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
that makes perfect sense now
thank you
My pleasure.
Hi Magician, I would really appreciate a little piece of advice from you please. I have trouble remembering things by heart. For example regarding the above formula, i would tend to reconstruct it at the exam the same way you did in your demonstration, in order to not have to learn the final formula by heart. Do you think it is a big timing issue for the exam and that i should really try to rather learn by heart? Thanks in advance for your input. Myriam
I would never bother to memorize these tax formulae. My poor little brain cannot handle the additional strain.
I’d be more than happy to reconstruct it on the exam if needed.
Perfect thanks :)) That’s the kind of answers that makes me happy!!
Ce était mon plaisir de vous aider.
woah woah - only english at the table (in mean poker voice).
Verzeihen Sie mir.
$100 asset, 6% return, 25% tax on CG
long method: (no formula)
end value before tax = 100 * 1.06^10 = 179.085
CG = 179.085 - 100 = 79.085
Tax on CG = 79.085 * .25 = 19.771
End Value after tax = 179.085 - 19.771 = 159.314
=============
Formula = [(1 + r)^n](1 – tcg) + tcg
= 1.06^10 (1-0.25) + 0.25 = 1.59314
Same answer
Take a bow <3
This is the way it should be. No Formula… or if there be any, derive the same at exam.