In a compound interest calculation, what will be the compound interest on a principal of Rs. 25,000 invested for 2 years at 5% per annum, if the interest is compounded annually?

Introduction:
In this question we apply the basic compound interest formula for a fixed principal, a known annual rate, and a small number of years. The aim is to compute only the compound interest earned, not the final amount, on Rs. 25,000 invested at 5% per annum for 2 years with annual compounding.

Given Data / Assumptions:

• Principal (P) = Rs. 25,000
• Rate of interest (r) = 5% per annum
• Time (t) = 2 years
• Interest is compounded once every year (annually)

Concept / Approach:
The compound amount after t years at rate r with principal P is given by:
A = P * (1 + r/100)^tOnce we find A, the compound interest (CI) is simply:
CI = A - PThis approach ensures that we first compute the total amount and then subtract the original principal to obtain the interest portion only.

Step-by-Step Solution:
Step 1: Convert the percentage rate to a decimal factor: r/100 = 5/100 = 0.05.Step 2: Use the formula A = P * (1 + r/100)^t.Step 3: Compute the growth factor (1 + r/100) = 1 + 0.05 = 1.05.Step 4: Raise this factor to the power of 2 years: (1.05)^2 = 1.05 * 1.05 = 1.1025.Step 5: Multiply by the principal to get the amount: A = 25,000 * 1.1025 = 27,562.5.Step 6: Subtract the principal to obtain the compound interest: CI = A - P = 27,562.5 - 25,000 = 2,562.5.Thus the compound interest earned over 2 years is Rs. 2,562.5.

Verification / Alternative check:
We can cross check by computing the interest year by year. For the first year, interest is 5% of 25,000 which is Rs. 1,250. The new amount becomes 26,250. For the second year, interest is 5% of 26,250 which equals Rs. 1,312.5. Adding the two years interests gives 1,250 + 1,312.5 = 2,562.5, which matches the previous result.

Why Other Options Are Wrong:
Option 2500 ignores the effect of compounding and treats the situation as simple interest only. Option 2425.25 corresponds to an incorrect rate or incorrect number of years. Option 2600 and option 2700 are rounded or guessed values that do not result from the correct compound interest calculation.

Common Pitfalls:
Students often confuse simple interest and compound interest and may simply multiply principal * rate * time without considering compounding. Another common mistake is to forget to square the factor (1.05) for 2 years, which leads to incorrect results. Careful attention to the formula and exponent is essential.

Final Answer:
The correct compound interest earned on Rs. 25,000 at 5% per annum compounded annually for 2 years is Rs. 2,562.5.