The difference between the compound interest (compounded annually) and the simple interest on a sum of Rs 400 for two years is Rs 9. Find the rate of interest per annum.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 15%
For two years, compound interest exceeds simple interest only by the interest on the first year’s interest, so \(\displaystyle \mathrm{CI}-\mathrm{SI}=P\left(\frac{R}{100}\right)^{2}\).
\(\displaystyle 400\times\left(\frac{R}{100}\right)^{2}=9\)
\(\displaystyle \left(\frac{R}{100}\right)^{2}=\frac{9}{400}\)
\(\displaystyle \frac{R}{100}=\frac{3}{20}\), so \(R=15\)
The rate of interest is 15% per annum.