The difference between simple interest and compound interest on a certain sum of money in three years at 10% per annum rate is ₹15.50. The sum is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → ₹500
Compound interest earns interest on the interest of earlier years, while simple interest does not; the difference between the two is that extra interest. Assuming the sum to be ₹100 at 10% a year:
Simple interest for 3 years \(=3\times10=30\)
Amount at compound interest \(=100\times1.1^3=133.1\), so compound interest \(=33.1\)
Difference on ₹100 \(=33.1-30=3.1\)
Sum giving a difference of ₹15.50 \(\displaystyle =\frac{15.50}{3.1}\times100=500\)
Tip: For 3 years, CI − SI \(\displaystyle =P\left(\frac{r}{100}\right)^2\left(3+\frac{r}{100}\right)\); for 2 years it is \(\displaystyle P\left(\frac{r}{100}\right)^2\). Here \(P\times0.01\times3.1=15.50\) gives \(P=500\) at once.