Find the compound interest on Rs 15,225 for 9 months at 16% per annum, if the interest is compounded quarterly (every three months).

Introduction / Context:
In this question, the time period is 9 months and the rate of interest is 16% per annum compounded quarterly. Since quarterly compounding means a three month compounding interval, 9 months corresponds to three compounding periods. We must carefully convert the annual rate to a quarterly rate and then compute the compound interest on the given principal.

Given Data / Assumptions:

• Principal P = Rs 15225.
• Annual rate r = 16% per annum.
• Compounding frequency = quarterly (4 times per year).
• Total time = 9 months = 3 quarters.
• We need to find compound interest for 3 quarters.

Concept / Approach:
For quarterly compounding, each quarter uses a rate of r / 4 percent. The number of periods n is the number of quarters in the total time. The amount A after n quarters is:
A = P * (1 + (r / 100) / 4)^n The compound interest is:
CI = A - P Here, r = 16, so the quarterly rate is 4%, and n = 3 quarters for 9 months.

Step-by-Step Solution:
Quarterly rate = 16 / 4 = 4% per quarter. Number of quarters n = 9 months / 3 months per quarter = 3. Amount factor = (1.04)^3. Compute (1.04)^2 = 1.0816. Then (1.04)^3 = 1.0816 * 1.04 = 1.124864. Amount A = 15225 * 1.124864 ≈ Rs 17126.05. Compound interest CI = A - P ≈ 17126.05 - 15225 = Rs 1901.05. Rounding to the nearest rupee, CI ≈ Rs 1901.

Verification / Alternative Check:
You can approximate by stepwise compounding each quarter. After first quarter: 15225 * 1.04 ≈ 158, then continue for three quarters. However, using the compact formula directly is more accurate, and the final CI value consistently comes out very close to Rs 1901.

Why Other Options Are Wrong:
Rs. 1911, Rs. 1909, and Rs. 1907 are all slightly off from the correct rounded value and result from incorrect rounding or erroneous intermediate computations. Only Rs. 1901 matches the precise calculation.

Common Pitfalls:
A frequent error is to treat 9 months as 0.75 years and apply annual compounding instead of quarterly compounding. Some candidates forget to divide the rate by 4 for quarterly compounding. Incorrect powers or calculator errors when computing (1.04)^3 can also lead to wrong answers.

Final Answer:
The compound interest on Rs 15225 for 9 months at 16% per annum compounded quarterly is approximately Rs. 1901.