The difference between the amount the amount of compound interest and simple interest accrued on an amount of ₹ 26000 at the end of 3 years is ₹ 2994.134. What is the rate of interest p.c.p.a.?
(a)17\%
(b)19\%
(c)22\%
(d)Cannot be determined
(e)None of these
Answer
Answer (as printed): B
Explanation
Let the rate be R\% p.a. Then $$\begin{aligned} & {\left[26000 \times\left(1+\frac{R}{100}\right)^{3}-26000\right]-\left(\frac{26000 \times R \times 3}{100}\right)=2994.134} \\ & \Rightarrow 26000\left[\left(1+\frac{R}{100}\right)^{3}-1-\frac{3 R}{100}\right]=2994.134 \\ & \Rightarrow 26000\left[\frac{(100+R)^{3}-1000000-30000 R}{1000000}\right]=2994.134 \\ & \Rightarrow 26\left\{\left[1000000+R^{3}+300 R(100+R)\right\}-1000000-30000 R\right\} \\ & =2994134 \\ & \Rightarrow R^{3}+300 R^{2}=\frac{2994134}{26}=115159 \\ & \Rightarrow R^{2}(R+300)=115159 \Rightarrow R=19 \% . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.