Compound Interest — A sum invested for 2 years at a nominal 20% p.a. yields ₹ 964 more when interest is payable half-yearly than when payable annually. Find the principal.

Introduction / Context:
Nominal 20% p.a. compounded semiannually means 10% every half-year across 4 periods in 2 years. Annual compounding at 20% uses 2 periods of 20% each. The difference in amounts is stated.

Given Data / Assumptions:

• Rate (nominal): 20% p.a.
• Time: 2 years.
• Amount difference (semiannual − annual) = ₹ 964.

Concept / Approach:
Let P be the principal. Annual factor: (1 + 0.20)^2 = 1.44. Semiannual factor: (1 + 0.10)^4 = 1.4641. Difference in amounts: P * (1.4641 − 1.44) = P * 0.0241 = 964.

Step-by-Step Solution:
P = 964 / 0.0241 = 964 * 10000 / 241 = ₹ 40,000

Verification / Alternative check:
40,000 * 1.4641 = 58,564; 40,000 * 1.44 = 57,600; difference = 964 ✔

Why Other Options Are Wrong:
They do not satisfy the exact 0.0241 multiplier relation.

Common Pitfalls:
Confusing nominal with effective annual rate; here we compare compounding frequencies at the same nominal rate.

Final Answer:
₹ 40,000