Monica had RD account in the Union Bank of India and deposited rupees 600 per month . If the maturity value of this account it was rupees 24 930 and the rate of interest was 10 % per annum; find the time for which the account was held.

Asked by nishabr7 | 20th May, 2019, 09:02: PM

Expert Answer:

begin mathsize 16px style Here space straight P space equals space Rs. space 600
Rate space of space interest space equals space 10 percent sign
Interest space equals space straight P space cross times space fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 space cross times space 12 end fraction cross times space straight r over 100
space space space space space space space space space space space space equals 600 space cross times space fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 space cross times space 12 end fraction cross times space 10 over 100
space space space space space space space space space space space space equals space fraction numerator 5 straight n left parenthesis straight n space plus space 1 right parenthesis over denominator 2 end fraction space space space space space space space... space left parenthesis straight i right parenthesis
Maturity space Value space equals space straight P space cross times space straight n space plus space straight P space space fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 space cross times space 12 end fraction cross times space straight r over 100
rightwards double arrow space space space 24930 space space space equals space 600 straight n space plus space space fraction numerator 5 straight n left parenthesis straight n space plus space 1 right parenthesis over denominator 2 end fraction space space space... space from space left parenthesis straight i right parenthesis
rightwards double arrow space space 24930 space cross times space 2 space equals space 1200 straight n space plus space 5 straight n squared space plus space 5 straight n space
rightwards double arrow space 5 straight n squared space plus space 1205 straight n space minus space 49860 space equals space 0
Divide space by space 5 comma space we space get
straight n squared space plus space 241 straight n space minus space 9972 space equals space 0
rightwards double arrow straight n space equals space fraction numerator negative straight b plus-or-minus square root of straight b squared space minus space 4 ac end root over denominator 2 straight a end fraction

rightwards double arrow straight n space equals space fraction numerator negative 241 plus-or-minus square root of left parenthesis 241 right parenthesis squared space minus space 4 space cross times space 1 space cross times negative 9972 straight c end root over denominator 2 space cross times 1 end fraction

rightwards double arrow straight n space equals space fraction numerator negative 241 plus-or-minus 313 over denominator 2 end fraction space space
rightwards double arrow straight n space equals space fraction numerator negative 241 space plus space 313 space over denominator 2 end fraction space or space straight n space equals space fraction numerator negative 241 space minus space 313 space over denominator 2 end fraction
rightwards double arrow straight n space equals space fraction numerator negative 241 space plus space 313 space over denominator 2 end fraction space equals space 72 over 2 space space equals space 36 space or space straight n space equals space fraction numerator negative 554 space over denominator 2 end fraction equals space minus 277 space end style
n can't be negative.
Therefore the time for which the account was held is 36 months or 3 years.

Answered by Yasmeen Khan | 21st May, 2019, 12:03: PM