Ajay invested some money in HDFC at 4% per annum rate of interest. What would be the corresponding simple interest (in Rs.) if after 2 years, Ajay got Rs. 204 as compound interest, considering annual compounding?

Correct option is B

Given:
Rate of interest (r) = 4% per annum
Time (t) = 2 years
Compound Interest (CI) = ₹204
Formula Used:
​$$\text{CI} = P \left(1 + \frac{R}{100} \right)^T - P\\\ \\\text{SI} = \frac{P \times R \times T}{100}$$​​
Solution:
Let the principal amount be P.
​$$\text{CI} = P \left(1 + \frac{4}{100} \right)^2 - P \\204 = P(1.04)^2 - P \\204 = P(1.0816) - P \\204 = P(1.0816 - 1) \\204 = P(0.0816) \\P = \frac{204}{0.0816} = 2500$$​​
Now, we need to calculate the simple interest (SI) for the same principal, rate, and time.
​$$\text{SI} = \frac{P \times r \times t}{100} \\\ \\\text{SI} = \frac{2500 \times 4 \times 2}{100} \\\ \\\text{SI} = \frac{20000}{100} \\\ \\\text{SI} = 200$$​​
∴ The simple interest is ₹200.