Growing Perpetuity

[nosit]

I am working on the derivation of the Growing Perpetuity formula, which is PV = C/(i-g)

But, as you can see below, I reach at a point that I already know the ending result will not be PV= C/(i-g)

If I go further with my last step, I would cancel out the (1+i), but as you see above in bold, I need to end up with (i-g) in the denominator

Does anyone know what am I doing wrong and could help me out?

Thank you in advance.

 

[lex]

(Just looking at the algebra) you need an extra step. After your second-last line, you must make your 'bottom line' into a single fraction before changing to a multiplication. (Your current final line therefore does not follow from the previous line).

 

[lex]

Perhaps I should have gone on to say that:

[MATH]\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}[/MATH]
You need to do that for your:

[MATH]\frac{1}{1}-\frac{(1+g)}{(1+i)}=...[/MATH]

 

[nosit]

Hi Lex, thank you for the help!

In the end I replaced 1/1 by (1+i)/(1+i), as both have the same value, namely 1.
This worked and I could complete the derivation.

 

[lex]

Excellent. Well done. (That's essentially the same thing in this case).