A computer is available for Rs. 39000 cash or Rs. 17000 as cash down payment followed by five monthly instalments of Rs. 4800 each. What is the rate of interest under the instalment plan?

Solution(By Examveda Team)

Total cost of the computer = Rs. 39000
Down payment = Rs. 17000
Balance = Rs. (39000 - 17000) = Rs. 22000.
Let the rate of interest be R% p.a.
Amount of Rs. 22000 for 5 months
$$\eqalign{ & = {\text{Rs}}{\text{.}}\left( {22000 + 22000 \times \frac{5}{{12}} \times \frac{{\text{R}}}{{100}}} \right) \cr & = {\text{Rs}}{\text{.}}\left( {22000 + \frac{{275{\text{R}}}}{3}} \right) \cr} $$
The customer pays the shopkeeper Rs. 4800 after 1 month,
Rs. 4800 after 2 months, ...... and Rs. 4800 after 5 months.

Thus, the shopkeeper keeps Rs. 4800 for 4 months, Rs. 4800 for 3 months, Rs. 4800 for 2 months, Rs. 4800 for 1 months and Rs. 4800 at the end.

∴ sum of the amounts of these installments
= (Rs. 4800 + S.I. on Rs 4800 for 4 months) + (Rs. 4800 + S.I. on Rs. 4800 for 3 months) + ...... + (Rs. 4800 + S.I. on Rs. 4800 for 1 month) + Rs. 4800

= Rs. (4800 × 5) + S.I. on Rs. 4800 for (4 + 3 + 2 + 1) months
= Rs. 24000 + S.I. on Rs. 4800 for 10 months
$$ = {\text{Rs}}{\text{.}}\left( {24000 + {\text{4800}} \times {\text{R}} \times \frac{{10}}{{12}} \times \frac{1}{{100}}} \right) = $$          $${\text{Rs}}{\text{.}}\left( {24000 + 40{\text{R}}} \right)$$
$$\eqalign{ & \therefore 22000 + \frac{{275{\text{R}}}}{3} = 24000 + 40{\text{R}} \cr & \Rightarrow \frac{{155}}{3} = 2000 \cr & \Rightarrow {\text{R}} = \frac{{2000 \times 3}}{{155}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\, = 38.71\% \,{\text{p}}{\text{.a}}{\text{.}} \cr} $$