Moving exponents

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Everydaylearner

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Dec 27, 2021
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Hey guys I hope this is in the right spot. I'm working on a Break Even Point equation for finance. I found this similar problem....

(fv÷pv)=((1+r)^4)
=> ($25000 / $11000) = ((1 + r) ^ 4)
=> 2.27272727 = ((1 + r) ^ 4)
=> 1 + r = 1.22782601
=> r = 0.2278601
=> r = 0.2279 = 22.79%

My question is about the highlighted area above. What process/formula do I need to use to get 2.27272727 to equal 1.22782601? Thank you in advance!
 
Well absolutely no one said that 2.27272727 = 1.22782601. Where did you even begin to think that someone said that: it is obvious nonsense.
 
Since [math](1+r)^4 \neq (1+r)[/math] it follows that [math]2.27272727\neq 1.22782601 [/math] which is obvious on its own.
 
Jomo said:
Since [math](1+r)^4 \neq (1+r)[/math] it follows that [math]2.27272727\neq 1.22782601 [/math] which is obvious on its own.
Click to expand...
Yes equals was the wrong choice of words. What I meant is what do I need to do to get 1.22782601 out of 2.27272727. Where does the number come from? If I remove the power from 2.27272727 it does't equal 1.22782601.
 
Everydaylearner said:
Hey guys I hope this is in the right spot. I'm working on a Break Even Point equation for finance. I found this similar problem....

(fv÷pv)=((1+r)^4)
=> ($25000 / $11000) = ((1 + r) ^ 4)
=> 2.27272727 = ((1 + r) ^ 4)
=> 1 + r = 1.22782601
=> r = 0.2278601
=> r = 0.2279 = 22.79%

My question is about the highlighted area above. What process/formula do I need to use to get 2.27272727 to equal 1.22782601? Thank you in advance!
Click to expand...
Everydaylearner said:
I appreciate your answer. Is there a formula you could show me? It seems like when I do it the number is smaller than it should be.
Click to expand...
First, it appears that when you say, "get 2.27272727 to equal 1.22782601" you are not using "equal" in the technical sense, but just mean "get from 2.27272727 to 1.22782601".

As you were told, what was done is to take the fourth root of both sides of [imath]2.27272727 = (1 + r)^4[/imath]:

[imath]\sqrt[4]{2.27272727} = \sqrt[4]{(1 + r)^4}[/imath]​
[imath]1.22782601... = 1 + r[/imath]​
[imath]r = 1.22782601... - 1 = 0.22782601...[/imath]​

Different calculators have different ways to take a fourth root. What calculator are you using, what did you enter, and what result did you get?
 
Perfect, that's what I needed! I must have been doing something wrong. I've never had to do that before but with the formula it makes sense. Thank you!
 
Taking the fourth root is the same as raising to the power of 1/4. How you enter that on your calculator will depend on which one you are using.
 
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