Find the compound interest on Rs 16,000 at 20% per annum for a period of 9 months, if the interest is compounded quarterly (every three months).

Introduction:
This question illustrates compound interest for a period less than one year, with quarterly compounding. You must correctly convert the annual rate into a quarterly rate and identify the correct number of compounding periods for 9 months. Such problems are standard in finance sections of aptitude exams.

Given Data / Assumptions:

• Principal P = Rs 16,000
• Annual interest rate r = 20% per annum
• Compounding quarterly (4 quarters per year)
• Total time = 9 months
• We need the compound interest, not the final amount

Concept / Approach:
Since interest is compounded quarterly, we first convert the annual rate to a quarterly rate and express time in quarters. Then we use:
A = P * (1 + r_quarterly)^nwhere n is the number of quarters. The compound interest is:
CI = A - P

Step-by-Step Solution:
Step 1: Convert annual rate to quarterly rate.r_annual = 20% = 0.20r_quarterly = r_annual / 4 = 0.20 / 4 = 0.05 (5% per quarter)Step 2: Convert time into quarters.9 months = 3 quarters (since each quarter is 3 months)So n = 3Step 3: Find the final amount A.A = 16,000 * (1 + 0.05)^3A = 16,000 * (1.05)^3(1.05)^2 = 1.1025 and (1.05)^3 = 1.157625A ≈ 16,000 * 1.157625 = Rs 18,522Step 4: Find compound interest.CI = A - P = 18,522 - 16,000 = Rs 2,522

Verification / Alternative check:
To confirm, you can approximate. For 9 months simple interest at 20% per annum, we would get:
SI ≈ 16,000 * 0.20 * (9 / 12) = 16,000 * 0.15 = Rs 2,400Compound interest should be slightly higher than simple interest, and Rs 2,522 is just above Rs 2,400, which is consistent and reasonable.

Why Other Options Are Wrong:

• Rs 2,422 and Rs 2,322: These are close to but less than the correct value, and do not match the precise compound interest.
• Rs 3,522: Too high; it overestimates the effect of compounding.
• Rs 2,650: Slightly higher than correct, likely from calculation or rounding mistakes.

Common Pitfalls:
Candidates sometimes take 9 months as 0.75 years and apply annual compounding directly instead of quarterly. Others forget that quarterly compounding needs both rate and time to be adjusted. Always ensure you express time in number of compounding periods and adjust the rate accordingly.

Final Answer:
The compound interest on Rs 16,000 at 20% per annum for 9 months, compounded quarterly, is Rs 2,522.