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ICSE Class 10 Answered

Mr. Kumar has a recurring deposit account is Rs.1,20,400. If each monthly instalment for this account is Rs.1.600 and the rate of interest is 10% per year, find [3] the time for which the account was held.
Asked by krrishjaiswal10 | 19 Jul, 2021, 08:56: AM
answered-by-expert Expert Answer
Recurring deposit interest I for n months is given as
 
begin mathsize 14px style I space equals space P space cross times fraction numerator n space left parenthesis space n plus 1 right parenthesis over denominator 2 cross times 12 end fraction cross times r over 100 space end style
where P is principal amount and r is rate of interest per annum
 
Hence Recurring deposit interest in this case is given as
 
begin mathsize 14px style I space equals space 1600 space cross times fraction numerator n space left parenthesis space n plus 1 right parenthesis over denominator 2 cross times 12 end fraction cross times 10 over 100 space space equals space 20 over 3 cross times n space left parenthesis n plus 1 right parenthesis end style
If depositor has received 1,20,400 , then we have
 
begin mathsize 14px style 20 over 3 n left parenthesis n plus 1 right parenthesis space plus space 1600 space n space equals space 120400 end style
After simplifying above expression, we get , n2 + 241 n - 18060 = 0
 
By solving above quadratic equation, we get n = 60 
 
Hence period of recurring deposit is 60 months
Answered by Thiyagarajan K | 17 Sep, 2021, 17:11: PM

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