The difference between compound and simple interest on a certain sum of money at the interest rate of 10% per annum for \(1\frac{1}{2}\) years is ₹183, when the interest is compounded half-yearly. Find the sum of money.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → ₹24,000
When interest is compounded half-yearly, the rate is halved and the number of periods doubled: 10% a year for \(1\frac{1}{2}\) years becomes 5% for 3 half-years. Simple interest stays at 10% a year for 1.5 years. Let the sum be P.
Compound interest \(=P\left(1.05^3-1\right)=P(1.157625-1)=0.157625P\)
Simple interest \(\displaystyle =\frac{P\times10\times1.5}{100}=0.15P\)
Difference: \(0.157625P-0.15P=0.007625P=183\)
\(\displaystyle P=\frac{183}{0.007625}=24000\)