₹8,000 compounded half-yearly — Aptitude Question
₹8,000 compounded half-yearly: What is the compound interest on ₹8,000 at 20% per annum for 1 year, compounded… Answer and worked solution on CodeKairo.
- Topic: Simple & Compound Interest
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 75 seconds
Question
What is the compound interest on ₹8,000 at 20% per annum for 1 year, compounded half-yearly?
Options
- ₹1,600
- ₹1,680
- ₹1,720
- ₹1,800
Show the answer and the worked solution
Correct answer: B. ₹1,680
Worked solution
- Rate per half-year = 10%; number of periods = 2.
- Amount = 8,000 × 1.1² = 8,000 × 1.21 = ₹9,680.
- CI = 9,680 − 8,000 = ₹1,680.
Answer: ₹1,680.
The idea
Compounding k times a year means rate ÷ k per period and n × k periods. More frequent compounding always earns a little more than annual (₹1,680 against ₹1,600).
Shortcut. Two 10% periods compound to 21% (10 + 10 + 1), and 21% of 8,000 is ₹1,680.
Common trap. ₹1,600 — applying 20% once, as if compounding were annual; the second half-year also earns 10% on the first half's ₹800.
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