Blended Taxation

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In my course of study, I usually avoid memorizing formulas, I simply cant and dont.
The blended taxation formula dont seem intuitive to me, can anyone explain it in an easy memorable way?
Why are we multiplying Tcg by the portion untaxed then divding it by the amount untaxed?
 
Tcg* = (1-[pi+pd+pcg])/ (1-(piTi + pdTd + PcgTcg)) * Tcg
“The adjustment to the capital gains tax rate takes account of the fact that some of the investment return had previously been taxed as interest income, dividends, or realized capital gain before the end of the investment horizon and will not be taxed again as a capital gain.”
 
Numerator = {Proportion that is left untaxed)
Denominator = (Proportion Of Investment Return that has is left untaxed taxed) (Because piti + pdtd +pcgtcg = Amount of return that was taxed).
now you need to tax the remainder only in the proportion of what has already been left untaxed.

you have to “learn some formulae by heart” in this case … not everything works with intuition. And if you leave your brain cells unchallenged, believe me - they will DIE!
 
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