Mr.Prabhakar opens a recurring deposit account of Rs.300 per month at 8% si p.a .On maturity,he gets Rs.9930.Find the period for which he continued with the account

Asked by sreenivasanmaralapadu | 24th May, 2015, 03:25: PM

Expert Answer:

L e t space t h e space n u m b e r space o f space m o n t h s space M r. space P r a b h a k a r space d e p o s i t e d space b e space apostrophe n apostrophe space m o n t h s. S u m space d e p o s i t e d space i n space apostrophe n apostrophe space m o n t h s space equals space 300 n N o. space o f space m o n t h s space o f space i n t e r e s t space equals space fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction E q u i v a l e n t space P r i n c i p l e space o f space o n e space m o n t h space equals space 300 cross times space fraction numerator n left parenthesis n plus 1 right parenthesis over denominator 2 end fraction equals 150 n left parenthesis n plus 1 right parenthesis I n t e r e s t space o n space R s. space 150 n left parenthesis n plus 1 right parenthesis space f o r space 1 space m o n t h space a t space 8 % space p. a. equals fraction numerator 150 n left parenthesis n plus 1 right parenthesis cross times 1 cross times 8 over denominator 12 cross times 100 end fraction equals n left parenthesis n plus 1 right parenthesis  T o t a l space a m o u n t space o n space m a t u r i t y space equals space R s space 9930 300 n plus n left parenthesis n plus 1 right parenthesis equals 9930 rightwards double arrow 300 n plus n squared plus n equals 9930 rightwards double arrow n squared plus 301 n minus 9930 equals 0 rightwards double arrow n squared plus 331 n minus 30 n minus 9930 equals 0 rightwards double arrow n left parenthesis n plus 331 right parenthesis minus 30 left parenthesis n plus 331 right parenthesis equals 0 rightwards double arrow left parenthesis n plus 331 right parenthesis left parenthesis n minus 30 right parenthesis equals 0 therefore left parenthesis n plus 331 right parenthesis rightwards double arrow n equals negative 331 space left square bracket N o t space a c c e p t a b l e right square bracket therefore n minus 30 equals 0 rightwards double arrow n equals 30 N o. space o f space m o n t h s space o f space m a t u r i t y space equals space 30  P e r i o d space f o r space w h i c h space h e space c o n t i n u e d space equals space 30 space m o n t h s.

Answered by Prasenjit Paul | 24th May, 2015, 08:29: PM

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