The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 12% per annum is Rs 900. What is the value of given sum (in Rs)?

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

Rate of interest = 12% and time period = 2 years

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

= $$100x [(1 + \frac{12}{100})^2 - 1]$$

= $$100x [(\frac{28}{25})^2 - 1] = 100x (\frac{784 - 625}{625})$$

= $$100x \times \frac{159}{625} = \frac{636 x}{25}$$

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

= $$\frac{100x \times 12 \times 2}{100} = 24x$$

=> Difference between simple and compound interests = $$\frac{636 x}{25} - 24x = 900$$

=> $$\frac{636x - 600x}{25} = 900$$

=> $$36x = 900 \times 25$$

=> $$x = \frac{900 \times 25}{36} = 25 \times 25 = 625$$

$$\therefore$$ Value of given sum = $$100 \times 625 = Rs. 62,500$$