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?

Let the principal amount = $$Rs. 100x$$ and rate of interest = $$r \%$$

Time period = 2 years

Simple Interest = $$\frac{P \times R \times T}{100} = 2400$$

=> $$\frac{100x \times r \times 2}{100} = 2400$$

=> $$2rx = 2400$$

=> $$x = \frac{2400}{2r} = \frac{1200}{r}$$

Compound Interest = $$P [(1 + \frac{R}{100})^T - 1] = 2544$$

=> $$100x [(1 + \frac{r}{100})^2 - 1] = 2544$$

=> $$100x [(1 + \frac{r^2}{100^2} + 2\frac{r}{100}) - 1] = 2544$$

=> $$(100 \times \frac{1200}{r}) [\frac{r^2}{10000} + \frac{2r}{100}] = 2544$$

=> $$12r + 2400 = 2544$$

=> $$12r = 2544 - 2400 = 144$$

=> $$r = \frac{144}{12} = 12 \%$$