Discussion
The price of a T.V. set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Answer: D
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Carry everything forward to the date of the last installment, 19 years after purchase.
The debt grows for 19 years:
\[ 20000\left(1 + \frac{6 \times 19}{100}\right) = 20000 \times 2.14 = \text{Rs. } 42{,}800 \]
The first 19 installments of Rs. 1000 earn interest for 19, 18, …, 1 years:
\[ 1000\left[19 + \frac{6}{100}(19 + 18 + \cdots + 1)\right] = 1000\left[19 + 0.06 \times 190\right] \]
\[ = 1000(19 + 11.4) = \text{Rs. } 30{,}400 \]
\[ \text{last installment} = 42800 - 30400 = \text{Rs. } 12{,}400 \]
That figure is not among the choices, so the answer is none of these.
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