What is the difference between compound interests on ₹5,000 compounded yearly and half-yearly for 1 year at 4% per annum?

Correct option is B

Given:
Principal (P) = ₹5000.
Rate of interest (r) = 4% per annum.
Time (t) = 1 year.
Formula Used:
$$\text{CI compounded yearly} = P \left(1 + \frac{r}{100}\right)^t - P$$ 
​$$\text{CI compounded half-yearly} = P \left(1 + \frac{r}{200}\right)^{2t} - P$$​​
Solution:
​$$\text{CI compounded yearly} = P \left(1 + \frac{r}{100}\right)^t - P = 5000 \left(1 + \frac{4}{100}\right)^1 - 5000 = 5000 \times 1.04 - 5000 = 200$$​​
For half-yearly compounding, r = $$\frac r2 = \frac42$$​ = 2%, and t = 2t = 2.
​$$\text{CI compounded half-yearly} = P \left(1 + \frac{r}{200}\right)^{2t} - P = 5000 \left(1 + \frac{2}{200}\right)^2 - 5000 = 5000 \times 1.02^2 - 5000 = 202.00$$​​
Difference = CI(compounded half-yearly) - CI(compounded yearly) = ₹202.00 - ₹200 = ₹2.00.
Alternate Solution:
Compounded yearly rate = 4%
Compounded half-yearly rate = 2%
Net interest: 2 + 2 × (2 × 2)/100 = 4.04%
Difference = 4.04% - 4% = 0.04%
Difference in Amount = 0.04% × 5000 = Rs. 2