The difference between simple and compound interests compounded annually on a certain sum of money for 2 years at 18% per annum is Rs 81. The sum is ...................

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

Rate of interest = 18% and time period = 2 years

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

= $$100x [(1 + \frac{18}{100})^2 - 1]$$

= $$100x [(\frac{118}{100})^2 - 1] = 100x (\frac{13924 - 10000}{10000})$$

= $$\frac{3924 x}{100}$$

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

= $$\frac{100x \times 18 \times 2}{100} = 36x$$

=> Difference between simple and compound interests = $$\frac{3924 x}{100} - 36x = 81$$

=> $$\frac{3924x - 3600x}{100} = 81$$

=> $$324x = 81 \times 100$$

=> $$x = \frac{81 \times 100}{324} = \frac{100}{4} = 25$$

$$\therefore$$ Value of given sum = $$100 \times 25 = Rs. 2500$$