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 will the tractor cost him?
Answer:
Cost of the tractor = 12000
Cash payment = 6000
Balance amount = 12000-6000 = 6000
Now interest on 1st installment = (6000*12*1)/100 = 720
Unpaid amount = 6000 - 500 = 5500
Interest on 1st installment = (5500*12*1)/100 = 660
Unpaid amount = 5500 - 500 = 5000
Interest on 3rd installment = (5000*12*1)/100 = 600
Unpaid amount = 5000 - 500 = 4500
and so on.
Total interest paid = 720+660+600+.......up to 12 terms
It forms an AP
where first term a = 720
common difference d = 660-720 = -60
Number of terms n = 12
Now total ineterest = (12/2)[2*720 + (12-1)*(-60)] [Sn = (n/2*{2a + (n-1)d})]
= 6*{1440 - 11*60}
= 6*(1440 - 660)
= 6*780
= 4680
Now total amount of the tractor = 12000 + 4680 = 16680 rupees
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