**Question:**

A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much the tractor cost him?

**Solution:**

Cost of the tractor = Rs 12000

It is given that the farmer pays Rs 6000 in cash.

Unpaid amount = Rs 6000

He has to pay Rs 6000 in annual instalments of Rs 500 plus 12% interest on the unpaid amount.

$\therefore$ Number of years taken by the farmer to pay the whole amount $=6000 \div 500=12$

Hence, the interest paid by farmer annually would be as follows:

$12 \%$ of Rs $6000+12 \%$ of Rs $5500+12 \%$ of Rs $5000 \ldots$

$=720+660+600 \ldots$

It is in an A.P. where $a=720, d=-60$ and $n=12$.

Total sum:

$\frac{12}{2}[2 \times 720+11 \times-60]$

$=6[1440-660]$

$=\operatorname{Rs} 4680$

∴ Amount the farmer has to pay = Rs 12000 + Rs 4680 = Rs 16680