A sum of Rs. 8,000 is deposited in a bank for 3 years at 5% per annum compound interest, with interest compounded annually. What will be the difference between the total compound interest earned for 3 years and the total compound interest earned for 2 years on the same principal at the same rate?

Introduction:
This compound interest question tests the idea that interest itself earns further interest. We are asked to compare the compound interest earned over 3 years with that earned over 2 years on the same principal at the same rate, and to find the difference between these two interest amounts.

Given Data / Assumptions:
Principal P = Rs. 8,000. Rate of interest r = 5% per annum. Interest is compounded annually. We need CI for 3 years and CI for 2 years, and then their difference.

Concept / Approach:
For annual compounding, the amount after n years is: A = P * (1 + r/100)^n. Compound interest for n years = A − P. The difference between CI for 3 years and CI for 2 years is simply the extra interest earned in the 3rd year on the amount standing after 2 years.

Step-by-Step Solution:
Step 1: Compute amount after 2 years. A₂ = 8000 * (1.05)^2 = 8000 * 1.1025 = Rs. 8,820. Step 2: Compute amount after 3 years. A₃ = 8000 * (1.05)^3 = 8000 * 1.157625 = Rs. 9,261. Step 3: Find CI for 2 years. CI₂ = A₂ − P = 8,820 − 8,000 = Rs. 820. Step 4: Find CI for 3 years. CI₃ = A₃ − P = 9,261 − 8,000 = Rs. 1,261. Step 5: Difference of interests. Difference = CI₃ − CI₂ = 1,261 − 820 = Rs. 441.

Verification / Alternative check:
We can also write directly: Difference = P * (1.05)^2 * (0.05) = 8000 * 1.1025 * 0.05. 8000 * 0.05 = 400; 400 * 1.1025 = 441. This matches our earlier answer exactly.

Why Other Options Are Wrong:
Rs. 387, Rs. 469, Rs. 503 and Rs. 425 all come from incorrect use of the compound interest formula, such as using simple interest logic or miscomputing powers of 1.05.

Common Pitfalls:
Learners sometimes subtract 2 years from 3 years interest by using simple interest formula P * r * t / 100, which is wrong for compound interest. Others forget that the third year interest is on the increased amount after 2 years, not on the original principal alone.

Final Answer:
The difference between the 3 year and 2 year compound interest amounts is Rs. 441.