Compounded half-yearly — Aptitude Question
Compounded half-yearly: What is the compound interest on ₹16,000 at 20% per annum for 1 year, compounded half-yearly? Answer and worked solution on CodeKairo.
- Topic: Simple & Compound Interest
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 60 seconds
Question
What is the compound interest on ₹16,000 at 20% per annum for 1 year, compounded half-yearly?
Options
- ₹3,200
- ₹3,360
- ₹3,400
- ₹3,520
Show the answer and the worked solution
Correct answer: B. ₹3,360
Worked solution
- Rate per half-year = 10%; periods = 2.
- Amount = 16,000 × 1.1² = 16,000 × 1.21 = 19,360.
- CI = 19,360 − 16,000 = ₹3,360.
Answer: ₹3,360.
The idea
Compounding k times a year: rate/k per period, n × k periods. More frequent compounding always earns slightly more than annual (here 3,360 versus 3,200).
Shortcut. Two 10% steps: 16,000 → 17,600 → 19,360, so ₹3,360; the ₹160 above simple interest is 10% of the first half's ₹1,600.
Common trap. ₹3,200 — 20% of 16,000, i.e. simple or annual interest; half-yearly compounding earns interest on the first half's ₹1,600 too.
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