A person borrows Rs. 4000 and agrees to repay Rs. 500 per month. He pays an interest at the rate if 5%per annum on the outstanding balance. Find the average rate of interest.
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Answer:
Total money repaid by Babubhai in 10 installments =S
10
= Principle + interest
∴s
10
=4000+500=4500
∴ number of installment (n)=10
∵ he repays each installment being less that the preceding installment by Rs. 10
∴ difference between two consecutive installments (d)=−10
First installment =a=?
Last installment (t
10
)=?
Therefore, S
n
=
2
n
[2a+(n−1)d]
⇒S
10
=
2
10
[2a+(10−1)−10]
⇒4500=5[2a+9(−10)]
⇒
5
4500
=2a−90
⇒900=2a−90
⇒2a=990
⇒a=495 ........(1)
Now t
n
=a+(n−1)d
⇒t
n
=495+(10−1)−10
⇒t
n
=495+−90
⇒t
10
=405
∴ first installment =495
Last installment =405
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