What is the difference between the compound interests on ₹1000 for 1 year at 10% per annum when compounded yearly and when compounded half-yearly?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ₹2.50
Compounded half-yearly, the rate per period is half the yearly rate (5%) and there are two periods in the year; the interest of the first half-year earns interest in the second.
Yearly: CI \(=1000\times\frac{10}{100}=\) ₹100
Half-yearly: amount \(=1000\times1.05\times1.05=\) ₹1102.50, so CI \(=\) ₹102.50
Difference \(=102.50-100=\) ₹2.50
Shortcut:
The extra amount is the interest on the first half-year's interest: 5% of ₹50 \(=\) ₹2.50