What is the compound interest on Rs. 25000 for 2 years at 5% per annum, when interest is compounded annually?

Introduction / Context:
This is a straightforward compound interest computation with a fixed rate of 5% per annum for 2 years. It is a classic application of the basic compound interest formula and is typically classified as an easier question, but it still requires careful handling of percentage calculations and correct subtraction of principal from the final amount to derive the interest.

Given Data / Assumptions:

• Principal P = Rs. 25000.
• Rate of interest r = 5% per annum.
• Time period n = 2 years.
• Interest is compounded annually.
• We must find the compound interest CI, not just the amount.

Concept / Approach:
For annual compounding, the amount A after n years is given by A = P * (1 + r) ^ n, where r is the annual rate expressed as a decimal. Once the amount is found, the compound interest is calculated as CI = A - P. Because the number of years is small and the rate is moderate, we can compute the powers of (1 + r) exactly and get a precise answer without excessive rounding. This reinforces the direct use of the standard formula.

Step-by-Step Solution:
Step 1: Convert the rate to decimal form: r = 5% = 0.05. Step 2: Compute the growth factor: (1 + r) = 1 + 0.05 = 1.05. Step 3: Compute the amount after 2 years: A = 25000 * (1.05) ^ 2. Step 4: Calculate (1.05) ^ 2 = 1.1025. Step 5: Multiply to get the amount: A = 25000 * 1.1025 = 27562.50. Step 6: Compute the compound interest: CI = A - P = 27562.50 - 25000 = 2562.50. Step 7: Therefore, the required compound interest is Rs. 2562.50.

Verification / Alternative check:
A simple verification method is to compute interest year by year. At the end of the first year, interest is 5% of 25000, which is 1250, so the amount becomes 26250. At the end of the second year, interest is 5% of 26250, which equals 1312.50. Total interest over two years is 1250 + 1312.50 = 2562.50. This matches the result we obtained using the compound interest formula, confirming the correctness of our calculation from two independent approaches.

Why Other Options Are Wrong:
The option 2500 is the simple interest for two years (25000 * 0.05 * 2) and ignores compounding, so it is slightly lower than the correct compound interest. The option 2425.25 is not supported by any correct sequence of calculations at 5% and appears to result from a misapplied percentage or arithmetic error. The option 5512.50 is far too large and would correspond to a much higher rate or a longer time period. The option 2600 is close but still higher than the actual value and might be due to rounding mistakes or treating 5% twice on an inflated base without exact computation.

Common Pitfalls:
Learners sometimes accidentally compute simple interest instead of compound interest when the rate and time look simple, as in this case. Another common mistake is to treat the rate as 0.5 instead of 0.05 because of a misinterpretation of the percent sign. Some candidates also use (1 + 2r) instead of (1 + r) ^ 2 for two years, which is only valid for a linear approximation and not for actual compounding. Careful squaring of 1.05 and correct multiplication with the principal are key to avoiding such errors.

Final Answer:
The compound interest on Rs. 25000 for 2 years at 5% per annum compounded annually is Rs. 2562.50, which is option B.