A sum of money place at compound interest doubles itself in 4 years. In how many years will it amount to eight times itself ?



A sum of money place at compound interest doubles itself in 4 years. In how many years will it amount to eight times itself ?

A. 16

B. 8

C. 12

D. 20

Answer : C. 12...


Explanation :

    Let, Principal = Rs. 100.
    Amount = Rs. 200.
    Rate = r%
    Time = 4 years.

    Now,
    A = P * [ 1 + (r/100) ]n
    200 = 100 * [ 1 + (r/100) ]4
    2 = [1 + (r/100)]4 ........... (i)
    If sum become 8 times in the time n years, then,
    8 = ( 1 + (r/100) )n
    23 = ( 1 + (r/100) )n ........ (ii)

    Using eqn (i) in (ii), we get
    ( [1 + (r/100) ]4)3 = ( 1 + (r/100) )n
    [1 + (r/100)]12 = (1 + (r/100))n
    n = 12 years.


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