Q. 303.9( 19 Votes )

A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.

Answer :

In simple interest, the interest remains same in all year.


Interest per year = 10000 × 5% = 500


Hence,


Amount in 1st year = Rs. 10000


Amount in 2nd year = Amount in 1st year + Interest


= 10000 + 500


= 10500


Amount in 3rd year = Amount in 2nd year + Interest


= 10500 + 500


= 11000


Hence, the series becomes


10000, 10500, 11000,…


Since the common difference between the consecutive terms is constant. Thus, Above Series are in AP.


Where,


first term(a) = 10000


common difference(d) = 10500 - 10000 = 500


Amount in 15th year is given by putting n = 15 in


an = a + (n - 1)d


a15 = 10000 + (15 - 1)500


= 10000 + 14(500)


= 10000 + 7000


= 17000


Thus, amount in 15th year is Rs. 17000.


Also, Amount after 20 years


= a21


= 10000 + (21 - 1)500


= 10000 + 20 × 500


= 10000 + 10000


= 20000


Thus, amount after 20th year is Rs. 20000.


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