In a compound interest calculation, find the compound interest on Rs 8000 at the rate of 15% per annum for a total time period of 2 years and 4 months, when the interest is compounded annually.

Introduction:
This question tests your understanding of compound interest with a non integral time period, where interest is compounded annually but the total time includes years and additional months. You must know how to treat the full years using the compound interest formula and the remaining fractional year using simple interest on the accumulated amount.

Given Data / Assumptions:

• Principal (P) = Rs 8000.
• Rate of interest (r) = 15% per annum.
• Total time = 2 years and 4 months.
• Interest is compounded annually.
• For the extra 4 months, interest is taken as simple interest on the amount at the end of 2 years.

Concept / Approach:
For full years, use the compound interest formula A = P * (1 + r/100)^n. For the fractional part of the year, treat the interest as simple interest on the amount already accrued. Finally, subtract the original principal from the final amount to get the compound interest earned over the entire period.

Step-by-Step Solution:
Amount after 2 years: A2 = 8000 * (1 + 15/100)^2A2 = 8000 * (1.15)^2 = 8000 * 1.3225 = Rs 10580Interest for remaining 4 months (which is 4/12 year) at 15% on Rs 10580:I4m = 10580 * 15/100 * (4/12)I4m = 10580 * 0.15 * 1/3 = 10580 * 0.05 = Rs 529Total amount at the end of 2 years 4 months = 10580 + 529 = Rs 11109Total compound interest = 11109 - 8000 = Rs 3109

Verification / Alternative Check:
You can separately compute the interest for 2 years: I2 = 10580 - 8000 = Rs 2580. Then add the extra 4 months interest of Rs 529 to get 2580 + 529 = Rs 3109, which confirms the result without redoing the full calculation.

Why Other Options Are Wrong:
Rs 2109: This ignores some part of the compounding or the extra 4 months.Rs 4109: This overestimates interest, possibly by compounding for 3 full years.Rs 6109: This is far too large and not consistent with a 15% rate for just over 2 years.Rs 2709: This underestimates the extra fractional year interest.

Common Pitfalls:
Students often either treat the whole 2 years 4 months as 2.33 years in the compound interest formula or forget that the extra months are to be treated using simple interest on the amount after full years. Another mistake is using the principal instead of the amount after 2 years to calculate interest for the last 4 months.

Final Answer:
The compound interest on Rs 8000 at 15% per annum for 2 years and 4 months, compounded annually, is Rs 3109.