1. On a certain Principal if the Simple interest for two years is Rs 2400 and Compound interest for the two years is Rs 2544, what is the rate of Interest?
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Time period = 2 years Simple Interest = $$frac{P imes R imes T}{100} = 2400$$ => $$frac{100x imes r imes 2}{100} = 2400$$ => $$2rx = 2400$$ => $$x = frac{2400}{2r} = frac{1200}{r}$$ Compound Interest = $$P [(1 + frac{R}{100})^T - 1] = 2544$$ => $$100x [(1 + frac{r}{100})^2 - 1] = 2544$$ => $$100x [(1 + frac{r^2}{100^2} + 2frac{r}{100}) - 1] = 2544$$ => $$(100 imes frac{1200}{r}) [frac{r^2}{10000} + frac{2r}{100}] = 2544$$ => $$12r + 2400 = 2544$$ => $$12r = 2544 - 2400 = 144$$ => $$r = frac{144}{12} = 12 \%$$