Find the compound interest on Rs. 2,680 at 8% per annum for 2 years, if interest is compounded annually.

Introduction / Context:
This question asks you to calculate the compound interest on a given principal with a moderate rate and a 2-year term. It reinforces the use of the compound interest formula and careful handling of decimals when the amount does not come out as a clean integer.

Given Data / Assumptions:
- Principal P = Rs. 2,680.
- Rate r = 8% per annum.
- Time n = 2 years.
- Compounding is annual.
- We must find the compound interest, not the final amount alone.

Concept / Approach:
Use the compound amount formula:
A = P * (1 + r/100)^n.
For r = 8% and n = 2 years, the factor is (1.08)^2. Once we compute the amount A, the compound interest is C.I. = A - P. Because the numbers are not round, we keep a couple of decimal places and then match with the nearest option provided.

Step-by-Step Solution:
Step 1: Write A = 2680 * (1 + 8/100)^2.Step 2: Simplify: 1 + 8/100 = 1.08.Step 3: Compute (1.08)^2 = 1.1664.Step 4: So A = 2680 * 1.1664.Step 5: Multiply: A ≈ 3125.952.Step 6: Compound interest C.I. = A - P ≈ 3125.952 - 2680 = 445.952.Step 7: Rounding to two decimal places, C.I. ≈ Rs. 445.95.

Verification / Alternative check:
You can do it year by year: After 1 year, amount = 2680 * 1.08 = 2894.4. After 2 years, amount = 2894.4 * 1.08 ≈ 3125.952, which matches the earlier computation. Subtracting the original 2680 again gives ≈ 445.952, confirming the compound interest value and its rounded form 445.95.

Why Other Options Are Wrong:
Rs. 548.68 and Rs. 664.21 come from incorrectly compounding for more than 2 years or misusing the rate. Rs. 692.57 arises from multiplying with an incorrect factor. Rs. 512.00 would be closer to 19% interest over 1 year, not 8% over 2 years. Only Rs. 445.95 correctly reflects the compound interest at 8% for 2 years on Rs. 2,680.

Common Pitfalls:
Errors usually occur in squaring 1.08 or in multiplying 2680 by 1.1664. Some students use simple interest instead and compute 2680 * 0.08 * 2 = 428.8, which is slightly less than the compound interest because it ignores interest-on-interest. Always remember that compound interest introduces a small extra amount compared to simple interest.

Final Answer:
The compound interest on Rs. 2,680 at 8% per annum for 2 years is approximately Rs. 445.95.