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math

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An amount of money is invested at 12%/a interest. Write an equation and solve it to determine the length of time it will take for the original amouunt to double if the interest is compounded annually.

  • math - ,

    The rule of 72 gives the rough period as 72/12=6 years.

    The accurate calculation is as follows:
    P=principal
    R=interest rate= 1.12 for 12%
    n=number of years required.
    So
    PRn=2P
    Rn=2
    Take log on both sides,
    log(Rn=log(2)
    n*log(R) = log(2)
    n=log(2)/log(R)
    =log(2)/log(1.12)
    =0.3010/0.0492
    =6.116 years.

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