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?

Answer 1

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.
∴ Number of years taken by the farmer to pay the whole amount = 6000 $÷$ 500 = 12
Hence, the interest paid by farmer annually would be as follows:
$$\begin{gathered} 12\%\mathrm{of}\mathrm{Rs}6000+12\%\mathrm{of}\mathrm{Rs}5500+12\%\mathrm{of}\mathrm{Rs}5000.. \\ =720+660+600.... \end{gathered}$$

It is in an A.P. where a = 720 , d = $-$60 and n = 12.
Total sum:
$$\begin{gathered} \frac{12}{2}\left[2\times 720+11\times -60\right] \\ =6\left[1440-660\right] \\ =\mathrm{Rs}4680 \end{gathered}$$

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