The difference between the compound interest and the simple interest on a certain amount at a rate of interest of 5% per annum for 2 years is Rs.25. Find the amount.

Correct option is A

Given:

Rate = 5%,

Time = 2 years

Formula Used:

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

Simple Interest  = $$\frac{P \times R \times t}{100}$$​​

Solution:

Let the amount = Rs. 100.

CI = $$P \left(1 + \frac{R}{100}\right)^t - P$$​​

CI =$$100 \left(1 + \frac{5}{100}\right)^2 - 100 = 100 \times 1.1025 - 100$$​ = 10.25

Simple interest 

SI = $$\frac{P \times R \times t}{100} = \frac{100 \times 5 \times 2}{100}$$​ = 10

The difference between CI and SI for Rs.100 is 10.25 - 10 = 0.25.

Since the actual difference is Rs. 25, the actual amount is:

Actual amount = $$\frac{100 \times 25}{0.25}$$​ = Rs.10000