# Thread: Transpose An Equation

1. ## Transpose An Equation

Can anyone transpose this equation to solve for n as a function of A, P, i ie, n = .....
A = P(((1 + i)n - 1)/( (1 - I) + (1 + i)n))

Please show each step!

Sorry for the typo! Added = sign after A

2. ## Re: Transpose An Equation

$A = P\dfrac{(1+i)^n-1}{(1-i)+(1+i)^n}$

$\dfrac{A}{P} = \dfrac{(1-i)-(1-i)+(1+i)^n-1}{(1-i)+(1+i)^n} = 1+\dfrac{i-2}{(1-i)+(1+i)^n}$

$\dfrac{A}{P}-1 = \dfrac{i-2}{(1-i)+(1+i)^n}$

$\left(\dfrac{A}{P}-1\right) ((1-i)+(1+i)^n) = i-2$

$\dfrac{A(1-i)}{P}-1+i+\left(\dfrac{A}{P}-1\right) (1+i)^n = i-2$

$\left(\dfrac{A}{P}-1\right) (1+i)^n = \dfrac{A(i-1)}{P}-1$

$(1+i)^n = \dfrac{\dfrac{A(i-1)}{P}-1}{\dfrac{A}{P}-1}$

$n = \dfrac{ \ln \left( \dfrac{A(i-1)}{P} - 1\right) - \ln \left( \dfrac{A}{P} - 1 \right) }{\ln (1+i) }$

6. ## Re: Transpose An Equation

Originally Posted by SGS
Both Post #2 and Reply With Quote have $, dfrac, left, right. Those commands have nothing to do with mathematics. They are type-settings to make the symbols. 1)n = \dfrac{ \ln \left( \dfrac{A(i-1)}{P} - 1\right) - \ln \left( \dfrac{A}{P} - 1 \right) }{\ln (1+i) } is the code required to see 2)$n = \dfrac{ \ln \left( \dfrac{A(i-1)}{P} - 1\right) - \ln \left( \dfrac{A}{P} - 1 \right) }{\ln (1+i) }$Line #1) is exactly the same as line #2) except 2) begin with and ends with$. That tell the browser to display LaTex.

SEE HERE

7. ## Re: Transpose An Equation

Thank you 1111

8. ## Re: Transpose An Equation

Now how do I copy and paste the answer in Post #2 into Word and see only standard mathematical notation?

9. ## Re: Transpose An Equation

Originally Posted by SGS
Can anyone transpose this equation to solve for n as a function of A, P, i ie, n = .....
A = P(((1 + i)n - 1)/( (1 - I) + (1 + i)n))
Please show each step!
Curious: that's obviously a financial formula;
WHAT does it do?
With p=100, i=.01 and n=12, result is a = 5.99128....
WHAT d'heck is that?

Also, you're showing i and I : are they the same?

10. ## Re: Transpose An Equation

OK; assuming i and I are SAME, this will work:

n = LOG[(a(1 - i) + p) / (p - a)] / LOG[1 + i]

11. ## Re: Transpose An Equation

Originally Posted by DenisB
OK; assuming i and I are SAME, this will work:

n = LOG[(a(1 - i) + p) / (p - a)] / LOG[1 + i]
$\displaystyle I$ is the identity matrix, you fool! Just kidding

12. ## Re: Transpose An Equation

Originally Posted by abender
$\displaystyle I$ is the identity matrix, you fool! Just kidding
You on A BENDER?!!!!

13. ## Re: Transpose An Equation

Simpler still:

u = 1 + i
v = 1 - i

n = LOG[(p + av)/(p - a)] / LOG[u]

14. ## Re: Transpose An Equation

Originally Posted by SGS
Now how do I copy and paste the answer in Post #2 into Word and see only standard mathematical notation?
You probably can't. As far as I have been able to figure out, Word does not support LaTeX but has its own (not very good in my opinion) mathematical option.

Do you see a summation symbol when you look below?

$\displaystyle \sum_{j=1}^nx^j$

If so, then your browser is rendering LaTeX properly.

If instead you see \displaystyle \sum_{j=1}^nx^j, your browser is not rendering LaTeX properly.