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Thread: How to Find the Percentage of Change

  1. #1
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    How to Find the Percentage of Change

    Hi,

    Say I had \$1,000 in the end of the year 2007, and \$1,500 in the of 2016.

    What is the function to find the annual constant change in %?

    It's easy to see that the total change is 50% increase, but it's not that the annual change is 5% (50% / 10 years)..

    Thanks
    Last edited by skeeter; Dec 29th 2016 at 11:19 AM.
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  2. #2
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    Re: How to Find the Percentage of Change

    so you want the interest rate at which \$1000 compounded annually would get you \$1500 in 9 yrs

    $1000(1+int)^9 = 1500$

    $\dfrac{1000}{1500} = (1+int)^{-9}$

    $\dfrac 2 3 = (1+int)^{-9}$

    $\dfrac 3 2 = (1+int)^9$

    $int = \left(\dfrac 3 2\right)^{1/9}-1 \approx 0.046 = 4.6 \%$
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  3. #3
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    Re: How to Find the Percentage of Change

    Thank you.

    Please explain how did you move from step 3 to step 4?
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  4. #4
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    Re: How to Find the Percentage of Change

    i took the reciprocal of both sides
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  5. #5
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    Re: How to Find the Percentage of Change

    Great, thanks a lot
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  6. #6
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    Re: How to Find the Percentage of Change

    1000(1 + i)^9 = 1500
    (1 + i)^9 = 1500/1000 = 1.5
    1 + i = 1.5^(1/9)
    i = 1.5^(1/9) - 1
    i = ~.046

    Standard formula:
    i = (f/p)^(1/n) - 1
    where:
    p = present value
    f = future value
    n = number of periods

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