Simple Interest — Harsha deposits ₹ 20,000 at 13% per annum simple interest (interest reckoned half-yearly but still simple). What total amount will he receive after 42 months (3.5 years)?

Introduction / Context:
In simple interest, interest grows linearly with time regardless of sub-year reckoning. If the stated rate is “per annum, charged half-yearly” but there is no compounding, we simply pro-rate the annual rate by the exact time in years.

Given Data / Assumptions:

• P = ₹ 20,000.
• r = 13% per annum (simple), reckoned half-yearly but not compounded.
• t = 42 months = 3.5 years.

Concept / Approach:
Simple interest SI = P * r * t. Amount A = P + SI.

Step-by-Step Solution:
SI = 20,000 * 0.13 * 3.5 = 20,000 * 0.455 = ₹ 9,100.Amount A = 20,000 + 9,100 = ₹ 29,100.

Verification / Alternative check:
13% per year for 3 years gives 39% (= ₹ 7,800); for 0.5 year gives 6.5% (= ₹ 1,300). Total 45.5% of 20,000 = 9,100; A = 29,100.

Why Other Options Are Wrong:
₹ 27,800 and ₹ 28,100 undercount interest; ₹ 30,000 assumes 50% return; ₹ 28,900 is an in-between distractor.

Common Pitfalls:
Confusing “charged half-yearly” with compounding; here it does not change linear SI.

Final Answer:
₹ 29,100