The difference between the compound interest and simple interest on a certain sum for 2 years at 15% per annum is ₹45. Find the sum.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → ₹2000
For 2 years, compound interest exceeds simple interest only by the interest earned on the first year's interest, so \(\displaystyle \text{CI}-\text{SI}=P\left(\frac{R}{100}\right)^2\).
With \(R=15\) and a difference of 45: \(\displaystyle P\left(\frac{15}{100}\right)^2=45\)
\(\displaystyle P\times\frac{9}{400}=45\)
\(\displaystyle P=\frac{45\times400}{9}=2000\), so the sum is ₹2000