Find the sum of money which will amount to ₹ 26010 in 6 months at the rate of 8\% per annum when the interest is compounded quarterly. (Section Officers', 2006)
Answer
Answer (as printed):
Explanation
Amount = ₹ 26010; Time = 6 months = 2 quarters; Rate $=8 \%$ p.a. $=2 \%$ per quarter. Let the sum be ₹ $x$. Then, $$\begin{aligned} & x \times\left(1+\frac{2}{100}\right)^{2}=26010 \Rightarrow\left(x \times \frac{51}{50} \times \frac{51}{50}\right)=26010 \\ & \Rightarrow x=\left(\frac{26010 \times 10 \times 50 \times 50}{51 \times 51}\right)=25000 \end{aligned}$$ Hence, required sum $=₹ 25000$.
Explanation as extracted from the printed page; notation may be imperfect.