What is the compound interest on Rs. 8000 for 3 years at 10 percent per annum, compounded annually?

Introduction / Context:
This is a straightforward compound interest question where the principal, rate, time, and compounding frequency are clearly specified. We must compute the compound interest on Rs. 8000 for 3 years at 10 percent per annum with annual compounding. Such problems help build comfort with the basic compound interest formula and repeated multiplication by a growth factor.

Given Data / Assumptions:

• Principal P = Rs. 8000.
• Rate r = 10 percent per annum.
• Time n = 3 years.
• Compounding is annual.
• We need the compound interest, that is the amount minus the principal.

Concept / Approach:
The compound amount after n years at rate r percent per annum is: A = P * (1 + r/100)^n The compound interest is: CI = A - P We substitute P = 8000, r = 10, and n = 3 to compute the amount and then subtract the principal to obtain the interest.

Step-by-Step Solution:
P = 8000, r = 10 percent, n = 3 years A = 8000 * (1 + 10/100)^3 1 + 10/100 = 1.10 (1.10)^3 = 1.10 * 1.10 * 1.10 = 1.331 A = 8000 * 1.331 = 10648 CI = A - P = 10648 - 8000 = 2648 Therefore, the compound interest is Rs. 2648

Verification / Alternative check:
We can also compute year by year. After 1 year: Amount A1 = 8000 * 1.10 = 8800 After 2 years: A2 = 8800 * 1.10 = 9680 After 3 years: A3 = 9680 * 1.10 = 10648 Again, CI = 10648 - 8000 = 2648. This matches our earlier result from the direct formula, confirming that the answer is correct.

Why Other Options Are Wrong:
Values such as Rs. 2145, Rs. 2587, Rs. 2784, and Rs. 2500 do not match the precise compound interest generated by compounding 8000 at 10 percent for 3 years. For example, 2500 is close but slightly lower than 2648, and 2784 is higher than the correctly computed interest. Only 2648 exactly matches the result of the calculation.

Common Pitfalls:
Some students mistakenly use the simple interest formula P * r * n / 100, which would give 2400 and thus an incorrect answer. Others miscompute (1.10)^3 or round the factor too early, leading to small but important differences. Confusing amount with interest and choosing the amount itself instead of the interest is another common error. Carefully following the formula and checking with the step by step approach helps avoid these traps.

Final Answer:
The compound interest on Rs. 8000 for 3 years at 10 percent per annum is Rs. 2648.