The compound interest earned by Sachin on a certain amount at the end of two years at the rate of 8 p.c.p.a. was ₹ 1414.40. What was the total amount that Sachin got back at the end of 2 years in the form of principal plus interest earned
(a)₹ 8914.40
(b)₹ 9014.40
(c)₹ 9414.40
(d)₹ 9914.40
(e)None of these
Answer
Answer (as printed): D
Explanation
Let the sum be ₹ $P$. Then, $$\begin{aligned} & P\left(1+\frac{8}{100}\right)^{2}-P=1414.40 \\ & \Rightarrow \quad\left(P \times \frac{27}{25} \times \frac{27}{25}\right)-P=1414.40 \\ & \Rightarrow \quad \frac{729}{625} P-P=1414.40 \\ & \Rightarrow \quad \frac{104}{625} P=1414.40 \\ & \Rightarrow \quad P=\left(\frac{1414.40 \times 625}{104}\right)=8500 . \end{aligned}$$ Hence, total amount $=₹(8500+1414.40)=₹ 9914.40$.
Explanation as extracted from the printed page; notation may be imperfect.