A taperecorder is sold for ₹ 3500 cash, or ₹ 1000 cash down payment and the balance in three equal easy instalments. If $12 \frac{1}{2} \%$ is the rate of interest compounded annually, find the amount of instalment.
(a)₹ 1000.35
(b)₹ 1049.85
(c)₹ 1050.65
(d)₹ 1100.45
Answer
Answer (as printed): B
Explanation
Total cost of taperecorder $=₹ 3500$. Down payment = ₹ 1000. Balance $=₹(3500-1000)=₹ 2500$. Let the value of each instalment be ₹ $x$. P.W. of ₹ $x$ due 1 year hence + P.W. of ₹ $x$ due 2 years hence + P.W. of $₹ x$ due 3 years hence $=2500$ $$\begin{aligned} & \Rightarrow \frac{x}{\left(1+\frac{25}{2 \times 100}\right)}+\frac{x}{\left(1+\frac{25}{2 \times 100}\right)^{2}}+\frac{x}{\left(1+\frac{25}{2 \times 100}\right)^{3}}=2500 \\ & \Rightarrow \frac{8 x}{9}+\frac{64 x}{81}+\frac{512 x}{729}=2500 \Rightarrow \frac{1736 x}{729}=2500 \\ & \Rightarrow x=\frac{2500 \times 729}{1736}=1049.83 \approx 1049.85 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.