The difference between the compound interest and the simple interest for a period of 2 years at the rate  of 10% per annum is Rs. 50. Find the principal.

Let the principal amount = $$Rs. 100x$$

Time = 2 years and rate = 10%

=> $$C.I. = P [(1 + \frac{R}{100})^T - 1]$$

= $$100x [(1 + \frac{10}{100})^2 - 1]$$

= $$100x [(\frac{11}{10})^2 - 1] = 100x (\frac{121 - 100}{100})$$

= $$100x \times \frac{21}{100} = 21x$$

=> $$S.I. = \frac{P \times R \times T}{100}$$

= $$\frac{100x \times 10 \times 2}{100} = 20x$$

It is given that difference between compound and simple interest = $$21x - 20x = 50$$

=> $$x = 50$$

$$\therefore$$ Principal = $$100 \times 50 = Rs. 5,000$$