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ICSE Class 10 Answered

samita has a recurring deposit account in a bank of RS.2000 per month at the rate of 10 percentage per annum . If she gets RS. 83100 at the time of maturity . find the total time for which the account was held
Asked by yesrajput12345 | 26 Dec, 2022, 08:26: AM
answered-by-expert Expert Answer
Let n be number of months for recurring deposit
 
Principal P = 2000 per month
 
Rate of interest, r = 10% per annum
 
Recurring deposit interest I is given as
 
begin mathsize 14px style I space equals space P space 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 space equals space 2000 space cross times fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 24 end fraction cross times 10 over 100 end style 
begin mathsize 14px style I space equals space 25 over 3 n left parenthesis n plus 1 right parenthesis end style  ......................................(1)

If total month paid after n months is Rs .83100,  then interest I is calculated as
 
begin mathsize 14px style I space equals space 83100 space minus space 2000 space cross times n space end style  ............................(2)
 
By equating (1) and (2) , begin mathsize 14px style space 25 over 3 n left parenthesis n plus 1 right parenthesis space equals space 83100 minus 2000 n end style
begin mathsize 14px style n left parenthesis n plus 1 right parenthesis space equals space 9972 space minus space 240 n end style
begin mathsize 14px style n squared plus 241 n space minus 9972 space equals space 0 end style
By solving above quadratic equation , we get n = 36 months.

Answered by Thiyagarajan K | 26 Dec, 2022, 10:44: AM
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