The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 12% per annum is Rs 72. 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 = $$P [(1 + \frac{R}{100})^T - 1]$$

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

= $$100x [(\frac{112}{100})^2 - 1] = 100x (\frac{12544 - 10000}{10000})$$

= $$\frac{2544 x}{100}$$

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

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

=> Difference between simple and compound interests = $$\frac{2544 x}{100} - 24x = 72$$

=> $$\frac{2544x - 2400x}{100} = 72$$

=> $$144x = 72 \times 100$$

=> $$x = \frac{72 \times 100}{144} = \frac{100}{2} = 50$$

$$\therefore$$ Value of given sum = $$100 \times 50 = Rs. 5000$$