Compound Frequency Effect — Half-yearly vs quarterly (same nominal rate, 1 year): Find the difference between compound interest on ₹ 800 for 1 year at a nominal 20% p.a. when compounded half-yearly versus quarterly.

Introduction / Context:For a fixed nominal annual rate, increasing compounding frequency increases the effective annual yield. Comparing half-yearly (2 times) to quarterly (4 times) over one year highlights the frequency effect while keeping the nominal rate unchanged.

Given Data / Assumptions:

• P = ₹ 800
• Nominal rate = 20% p.a.
• Case H: half-yearly compounding (2 periods at 10% each)
• Case Q: quarterly compounding (4 periods at 5% each)
• Time = 1 year in both cases

Concept / Approach:Compute amounts separately, then subtract to get the difference in interest. With n compounding periods: A = P (1 + r/n)^(n t). For 1 year, t = 1.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• Nil, ₹ 2.50, ₹ 6.60, ₹ 3.20 do not match the computed frequency effect at 20% nominal on ₹ 800 over one year.

Common Pitfalls:

• Using 20% for each subperiod instead of dividing by the number of periods.
• Comparing amounts instead of interest and then forgetting to subtract principal.

Final Answer:Rs. 4.40.