Find the compound interest on Rs 8000 for \(1\frac{1}{2}\) years at 10% per annum, the interest being compounded half-yearly.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs 1261
Compounded half-yearly, the rate is 5% per half-year and the number of periods is the number of half-years.
Rate per half-year \(=10\div2=5\%\); number of half-years \(=3\)
Amount \(=8000\times1.05^{3}=9261\)
CI \(=9261-8000=1261\)
The compound interest is Rs 1261.
Why the other options are incorrect
Option (2) Rs 9261 — Incorrect. This is the amount, not the compound interest.
Option (3) Rs 1200 — Incorrect. This is simple interest for the period, not compound interest.
Option (4) Rs 1240 — Incorrect. This compounds yearly for the first year and adds a half-year after it.