Under the Rural Housing Scheme, the Delhi Development Authority (DDA) allotted a house to Kamal Raj for ₹ 1,26,100. This payment is to be made in three equal annual instalments. If the money is reckoned at 5\% per annum compound interest, then how much is to be paid by Kamal Raj in each instalment?
(a)₹ 45205
(b)₹ 46305
(c)₹ 47405
(d)₹ 48505
Answer
Answer (as printed): B
Explanation
Let the value of each instalment be ₹ $x$. Then, (P.W. of ₹ $x$ due 1 year hence) + (P.W. of ₹ $x$ due 2 years hence) + (P.W. of ₹ $x$ due 3 years hence) $=₹ 126100$ $$\begin{aligned} & \Rightarrow \frac{x}{\left(1+\frac{5}{100}\right)}+\frac{x}{\left(1+\frac{5}{100}\right)^{2}}+\frac{x}{\left(1+\frac{5}{100}\right)^{3}}=126100 \\ & \Rightarrow \frac{20 x}{21}+\frac{400 x}{441}+\frac{8000 x}{9261}=126100 \\ & \Rightarrow \frac{8820 x+8400 x+8000 x}{9261}=126100 \\ & \Rightarrow \frac{25220 x}{9261}=126100 \Rightarrow x=\left(\frac{126100 \times 9261}{25220}\right)=46305 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.