# Thread: Crossover rate - How to solve r?

1. ## 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

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

Originally Posted by sebastiaan
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

3. ## 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!

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

Originally Posted by sebastiaan
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

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

Thanks! Helped a lot

6. ## 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.