Question : In a store, Arun has two options to buy a mobile phone, either he can pay the full amount of Rs. 2,500 or he may buy at an instalment scheme, i.e. Rs. 520 in down payment and four equal instalments, rate of interest is charged at 25% p.a. simple interest. Arun buys a mobile phone on an instalment scheme. What is the monthly instalment for Arun?
Option 1: Rs. 510
Option 2: Rs. 530
Option 3: Rs. 550
Option 4: Rs. 520
Correct Answer: Rs. 520
Solution : Full amount = Rs. 2,500 Down payment = Rs. 520 Remaining amount = 2,500 – 520 = Rs. 1980 Rate of interest = 25% per annum = $\frac {25}{12}$% per month Let the four equal monthly instalments be $x$. Total interest paid $=4x-1980$ Interest paid before the first instalment $=\frac{1980×\frac{25}{12}×1}{100}=\frac{1980}{48}$ Interest paid before the second instalment $=\frac{(1980-x)×\frac{25}{12}×1}{100}=\frac{1980-x}{48}$ Interest paid before the third instalment $=\frac{(1980-2x)×\frac{25}{12}×1}{100}=\frac{1980-2x}{48}$ Interest paid before the fourth instalment $=\frac{(1980-3x)×\frac{25}{12}×1}{100}=\frac{1980-3x}{48}$ Now, $4x-1980=\frac{1980}{48}+\frac{1980-x}{48}+\frac{1980-2x}{48}+\frac{1980-3x}{48}$ ⇒ $4x-1980=\frac{1}{48}×(1980+1980-x+1980-2x+1980-3x)$ ⇒ $192x-95040=7920-6x$ ⇒ $198x=102960$ ⇒ $x=\frac{102960}{198}=520$ Hence, the correct answer is Rs. 520.
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