A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount. How much will be the tractor cost him?
The given rate at which farmer bought tractor is Rs 12000 for which he has made down payment of Rs 6000 and agreed to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount.
Unpaid Amount = Rs 12000 − Rs 6000 = Rs 6000
Interest to be paid annually is,
Total Interest = 12 % of 6000 + 12 % of 5500 + 12 % of 5000 … .. + 12 % of 500 = 12 % of ( 500 + 1000 + 1500 + ....... + 6000 )
Now, the series forms an A.P. with both first term and common difference 500 and it is known that the n t h term a n is 6000.
The n t h term a n of an A.P. with first term a , common difference d and number of terms n is given by,
a n = a + ( n − 1 ) d
Substitute the value of a , d and a n in the above formula,
6000 = 500 + ( n − 1 ) 500 1 + ( n − 1 ) = 12 n = 12
Sum of A.P. is given by,
S n = n 2 ( 2 a + ( n − 1 ) d ) = 12 2 ( 2 ( 500 ) + ( 12 − 1 ) ( 500 ) ) = 6 [ 1000 + 5500 ] = 39000
Total interest to be paid is,
Total Interest = 12 % of ( 500 + 1000 + 1500 + ....... + 6000 ) = 12 % of 39000 = 12 100 × 39000 = Rs 4680
Total cost of tractor = Unpaid Amount + Fixed Cost of every transaction + Total Interest = Rs 6000 + Rs 500 × 12 + Rs 4680 = Rs 16680
Thus, the farmer has to pay the total cost of Rs 16680.
The given rate at which farmer bought tractor is Rs 12000 for which he has made down payment of Rs 6000 and agreed to pay the balance in annual installments of Rs 500 plus 12% interest on the unpaid amount.
Interest to be paid annually is,
Now, the series forms an A.P. with both first term and common difference 500 and it is known that the
The
Substitute the value of
Sum of A.P. is given by,
Total interest to be paid is,
Thus, the farmer has to pay the total cost of Rs 16680.
