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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
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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