x = frac{320 imes 25}{64} = 5 imes 25 = 125$$ $$ herefore$$ Value of given sum = $$100 imes 125 = Rs. 12,500$$