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2015-08-21T01:40:40+05:30

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Deposited amount = P
maturity amount = 2 P at the end of one year.
balance after Rs 65 taken out :  P1 = 2 P - 65

balance after year 2 :  P2 = 2 P1 - 65  = 2² P - 65 (2 + 1)
balance after year 3 :    P3 = 2 P2 - 65  = 2³ P - 65 * (4 + 2 + 1)

balance after n th year  =  Pn  = 2^n P - 65 * (2^{n-1} + 2^{n-2} + ... + 4 + 2 + 1)
                 = Pn = 2^n * P - 65 * (2^n - 1)            using G.P.
                 = 2^n * (P - 65) + 65
 for n = 6,  Pn = 0 
    =>    64 * (P - 65) = - 65

         =>  P = 65 - 65/64 = 65 * 63/64 = Rs 63.984375 

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