The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 4% per annum is Rs 8. The sum is................

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

Rate of interest = 4% and time period = 2 years

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

= $$100x [(1 + \frac{4}{100})^2 - 1]$$

= $$100x [(\frac{26}{25})^2 - 1] = 100x (\frac{676 - 625}{625})$$

= $$100x \times \frac{51}{625} = \frac{204 x}{25}$$

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

= $$\frac{100x \times 4 \times 2}{100} = 8x$$

=> Difference between simple and compound interests = $$\frac{204 x}{25} - 8x = 8$$

=> $$\frac{204x - 200x}{25} = 8$$

=> $$4x = 8 \times 25$$

=> $$x = \frac{8 \times 25}{4} = 2 \times 25 = 50$$

$$\therefore$$ Value of given sum = $$100 \times 50 = Rs. 5,000$$