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# A sum of Rs. 1000 is invested at 8% per annum simple interest. Calculate the interest at the end of the each year. Show that these interest form an AP. using the fact, find the interest at the end of 30 years.

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This is the Important question based on Arithmetic progression Chapter of R.S Aggarwal book for ICSE & CBSE Board.
Question Number 30 of Exercise 11A of RS Aggarwal Solution
Here You have to show that the given Information is forming an AP with the help of Finding the Interest as well as the end of given time(year).

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1. Simple Interest = PÂ Ã— RÂ Ã— TÂ Ã· 100

So S.I in first yr.Â â‡’ P x R x T / 100
â‡’ 1000 x 1 x 8 Â Ã· 100Â
â‡’ 80

In second Yr.Â â‡’ 1000 x 2 x 8Â Ã· 100
â‡’ 160
Similarly in third Yr.Â â‡’ 240

So , we get the A.P. like this i.e. 80, 160, 240

Therefor Â a= 80 , d= 80.

we have to find out the interest at the end of 30 yr.
â‡’ aÂ = a + ( n-1 ) d

â‡’ 80 + ( 30 – 1 ) 80
â‡’ 80 + 29Â Ã— 80
Â â‡’ 2400

There fore , the Interest at the end of 30 yrs isÂ 2400

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