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Thread: What is the math behind this?

  1. #1
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    What is the math behind this?

    I would like to understand how to solve for r in this problem.

    2773=1000(1+r)^36

    I know that r=.0287 but I do not understand how to solve with the exponents. Do I use Ln? and how is that done? Thanks
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  2. #2
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    Quote Originally Posted by Smoriginal View Post
    I would like to understand how to solve for r in this problem.

    2773=1000(1+r)^36

    I know that r=.0287 but I do not understand how to solve with the exponents. Do I use Ln? and how is that done? Thanks
    yes you have to use ln, see here,

    $\displaystyle
    \frac{2773}{1000}=(1+r)^{36}$

    $\displaystyle 2.773=(1+r)^{36}$

    Now take natural log on both sides:

    $\displaystyle
    \ln{2.773}= \ln \left[(1+r)^{36}\right]$

    $\displaystyle
    1.019929767= 36 \ln (1+r)$

    $\displaystyle
    \frac{1.019929767}{36}= \ln (1+r)$

    $\displaystyle 0.028331382= \ln (1+r)$

    Now take antilog,

    $\displaystyle e^{0.028331382}= 1+r$

    $\displaystyle 1.028736533= 1+r$

    $\displaystyle 1.028736533-1= r$

    $\displaystyle r=0.028736533$

    $\displaystyle r = 2.87 \% $
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  3. #3
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    ahh I see. Thanks so much!!
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