Govind 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, Govind got Rs. 178.5 as compound interest, considering annual compounding?

Correct option is A

Given:
​​Rate of interest (r) = 4% per annum
​​Time (t) = 2 years
​​Compound Interest (CI) = 178.5
​​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.
​​​​$$\text{Given: Compound Interest} = 178.5, \quad R = 4\%, \quad T = 2 \text{ years} \\CI = P \left( \left(1 + \frac{R}{100} \right)^2 - 1 \right) \\178.5 = P \left( \left(1 + \frac{4}{100} \right)^2 - 1 \right)\\178.5 = P \left( (1.04)^2 - 1 \right)\\178.5 = P (1.0816 - 1)\\178.5 = P \times 0.0816\\ P = \frac{178.5}{0.0816}$$​​​​
​​Now, we need to calculate the simple interest (SI) for the same principal, rate, and time.
​​​$$\text{SI} = \frac{P \times r \times t}{100} \\\ \\\text{SI} = \frac{ \frac{178.5}{0.0816} \times 4 \times 2}{100} \\\ \\\text{SI}= 175$$​​​​
​​∴ The simple interest is ₹175​