Saurabh has a recurring deposit in a bank of5000 per month at the rate of 9% p.a. If he gets 1,07,875 at the time of maturity, the total time for which the account was held was
Answers
Given : Saurabh has a recurring deposit in a bank of5000 per month at the rate of 9% p.a. he gets 1,07,875 at the time of maturity
To find : total time for which the account was held was
Solution:
Amount deposited per month = Rs 5000
Rate of interest = 9 % pa = 9/12 = 0.75 % per month
Let say Deposit was for n months
Amount deposited = 5000 * n Rs
Interest for 1st Deposit is for n months
interest for 2nd deposit for n-1 months
and so on
Interest = P * R * T /100
Interest = ( (5000 * 0.75 )/100) ( n + (n-1) + (n-2) +...................+ 1)
= (75/2) (n)(n+1)/2
5000 * n + 75(n)(n+1)/4 = 107875
=> 200n + 3(n)(n+1)/4 = 4315
=> 800n + 3n² +3n = 17260
=> 3n² + 803n - 17260 = 0
=> 3n² + 863n - 60n - 17260 = 0
=> 3n(n - 20) + 863(n-20) = 0
= > (3n + 863)(n-20) = 0
=> n = 20
Account was held for 20 months
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