What is the difference between the compound interests on Rs 20000 for 1 year at 10% per annum when the interest is compounded yearly and when it is compounded half-yearly?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 50
Compounded half-yearly, the rate is 5% for each half-year and there are 2 half-years in a year.
Yearly: CI \(\displaystyle =20000\times\frac{10}{100}=2000\)
Half-yearly: amount \(=20000\times1.05^{2}=22050\), so CI \(=2050\)
Difference \(=2050-2000=50\)
The difference is Rs 50.
Why the other options are incorrect
Option (1) Rs 2000 — Incorrect. This is the yearly compound interest itself, not the difference.
Option (3) Rs 2050 — Incorrect. This is the half-yearly compound interest itself, not the difference.
Option (4) Rs 100 — 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 50.