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.

Answer 1

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