The difference between the amount of compound interest and simple interest accrued on an amount of Rs. 26000 at the end of 3 years is Rs. 2994.134. What is the rate of interest p.c.p.a ?

Solution(By Examveda Team)

Let the R% p.a.
Then,
$$\left[ {26000 \times {{\left( {1 + \frac{{\text{R}}}{{100}}} \right)}^3} - 26000} \right] - $$       $$\left( {\frac{{26000 \times {\text{R}} \times 3}}{{100}}} \right) = $$     $$2994.134$$
$$ \Rightarrow 26000\left[ {{{\left( {1 + \frac{{\text{R}}}{{100}}} \right)}^3} - 1 - \frac{{3{\text{R}}}}{{100}}} \right] = $$        $$2994.134$$
$$ \Rightarrow 26000$$ $$\left[ {\frac{{{{\left( {100 - {\text{R}}} \right)}^3} - 1000000 - 30000{\text{R}}}}{{1000000}}} \right] = $$        $$2994.134$$
$$ \Rightarrow 26\left[ {\left\{ {1000000 + {{\text{R}}^3} + 300{\text{R}}\left( {100 + {\text{R}}} \right) - 1000000 - 30000{\text{R}}} \right\}} \right] = 2994134$$
$$ \Rightarrow {{\text{R}}^3} + 300{{\text{R}}^2} = \frac{{2994134}}{{26}} = $$      $$115159$$
$$ \Rightarrow {{\text{R}}^2}\left( {{\text{R}} + 300} \right) = 115159$$
$$ \Rightarrow {\text{R = 19}}\% $$