The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 16% per annum is Rs 320. What is the value of given sum (in Rs)?

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

Rate of interest = 16% and time period = 2 years

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

= $$100x [(1 + \frac{16}{100})^2 - 1]$$

= $$100x [(\frac{29}{25})^2 - 1] = 100x (\frac{841 - 625}{625})$$

= $$100x \times \frac{216}{625} = \frac{864 x}{25}$$

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

= $$\frac{100x \times 16 \times 2}{100} = 32x$$

=> Difference between simple and compound interests = $$\frac{864 x}{25} - 32x = 320$$

=> $$\frac{864x - 800x}{25} = 320$$

=> $$64x = 320 \times 25$$

=> $$x = \frac{320 \times 25}{64} = 5 \times 25 = 125$$

$$\therefore$$ Value of given sum = $$100 \times 125 = Rs. 12,500$$