The difference between the compound interest and the simple interest on a certain sum of money at 40% per annum for 1 year is Rs 300, the compound interest being compounded half-yearly. What is the sum?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 7500
Half-yearly compounding gives two periods at 20%; the extra over simple interest is the interest earned in the second half-year on the first half-year's interest.
Compound interest \(=P\,(1.2^{2}-1)=0.44P\)
Simple interest \(=0.40P\)
Difference \(=0.04P=300\)
\(\displaystyle P=\frac{300}{0.04}=7500\)
The sum is Rs 7500.