# 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.

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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