On a certain sum the difference in the compound interest and the simple interest for 2 years at 15% per annum is ₹270. Find the simple interest on the same sum for 5 years at 10% per annum.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ₹6,000
For 2 years, compound interest exceeds simple interest only by the interest earned on the first year’s interest, so the difference is \(P\left(\frac{r}{100}\right)^2\).
The sum (the difference is the given ₹270):
\(\displaystyle P\times\left(\frac{15}{100}\right)^2=270\)
\(P\times0.0225=270\)
Sum \(P=\) ₹12,000
Simple interest for 5 years at 10%:
\(\displaystyle SI=\frac{12000\times10\times5}{100}=6000\), that is, ₹6,000