The difference between simple interest and compound interest on a certain sum of money for 3 years at 10% per annum is ₹62. The sum is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → ₹2,000
Simple interest is the same every year, but compound interest also earns interest on the interest already added, so CI − SI grows each year.
Assuming the sum to be \(P\), at 10% a year:
Simple interest for 3 years: \(0.3P\)
Amount at compound interest: \(P(1.1)^3=1.331P\), so compound interest \(=0.331P\)
The difference is the given ₹62: \(0.331P-0.3P=0.031P=62\)
The sum: \(\displaystyle P=\frac{62}{0.031}=2000\)
Shortcut:
For 3 years, \(\mathrm{CI}-\mathrm{SI}=P\left(\displaystyle\frac{r}{100}\right)^2\left(3+\displaystyle\frac{r}{100}\right)\).
At 10%: \(P\times0.01\times3.1=0.031P=62\), so \(P=2000\).