Help please, solve for X - simple algebra

Posted on 2013-12-18
Last Modified: 2013-12-18
Can you help me reorder this equation?  I know it must be possible:

F = ( (X/Y)^(1/P-1) ) -1)
Question by:Geoff Millikan
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LVL 27

Expert Comment

ID: 39727693
What order do you want?

let r = (1/P)-1          (not 1/(P-1)

F = (X^r)/Y^r) - 1
LVL 84

Expert Comment

ID: 39727694
F = ( (X/Y)^(1/P-1) ) -1
F+1 = (X/Y)^(1/P-1)
(F+1)^-(1/P-1) = (X/Y)
Y*(F+1)^-(1/P-1) = X

Author Comment

by:Geoff Millikan
ID: 39727757
ozo, your equation doesn't seem to work when I put in real numbers.  I get 18.43 on your formula but was expecting 34.

F = 2.4
X = 34
Y = 10
P = 2

2.4    = ((34/10)^(1/(2-1))-1)

10*(2.4+1)^-(1/2-1) = 18.43
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LVL 84

Expert Comment

ID: 39727781
when you plug in
X = 34
Y = 10
P = 2
( (34/10)^(1/2-1) ) -1 = -0.4576738554533 != 34
LVL 84

Expert Comment

ID: 39727784
is different from ( (X/Y)^(1/P-1) ) -1)
LVL 84

Accepted Solution

ozo earned 500 total points
ID: 39727803
(F+1)^-(1/P-1) = (X/Y)
Y*(F+1)^-(1/P-1) = X
Should have been
(F+1)^(1/P-1)^-1 = (X/Y)
Y*(F+1)^(1/P-1)^-1 = X
or if (1/P-1) was really  (1/(P-1))
(F+1)^(P-1)/1 = (X/Y)
Y*(F+1)^(P-1)/1 = X

Author Comment

by:Geoff Millikan
ID: 39728051
I get 2.4 when I cut and paste the following into Excel :  ((34/10)^(1/(2-1))-1)

But this formula works great!   Y*(F+1)^(P-1)/1 = X

For proof, I get 34 in Excel when I plug in the numbers: 10*(2.4+1)^(2-1)/1

Awesome, thanks so much!!!!!!!!!!!!!!!

Note to self:

This is the reverse CAGR formula

F = 2.4 (CAGR, in percent, annualized)
X = 34  (Ending dollar amount)
Y = 10 (starting dollar amount)
P = 2 (period [in years])

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