tax formulas with deferred capital gains

[cgrady40]

if the forumla is: (1+r)^n(1-tcg)+tcg
I understand that you take the pretax return and compute its FV, and then multiply by 1 - tax rate to get the after tax value. I don’t get why the cg rate is then added (last part of the equation)
what am i missing here?

 

[S2000magician]

cgrady40 wrote:if the forumla is: (1+r)^n(1-tcg)+tcg
I understand that you take the pretax return and compute its FV, and then multiply by 1 - tax rate to get the after tax value. I don’t get why the cg rate is then added (last part of the equation)
what am i missing here?

You’re taxed only on the gain, not on the total future value. The future value (before taxes) is:
(1 + r)^n
the gain is:
(1 + r)^n – 1
the tax on the gain is:
[(1 + r)^n – 1]tcg
so the remainder after taxes is:
(1 + r)^n – [(1 + r)^n – 1]tcg
= (1 + r)^n – [(1 + r)^n]tcg + (1)tcg
= [(1 + r)^n](1 – tcg) + tcg

 

[cgrady40]

that makes perfect sense now
thank you

 

[S2000magician]

My pleasure.