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Question:
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A farmer buys a used tractor for $₹ 12000$. He pays $₹ 6000$ cash and agrees to pay the balance in annual instalments of $₹ 500$ plus $12 \%$ interest on the unpaid amount. How much will the tractor cost him ?
Solution:
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Verified Answer
Total cost of the tractor $=₹ 12000$
Paid cash $=₹ 6000$
Balance $=₹ 6000$
Number of instalments@ $₹ 500$ each $=12$
Interest on first instalment $=₹ \frac{6000 \times 12 \times 1}{100}$
$=₹ 720$
First instalment $=₹(500+720)=₹ 1220$
Interest on second instalment
$=₹ \frac{5500 \times 12 \times 1}{100}=₹ 660$
$\therefore \quad$ Second instalment $=₹(500+660)$
$=\text { ₹ } 1160$
Interest on third instalment
$=₹\left(\frac{5000 \times 12 \times 1}{100}\right)=₹ 600$
First instalment $=₹(500+720)=₹ 1220$
Interest on second instalment
$\begin{aligned}
&=₹ \frac{5500 \times 12 \times 1}{100}=₹ 660 \\
&\therefore \quad \text { Third instalment }=₹(500+600) \\
&=₹ 1100 \\
&\therefore \quad \text { Total amount paid in instalments } \\
&=₹(1220+1160+1100+\ldots \ldots \ldots \text { to } 12 \text { terms }) \\
&=\frac{12}{2}[2 \times 1220+(12-1)(-60)] \\
&=6[2440-11 \times 60] \\
&=6[(2440-660)]=6 \times 1780=10680 \\
&\therefore \text { Amount paid by farmer } \\
&=₹ 6000+10680=₹ 16680
\end{aligned}$
Paid cash $=₹ 6000$
Balance $=₹ 6000$
Number of instalments@ $₹ 500$ each $=12$
Interest on first instalment $=₹ \frac{6000 \times 12 \times 1}{100}$
$=₹ 720$
First instalment $=₹(500+720)=₹ 1220$
Interest on second instalment
$=₹ \frac{5500 \times 12 \times 1}{100}=₹ 660$
$\therefore \quad$ Second instalment $=₹(500+660)$
$=\text { ₹ } 1160$
Interest on third instalment
$=₹\left(\frac{5000 \times 12 \times 1}{100}\right)=₹ 600$
First instalment $=₹(500+720)=₹ 1220$
Interest on second instalment
$\begin{aligned}
&=₹ \frac{5500 \times 12 \times 1}{100}=₹ 660 \\
&\therefore \quad \text { Third instalment }=₹(500+600) \\
&=₹ 1100 \\
&\therefore \quad \text { Total amount paid in instalments } \\
&=₹(1220+1160+1100+\ldots \ldots \ldots \text { to } 12 \text { terms }) \\
&=\frac{12}{2}[2 \times 1220+(12-1)(-60)] \\
&=6[2440-11 \times 60] \\
&=6[(2440-660)]=6 \times 1780=10680 \\
&\therefore \text { Amount paid by farmer } \\
&=₹ 6000+10680=₹ 16680
\end{aligned}$
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