A computer is available for ₹ 39000 cash or ₹ 17000 as cash down payment followed by five monthly instalments of ₹ 4800 each. What is the rate of interest under the instalment plan?
(a)35.71\% p.a
(b)36.71\% p.a.
(c)37.71\% p.a.
(d)38.71\% p.a.
Answer
Answer (as printed): D
Explanation
Total cost of the computer $=₹ 39000$. Down payment = ₹ 17000 Balance $=₹(39000-17000)=₹ 22000$. Let the rate of interest be R\% p.a. Amount of ₹ 22000 for 5 months $$\begin{aligned} & =₹\left(22000+22000 \times \frac{5}{12} \times \frac{R}{100}\right) \\ & =₹\left(22000+\frac{275 R}{3}\right) . \end{aligned}$$ The customer pays the shopkeeper ₹ 4800 after 1 month, ₹ 4800 after 2 months,...... and ₹ 4800 after 5 months. Thus, the shopkeeper keeps ₹ 4800 for 4 months, ₹ 4800 for 3 months, ₹ 4800 for 2 months, ₹ 4800 for 1 month and gets ₹ 4800 at the end.
Explanation as extracted from the printed page; notation may be imperfect.