A man deposits Rs. 400 per month at 10%p.a in a recurring deposit account and gets R.s.30100 at the time of maturity. Find the total time for which the account is held.
Answers
Given : A man deposits Rs. 400 per month at 10% p.a in a recurring deposit account and gets R.s.30100 at the time of maturity.
To Find : the total time for which the account is held.
Solution:
Man Deposit Rs 400 per month
Account held for n months
Amount deposited = 400 n
Interest Earned on 1st deposit amount = 400 x 10 *(n/12)/100 = (10/3)n
Interest Earned on 2nd deposit amount = 400 x 10 *((n-1)/12)/100 = (10/3)(n-1)
Interest Earned on nth deposit amount = 400 x 10 *(1/12)/100 = (10/3)
Total amount = 400n + (10/3)n + (10/3)(n-1) + ... ... .. + (10/3) = 30100
= 400n + (10/3)(n)(n+ 1)/2 = 30100
=> 1200n + 5n(n + 1) = 90300
=>240n + n² + n = 18060
=> n² + 241n - 18060 = 0
=> n² + 301n - 60n - 18060 = 0
=> (n + 301)(n - 60) = 0
=> n = 60
60 months = 5 years
time for which the account is held. is 5 years
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