Find the compound interest on Rs 40000 for 1 year at 8% per annum, the interest being compounded half-yearly.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Rs 3264
Compounded half-yearly, the rate is 4% per half-year and the number of periods is the number of half-years.
Rate per half-year \(=8\div2=4\%\); number of half-years \(=2\)
Amount \(=40000\times1.04^{2}=43264\)
CI \(=43264-40000=3264\)
The compound interest is Rs 3264.
Why the other options are incorrect
Option (1) Rs 3200 — Incorrect. This compounds yearly, not half-yearly.
Option (2) Rs 43264 — Incorrect. This is the amount, not the compound interest.
Option (4) Rs 6656 — Incorrect. This uses the full 8% for each half-year instead of 4%.