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Question

Priyanka has a recurring deposit account of Rs. 1000 per month at 10% per annum. If she gets Rs. 5550 as interest at the time of maturity, find the total time for which the account was held.

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Solution

Let the maturity period be n months,

P be the money deposited every month which is Rs.1000

and r be the rate of interest per annum which is 10%.

Now, the interest I received at the end of maturity is calculated by the following formula:

I=P×n(n+1)24×r100

We are given I=5500, so
substituting the values, we get

5550=1000×n(n+1)24×10100

n(n+1)=5550×24100=1332

n2+n1332=0

n2+37n36n1332=0

(n36)(n+37)=0

n=36, 37

Since the maturity period cannot be negative, n=36.

Therefore, the total time for which the account was held was 36 months which is the same as 3 years. So the maturity period was 3 years.

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