The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 9% per annum is Rs 405. The sum is .

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

Rate of interest = 9% and time period = 2 years

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

= $$100x [(1 + \frac{9}{100})^2 - 1]$$

= $$100x [(\frac{109}{100})^2 - 1] = 100x (\frac{11881 - 10000}{10000})$$

= $$\frac{1881 x}{100}$$

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

= $$\frac{100x \times 9 \times 2}{100} = 18x$$

=> Difference between simple and compound interests = $$\frac{1881 x}{100} - 18x = 405$$

=> $$\frac{1881x - 1800x}{100} = 405$$

=> $$81x = 405 \times 100$$

=> $$x = \frac{405 \times 100}{81} = 5 \times 100 = 500$$

$$\therefore$$ Value of given sum = $$100 \times 500 = Rs. 50,000$$