The difference between compound interest and simple interest on a certain sum of money for 2 years at 5% per annum is Rs. 41. What is the sum of money?

Let the given sum = Rs. $$100x$$

Rate of interest = 5% and time period = 2 years

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

= $$100x [(1 + \frac{5}{100})^2 - 1]$$

= $$100x [(\frac{21}{20})^2 - 1] = 100x (\frac{441 - 400}{400})$$

= $$100x \times \frac{41}{400} = 10.25x$$

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

= $$\frac{100x \times 5 \times 2}{100} = 10x$$

=> Difference between simple and compound interests = $$10.25-10x = 41$$

=> $$0.25x = 41$$

=> $$x = \frac{41}{0.25} = 164$$

$$\therefore$$ Value of given sum = $$100 \times 164 = Rs. 16,400$$