Question

The difference between simple interest and compound interest at the same rate for rupees 5,000 for two years is rupees 98. The rate of interest is:

• A. 10%
• B. 12%
• C. $10\frac{1}{2}\%$
• D. 14%

Answer 1

The correct option is D 14%

$\begin{array}{c}SI-CI=-98\\ \frac{P\times R\times T}{100}-\left[P{\left(1+\frac{R}{100}\right)}^T-P\right]=98\\ \Rightarrow \frac{5.000\times R\times 2}{100}-5000\left({\left(1+\frac{R}{100}\right)}^2-1\right)=98\\ \Rightarrow 100R-\left[5000\frac{{\left(100+R\right)}^2}{100\times 100}-5000\right]=98\\ \Rightarrow 100R-\left[\frac{10000+R^2+200R-10000}{2}\right]=98\\ \Rightarrow 200R-R^2-200R=-98\times 2\\ \Rightarrow -R^2=-196\end{array}$

$R=\sqrt{196}=14\%$