A man borrows rs. 8000 and agrees to repay with a total interest of rs.1360 in 12 monthly instalments.Each instalment being less than the preceding one by rs.40. find the amount of the first and last instalment.
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Answered by
222
Money he borrows = 8000
Interest he will pay = 1360
Total money he will pay after = 8000 + 1360 = 9360
Now he will pay in 12 installments with a difference of 40 in each installment.
This is a form of AP,
where common difference d = -40, number of terms n = 12, and sum of 12 terms is 9360
So,
Sum of n terms in AP is
Sum = n/2 [ 2a + (n - 1)d ]
9360 = 12/2 [ 2a - 40(12 - 1) ]
9360 = 6 [ 2a - 440 ]
1560 = 2a - 440
2a = 2000
a = 1000
nth term in AP is given by:
a(n) = a + (n - 1)d
Last term = 1000 - 40(12 - 1)
=1000 - 440 = 560
Therefore first installment is 1000 and last one is 560.
Interest he will pay = 1360
Total money he will pay after = 8000 + 1360 = 9360
Now he will pay in 12 installments with a difference of 40 in each installment.
This is a form of AP,
where common difference d = -40, number of terms n = 12, and sum of 12 terms is 9360
So,
Sum of n terms in AP is
Sum = n/2 [ 2a + (n - 1)d ]
9360 = 12/2 [ 2a - 40(12 - 1) ]
9360 = 6 [ 2a - 440 ]
1560 = 2a - 440
2a = 2000
a = 1000
nth term in AP is given by:
a(n) = a + (n - 1)d
Last term = 1000 - 40(12 - 1)
=1000 - 440 = 560
Therefore first installment is 1000 and last one is 560.
Answered by
19
Hii friends
Your answer is here.
First installment = 1000
Last installment = 560
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