Find the compound interest on Rs. 2680 at 8 percent per annum for 2 years, assuming annual compounding.

Introduction / Context:
This question returns to a standard compound interest calculation with a modest rate and a 2 year time frame. We are given a principal of Rs. 2680 and a rate of 8 percent per annum, with annual compounding. The task is to compute the compound interest for the full 2 years. This problem consolidates basic skills in applying the compound interest formula and handling decimal amounts.

Given Data / Assumptions:

• Principal P = Rs. 2680.
• Rate r = 8 percent per annum.
• Time n = 2 years.
• Compounding is annual.
• We need only the compound interest, not the final amount.

Concept / Approach:
The compound amount after n years at r percent per annum is: A = P * (1 + r/100)^n The compound interest CI is: CI = A - P We substitute P = 2680, r = 8, and n = 2. Computation involves squaring the growth factor (1.08) and then multiplying by the principal, followed by subtracting the original principal.

Step-by-Step Solution:
P = 2680, r = 8 percent, n = 2 years A = 2680 * (1 + 8/100)^2 1 + 8/100 = 1.08 (1.08)^2 = 1.08 * 1.08 = 1.1664 A = 2680 * 1.1664 2680 * 1.1664 = 3125.952 (approximately) CI = A - P = 3125.952 - 2680 = 445.952 Rounded to two decimal places, CI ≈ Rs. 445.95

Verification / Alternative check:
We can perform a rough check using simple interest as an approximation. Simple interest for 2 years at 8 percent on 2680 is: SI ≈ 2680 * 8 * 2 / 100 = 2680 * 0.16 = 428.8 Compound interest over 2 years should be slightly more than this due to interest on interest, and 445.95 is indeed reasonably higher than 428.8 but not excessively so. This supports that the detailed compound calculation is sensible.

Why Other Options Are Wrong:
Rs. 548.68 and Rs. 664.21 are much larger than the approximate simple interest and do not align with the modest rate of 8 percent for only 2 years. Rs. 692.57 is even higher and clearly unrealistic for these parameters. Rs. 500.00 is closer but still significantly larger than the exact calculation. Only Rs. 445.95 matches the precise result of subtracting the principal from the computed amount of 3125.952.

Common Pitfalls:
Students may miscalculate (1.08)^2 or forget to square the factor altogether and use only 1.08 once. Another frequent error is mixing up amount and interest and reporting 3125.95 instead of the interest. Rounding early in the calculation and using an approximate growth factor can cause small discrepancies. Keeping the steps clear and rounding only at the end helps maintain accuracy.

Final Answer:
The compound interest on Rs. 2680 at 8 percent per annum for 2 years is approximately Rs. 445.95.