The difference between the compound interest (compounded annually) and the simple interest on a certain sum at 10% per annum for 2 years is ₹547. Find the sum.

Correct option is B

Given:

Rate of interest = 10% per annum

Time = 2 years

Difference between compound interest and simple interest = ₹547

Formula Used:

Simple Interest (SI) =$$\frac{P \times R \times T}{100}$$​​

Compound Interest (CI) = $$P \times \left(1 + \frac{R}{100}\right)^T - P$$​​

Difference between CI and SI = P $$× \left(\frac{R}{100}\right)^2$$​​

Solution:
Let the sum be P.

Simple Interest (SI) =$$\frac{P \times 10 \times 2}{100} = \frac{20P}{100} = \frac{P}{5}$$​​

Compound Interest (CI) = $$P \times \left(1 + \frac{10}{100}\right)^2 - P = P \times \left(1.1\right)^2 - P = P \times 1.21 - P = 0.21P$$​​

Difference between CI and SI = 0.$$21P - \frac{P}{5} = 547$$​​

0.21P - 0.2P = 547

0.01P = 547

P $$= \frac{547}{0.01} = 5$$​4700