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# 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. - ICSE Class 10 - Mathematics

#### 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.

#### Solution

Amount of recurring deposit per month = Rs. 1000

Rate of interest = 10 % p.a

let period = n months

Amount of interest = 5550   .....(1)

Total principal for one month = (1000xxn(n+1))/2

"Interest" = (1000n(n+1))/2 xx 10/100 xx 1/12

= 25/6 n (n+1)  ......(2)

From (1) nd (2) , we get

25/6n(n+1) = 5550

25n^2 + 25n = 33300

25n^2 + 25n - 33300 = 0

n^2 + n - 1332 = 0

n^2 + 37n - 36n - 1332 = 0

n(n+37) - 36(n+37) = 0

(n - 36)(n +  37) = 0

n = 36

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Solution 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. Concept: Computation of Interest.
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