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Math Help - Crossover rate - How to solve r?

  1. #1
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    Crossover rate - How to solve r?

    Hi all!

    My math problem is about a Finance class, but it is really the math that gets me into trouble. Please see the equation:

    (15/(1+r))+(10/(1+r)^2)+(8/(1+r)^3)-25=(2.5/(1+r))+(2.5/(1+r)^2)+(2.5/(1+r)^3)

    I guess the first step would be to get it all to one side of the equation. In particular, I am wondering what to do with the denominators. Can I add them up?

    Please note I'm only allowed to use a basic (i.e. non-graphic) calculator.

    Thank you!

    Sebastiaan
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  2. #2
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    Re: Crossover rate - How to solve r?

    Quote Originally Posted by sebastiaan View Post
    Hi all!

    My math problem is about a Finance class, but it is really the math that gets me into trouble. Please see the equation:

    \dfrac{15}{(1+r)}+\dfrac{10}{(1+r)^2}+\dfrac{8}{(1  +r)^3}-25=\dfrac{2.5}{(1+r)}+ \dfrac{2.5}{(1+r)^2}+\dfrac{2.5}{(1+r)^3}

    I guess the first step would be to get it all to one side of the equation. In particular, I am wondering what to do with the denominators. Can I add them up?

    Please note I'm only allowed to use a basic (i.e. non-graphic) calculator.

    Thank you!

    Sebastiaan
    You can't add the denominators because they are not the same. I would multiply both sides by the LCD of (1+r), (1+r)^2 \text{ and } (1+r)^3 to clear the denominator.

    You can then collect like terms
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  3. #3
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    Re: Crossover rate - How to solve r?

    Do you mean that for the right side of the equation I could end up with:

    ((2.5^6)/((1+r)^6))+((2.5^3)/((1+r)^6))+((2.5^2)/((1+r)^6))

    So that all denominators share the common '^6'?

    Thanks a lot!
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  4. #4
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    Re: Crossover rate - How to solve r?

    Quote Originally Posted by sebastiaan View Post
    Do you mean that for the right side of the equation I could end up with:

    ((2.5^6)/((1+r)^6))+((2.5^3)/((1+r)^6))+((2.5^2)/((1+r)^6))

    So that all denominators share the common '^6'?

    Thanks a lot!
    Something I should have mentioned in the last post: r \neq -1.

    Nope, you can't raise both sides to the power. To use an example: \dfrac{2}{3} \neq \dfrac{2^2}{3^2}. If you multiply both sides of your equation by the LCD you will clear the denominator making the equation easier to solve.

    Do you know what the LCD of (1+r), (1+r)^2 \text{ and } (1+r)^3 is? Hint: 1+r and (1+r)^2 are both factors of (1+r)^3
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    Re: Crossover rate - How to solve r?

    Thanks! Helped a lot
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  6. #6
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    Re: Crossover rate - How to solve r?

    You really only need to multiply both sides by (1+ r)^3 since this will cancel 1+ r and (1+ r)^2 also.
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