The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 5% per annum is Rs 45. The sum is

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

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

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

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

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

= $$100x \times \frac{41}{400} = \frac{41 x}{4}$$

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

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

=> Difference between simple and compound interests = $$\frac{41 x}{4} - 10x = 45$$

=> $$\frac{41x - 40x}{4} = 45$$

=> $$x = 4 \times 45 = 180$$

$$\therefore$$ Value of given sum = $$100 \times 180 = Rs. 18,000$$

=> Ans - (C)