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)?
Correct Answer: ₹ 29,100
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