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Math Help - What have I done wrong in this rearrangment

  1. #1
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    What have I done wrong in this rearrangment

    To make i the subject of the following equation, these are my workings

     r=[1+i/12]^{12}-1

    1. Add 1 to both sides

     r+1=[1+i/12]^{12}

    2. Open the brackets so that

     r+1=1+i^{12}/12^{12}

    3. Then multiply both sides by 12^{12} to give

     12^{12}(r+1)=1+i^{12}

    4. And then finally

     12^{1/12}(r+1)-1=i

    The answer in the book though is

     12((r+1)^{1/12})-1=i

    But I don't understand why I was supposed raise (r+1) to the power of 12 when I multiplied by  12^{12} in step 3
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  2. #2
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    Are you sure that you posted the correct statement.
    For one: \left( {1 + \frac{i}{{12}}} \right)^{12}  \ne 1 + \frac{{i^{12} }}{{12^{12} }}. It is much more complicated.
    I don't think it is a pre-algebra/elementry algebra question.
    What level question is this?
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  3. #3
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    Is that my mistake then

    why is

    \left( {1 + \frac{i}{{12}}} \right)^{12}  \ne 1 + \frac{{i^{12} }}{{12^{12} }}
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  4. #4
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    Quote Originally Posted by cistudent View Post
    why is
    \left( {1 + \frac{i}{{12}}} \right)^{12}  \ne 1 + \frac{{i^{12} }}{{12^{12} }}
    I told that it is much more complicated.
    Do you understand the binominal expansion theorem?
     \left( {1 + \frac{i}{{12}}} \right)^{12}  = \sum\limits_{k = 0}^{12} {\binom{12}{k}\left( {\frac{i}{{12}}} \right)^k } .

    So either you have posted the wrong problem or you are not ready to work it.
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  5. #5
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    OK this is the problem word for word and is included in a series of essential maths exercises all of which I got right except for this one. The binominal expansion theorem has not been mentioned thus far in the text book, so I'm guessing I wrote the problem wrong and am missing something obvious.

    When interest is paid by monthly instalments, at a nominal rate of i\% the actual rate of interest (the annual percentage rate) is

    r= \left( {1 + \frac{i}{{12}}} \right)^{12}  - 1

    Express the nominal rate as a function of r.

    My workings and the answer are as per the OP.
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  6. #6
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    Sorry, but I thought you were working with mathematics.
    That appears to have something to do with finance.
    I cannot help with that. It is not mathematics.
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  7. #7
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    Eh? Finance is Maths.

    Is the problem not a practical application of mathematics? Perhaps I have put this in the wrong thread?
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