The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 8% per annum is Rs 40. What is the sum?

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 = $$\frac{P \times R \times T}{100}$$

= $$\frac{100x \times 8 \times 2}{100} = 16x$$

=> Difference between simple and compound interests = $$\frac{1664 x}{100} - 16x = 40$$

=> $$\frac{1664x - 1600x}{100} = 40$$

=> $$64x = 40 \times 100$$

=> $$x = \frac{4000}{64} = \frac{500}{8} = 62.5$$

$$\therefore$$ Value of given sum = $$100 \times 62.5 = Rs. 6250$$