Find the compound interest on Rs. 15,225 for 9 months at 16% per annum, if the interest is compounded quarterly (that is, every 3 months).

Introduction:
This problem combines compound interest with quarterly compounding and a time period expressed in months. Such questions are common in banking and finance aptitude sections and require careful conversion of the annual rate and time into quarterly equivalents before applying the compound interest formula.

Given Data / Assumptions:
Principal P = Rs. 15,225. Annual rate r = 16% per annum. Interest is compounded quarterly. Total time = 9 months.

Concept / Approach:
Since compounding is quarterly, we need: Rate per quarter = r / 4 = 16 / 4 = 4%. Number of quarters in 9 months = 9 / 3 = 3. Then we apply the quarterly compound interest formula: A = P * (1 + rate per quarter / 100)^(number of quarters). Finally, CI = A − P.

Step-by-Step Solution:
Step 1: Quarterly rate and periods. Quarterly rate = 4%. Number of quarters n = 3. Step 2: Compute amount. A = 15225 * (1.04)^3. (1.04)^2 = 1.0816. (1.04)^3 = 1.0816 * 1.04 = 1.124864. A ≈ 15225 * 1.124864 ≈ Rs. 17,126.05. Step 3: Compound interest. CI = A − P ≈ 17,126.05 − 15,225 ≈ Rs. 1,901.05. Rounded to the nearest rupee, CI ≈ Rs. 1,901.

Verification / Alternative check:
We can partially verify by approximating. A 4% increase three times roughly corresponds to an overall increase a little above 12%. Twelve percent of 15,225 is about 1,827. Since compounding makes it slightly higher, a value near 1,900 is reasonable, and the precise calculation yields about 1,901. This confirms our answer lies in the expected range.

Why Other Options Are Wrong:
Rs. 1,911 and Rs. 1,909 are close but arise from rounding the intermediate steps differently or miscalculating the product 15225 * 1.124864. Rs. 1,907 and Rs. 1,895 are further away and come from cruder approximations or using simple interest instead of compound interest.

Common Pitfalls:
A very common mistake is to treat 9 months as 9 years or 0.75 years and then apply annual compounding incorrectly. Another error is to divide the rate by 3 instead of by 4 when compounding quarterly. Always align the number of compounding periods with the chosen time units.

Final Answer:
The compound interest on Rs. 15,225 for 9 months at 16% per annum compounded quarterly is approximately Rs. 1,901.