The difference between simple and compound interests, compounded annually, on acertain sum of money for 2 years at 5% per annum is ₹1,600. Find the sum (in ₹).

Correct option is D

Given:

The difference between simple and compound interest for 2 years = ₹1600

Rate of interest = 5% per annum.

Time period = 2 years.

Formula Used:

The difference between CI and SI for 2 years is given by:

Difference = $$P \times \left(\frac{R}{100}\right)^2$$​​

Solution:

Substituting values into the formula:

$$1600 = P \times \left(\frac{5}{100}\right)^2$$​​

​$$1600 = P \times \frac{25}{10000}$$​​

​$$P = \frac{1600\times 10000}{25} = 640000$$​​

Thus, the sum of money is ₹6,40,000