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ICSE Class 10 Answered

Beena has a cumulative deposit account of ₹400 per month at 10% per annum simple interest. If she gets ₹30100 at the time of maturity, find the total time for which the account was held.
Asked by www.adityakumarjaiswal622 | 21 Jan, 2019, 07:55: AM
answered-by-expert Expert Answer
If p is deposit amount every month and r is rate of interest, then interest I of cumulative deposit for n months is given by
 
begin mathsize 12px style I space equals space p cross times fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 cross times 12 end fraction cross times r over 100 end style
hence we have, begin mathsize 12px style 400 cross times fraction numerator n open parentheses n plus 1 close parentheses over denominator 2 cross times 12 end fraction cross times 10 over 100 space equals space 30100 space minus space 400 n end style
above equation is simplified as : n2 + 241n - 18060 = 0 ..............(1)
 
after factorising LHS of eqn.(1), it is rewritten as,  (n+301)(n-60) = 0
 
hence n = 60 months = 5 years
Answered by Thiyagarajan K | 21 Jan, 2019, 08:19: AM
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