What is the difference between the compound interests on Rs 32000 for 1 year at 15% per annum when the interest is compounded yearly and when it is compounded half-yearly?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Rs 180
Compounded half-yearly, the rate is 7.5% for each half-year and there are 2 half-years in a year.
Yearly: CI \(\displaystyle =32000\times\frac{15}{100}=4800\)
Half-yearly: amount \(=32000\times1.075^{2}=36980\), so CI \(=4980\)
Difference \(=4980-4800=180\)
The difference is Rs 180.
Why the other options are incorrect
Option (1) Rs 4800 — Incorrect. This is the yearly compound interest itself, not the difference.
Option (2) Rs 4980 — Incorrect. This is the half-yearly compound interest itself, not the difference.
Option (3) Rs 360 — Incorrect. This is twice the difference; the extra interest is only the interest for the second half-year on the first half-year’s interest, Rs 180.