Compound Interest — On ₹ 4,000 the compound interest earned in 9 months (interest compounded quarterly) is ₹ 630.50. Find the annual nominal rate (compounded quarterly).

Introduction / Context:
Quarterly compounding over 9 months means 3 compounding periods. We can infer the per-quarter growth factor from the stated interest and back out the nominal annual rate.

Given Data / Assumptions:

• P = ₹ 4,000.
• n = 3 quarters (9 months).
• Interest (CI over 3 quarters) = ₹ 630.50 ⇒ Amount factor over 3 quarters = 1 + 630.50/4,000 = 1.157625.

Concept / Approach:
Let quarterly rate be r_q. Then (1 + r_q)^3 = 1.157625. Recognize 1.157625 = 1.05^3 ⇒ r_q = 0.05 per quarter.

Step-by-Step Solution:
r_q = 5% per quarter ⇒ nominal annual rate (compounded quarterly) = 4 * 5% = 20% p.a.

Verification / Alternative check:
Compute amount: 4,000 * (1.05)^3 = 4,000 * 1.157625 = 4,630.50 ⇒ CI = 630.50 ✔

Why Other Options Are Wrong:
They correspond to different quarterly rates that do not cube to 1.157625.

Common Pitfalls:
Using 9 months as 0.75 years with annual compounding instead of 3 quarterly periods.

Final Answer:
20%