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 will the tractor cost him?

Amount Paid to buy tractor = Rs. 12,000

Farmer Pays Cash = Rs. 6000

Remaining Balance = 12000 - 6000 = 6000

Annual Instalment = Rs 500 + interest@12% on unpaid amount

1st Instalment

Unpaid Amount = Rs. 6000

Interest on Unpaid Amount = (12/100) × 6000 = 720

Amount of Instalment = Rs. 500 + Rs. 720 = Rs. 1220

2nd Instalment

Unpaid Amount = Rs. (6000 - 500) = Rs. 5500

Interest on Unpaid Amount = (12/100) × 5500 = 6600

Amount of Instalment = Rs. 500 + Rs. 660 = Rs. 1160

3rd Instalment

Unpaid Amount = Rs. (5500 - 500) = Rs. 5000

Interest on Unpaid Amount = (12/100) × 5000 = 600

Amount of Instalment = Rs. 500 + Rs. 600 = Rs. 1100

Total no. of Instalments = 6000/500 = 12

Thus, Annual Instalments are 1220, 1160, 1100, …upto 12 terms

Since the common difference between the consecutive terms is constant. Thus, Annual Instalments are in AP.

Here

first term(a) = 1220

Common difference(d) = 1160 - 1220 = - 60

Number of terms(n) = 12

Total amount paid in 12 instalments is given by -

S_n = (n/2)[2a + (n - 1)d]

∴ S₁₂ = (12/2)[2(1220) + (12 - 1)( - 60)]

= 6[2440 + 11( - 60)]

= 6[2440 - 660]

= 6 × 1780

= 10680

Hence, total amount paid in 12 Instalments = Rs 10680

Hence,

Total Cost of Tractor

= Amount paid earlier + Amount paid in 12 Instalments

= Rs. (6000 + 10680)

= Rs. 16680