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 -
Sn = (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