Question

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?

Answer 1

Given: Price of the tractor is ₹12000.

We need 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’ number of installments of ₹ 500 each.

So, 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) + … up to 12 terms

500 × 12 + 12% of (6000 + 5500 + … up to 12 terms)

By using the formula,

S_n = n/2 [2a + (n – 1)d]

n = 12, a = 6000, d = -500

S₁₂ = 500×12 + 12/100 × 12/2 [2(6000) + (12 - 1) (-500)]

= 6000 + 72/100 [12000 + 11 (-500)]

= 6000 + 72/100 [12000 – 5500]

= 6000 + 72/100 [6500]

= 6000 + 4680

= 10680

Total cost = 6000 + 10680

= 16680

∴ The total cost of the tractor if he buys it in installment is ₹ 16680.