Compound Interest with Quarterly Compounding – 9 months at 16% p.a.: find CI only: Find the compound interest on ₹ 31,250 at 16% per annum compounded quarterly for 9 months.

Introduction / Context:
When compounding quarterly, a nominal annual rate is split into four equal parts, and the number of periods equals the number of quarters. Nine months corresponds to three quarters, so we apply the quarterly factor three times to get the amount, then subtract the principal to obtain the compound interest (CI) alone.

Given Data / Assumptions:

• P = 31,250
• Nominal r = 16% per annum ⇒ per quarter i = 16%/4 = 4%
• Time = 9 months ⇒ n = 3 quarters

Concept / Approach:
Compute amount: A = P * (1 + i)^n = 31,250 * (1.04)^3. Then CI = A − P. Be careful to report CI (interest) rather than the final amount.

Step-by-Step Solution:
(1.04)^3 = 1.124864A = 31,250 * 1.124864 = 35,152.00CI = 35,152.00 − 31,250 = 3,902.00

Verification / Alternative check:
Quarter-by-quarter: 31,250 → 32,500 → 33,800 → 35,152; total interest added = 3,902, confirming the calculation.

Why Other Options Are Wrong:
₹ 4,000 and ₹ 4,200 overstate CI; ₹ 3,500 and ₹ 3,750 understate it; only ₹ 3,902 matches the exact quarterly compounding result for 3 periods at 4% each.

Common Pitfalls:
Reporting the amount instead of the CI is a frequent error. Also, do not treat nine months as three simple-interest quarters; apply compounding each quarter.

Final Answer:
₹ 3,902