What is the difference between the compound interests on Rs 15000 for 1 year at 20% per annum when the interest is compounded yearly and when it is compounded half-yearly?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → Rs 150
With half-yearly compounding the rate is halved and the number of periods is doubled, so 20% for 1 year becomes 10% for 2 half-years.
Compounded yearly: interest \(=15000\times\displaystyle\frac{20}{100}=3000\)
Compounded half-yearly: amount \(=15000\times1.1^{2}=15000\times1.21=18150\)
Interest compounded half-yearly \(=18150-15000=3150\)
Difference \(=3150-3000=150\)
The difference is Rs 150, which is the 10% interest earned in the second half-year on the first half-year’s interest of Rs 1500.