What is the difference (in rupees) between the compound interest earned in 1 year on a sum of Rs 25,000 at 20% per annum when interest is compounded semi-annually and when it is compounded annually?

Introduction / Context:
This problem compares the compound interest earned when the same nominal annual rate is compounded with different frequencies: annually versus semi-annually. Although the stated rate is 20% per annum, compounding more frequently leads to a slightly higher effective rate, and the question asks for the difference between the two interest amounts for 1 year.

Given Data / Assumptions:

• Principal P = Rs 25,000.
• Nominal annual rate r = 20% per annum.
• Case 1: Interest compounded annually.
• Case 2: Interest compounded semi-annually (twice a year).
• Time period = 1 year.

Concept / Approach:
For annual compounding, we use factor (1 + r/100). For semi-annual compounding, each half-year uses half the rate, r/2, and there are two compounding periods in one year. Hence, the factor becomes (1 + r/(2*100))^2. We calculate the compound amount in each case, subtract the principal to get interest, and then find the difference between the two interests.

Step-by-Step Solution:
Step 1: Annual compounding: A1 = P * (1 + 20/100) = 25000 * 1.20 = 30000. Step 2: Compound interest for annual case: CI1 = A1 - P = 30000 - 25000 = Rs 5000. Step 3: Semi-annual compounding: Half-yearly rate = 20/2 = 10%. Step 4: Amount after 1 year with semi-annual compounding: A2 = P * (1 + 10/100)^2 = 25000 * (1.10)^2 = 25000 * 1.21 = 30250. Step 5: Compound interest for semi-annual case: CI2 = A2 - P = 30250 - 25000 = Rs 5250. Step 6: Difference in interest: Difference = CI2 - CI1 = 5250 - 5000 = Rs 250.
Verification / Alternative check:
You can also verify by computing the effective annual rate for semi-annual compounding: (1.10)^2 - 1 = 0.21, or 21%. Thus, effective interest is 21% of 25000, which is 5250, confirming the semi-annual interest figure.
Why Other Options Are Wrong:
125, 375, and 500 do not match the precise difference between 21% and 20% of 25000. Those values might occur if the principal or rate were different.
Common Pitfalls:
One common error is to treat both cases as simple interest, in which case there would be no difference. Another is to use 20% for each half-year instead of 10%, which greatly exaggerates the final amount.
Final Answer:
The difference between the two compound interest amounts is Rs 250.