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 the tractor cost him?

Home » 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 the tractor cost him?

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 the tractor cost him?

Solution:

We have to find the total cost of the tractor if he buys it in installments.
Total price $=$ ₹ 12000
Paid amount $=$ ₹ 6000
Unpaid amount $=$ ₹ $12000-6000=$ ₹ 6000
He pays remaining ₹ 6000 in ‘ $n$ ’ no. of installments of ₹ 500 each.
$\mathrm{So}, \mathrm{n}=6000 / 500=12$
Cost incurred by him to pay remaining 6000 is
The AP will be:
$(500+12 \%$ of 6000 $)+(500+12 \%$ of 5500 $)+\ldots$ up to 12 terms
$500 \times 12+12 \%$ of $(6000+5500+\ldots$ up to 12 terms $)$
Using the formula,
$\begin{array}{l} S_{n}=n / 2[2 a+(n-1) d] \\ n=12, a=6000, d=-500 \\ S_{12}=500 \times 12+12 / 100 \times 12 / 2[2(6000)+(12-1)(-500)] \\ =6000+72 / 100[12000+11(-500)] \\ =6000+72 / 100[12000-5500] \\ =6000+72 / 100[6500] \\ =6000+4680 \end{array}$
$= 10680$
Total cost $= 6000 + 10680$
$= 16680$
As a result, the total cost of the tractor if he buys it in installment is ₹ 16680.