Discussion
A TV can be bought for Rs. 20000 cash or by paying in four equal monthly installments with an initial down payment of Rs. 4000. If the rate of interest for this facility is 8% per annum, then what would be the installment charged for each month?
Answer: D
After the down payment the balance is \( 20000 - 4000 = \text{Rs. } 16{,}000 \), cleared by four monthly installments of \( x \).
Carry everything forward to the end of month 4. The debt grows for 4 months, while the installments earn interest for 3, 2, 1 and 0 months:
\[ 16000\left(1 + \frac{8}{100} \times \frac{4}{12}\right) = x\left[\left(1 + \tfrac{8}{100}\cdot\tfrac{3}{12}\right) + \left(1 + \tfrac{8}{100}\cdot\tfrac{2}{12}\right) + \left(1 + \tfrac{8}{100}\cdot\tfrac{1}{12}\right) + 1\right] \]
\[ 16000 \times 1.026667 = x(1.02 + 1.013333 + 1.006667 + 1) \]
\[ 16426.67 = 4.04\,x \quad\Longrightarrow\quad x = \text{Rs. } 4066.01 \]
Dividing the balance by four gives Rs. 4000, which ignores the interest entirely - hence that distractor.
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