The difference between compound interest and simple interest on an amount of Rs. 15,000 for 2 years is Rs. 96. What is the rate of interest per annum?

Solution(By Examveda Team)

$$\left[ {15000 \times {{\left( {1 + \frac{R}{{100}}} \right)}^2} - 15000} \right]$$       $$ - $$ $$\left( {\frac{{15000 \times R \times 2}}{{100}}} \right)$$    $$ = 96$$
$$ \Rightarrow 15000\left[ {{{\left( {1 + \frac{R}{{100}}} \right)}^2} - 1 - \frac{{2R}}{{100}}} \right] = 96$$
$$ \Rightarrow 15000$$  $$\left[ {\frac{{{{\left( {100 + R} \right)}^2} - 10000 - \left( {200 \times R} \right)}}{{10000}}} \right]$$       $$ = 96$$
$$\eqalign{ & \Rightarrow {R^2} = {\frac{{96 \times 2}}{3}} = 64 \cr & \Rightarrow R = 8 \cr & \therefore {\text{Rate}} = 8\% \cr} $$