After tax return

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FrankCFA

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After-tax future value for
Investment income tax: [1+R(1-T)]^n
Wealth-based tax: [(1-T)+R(1-T)]^n <– I think this one is easier to remember than the Curriculum/Kaplan one and more consistent with investment income tax.
There should be the reason Curriculum/Kaplan use {(1+R)(1-T)]^n approach. Any idea?
 
your formula is absolutely WRONG Mr Frank.
It is [(1+r)(1-T)]^n
1 $ become 1 + R at the end of year.
the entire (1+R) gets taxed @ T so (1+r)(1-T) is what 1 $ becomes at the end of 1 year.
at the end of N years => [(1+r)(1-T)]^n
 
Wealth tax is applied on both return and principal.
Investment tax is only applied on return.
Think of this as 1st year. Then compound n years.
 
I think Frank is right
(1+r)(1-T)= 1-T+r-rT=1-T+r(1-T)
but the curriculum’s is more intuitive
 
that works ONLY for 1 period. It is not the same when that is raised to N years.
the formula - when I commented on Frank’s original post - missed the bracketing.
think about what would be easier to do
(1.1 * 0.98)^20
or
[(1-T)+R(1-T)]^n
(0.98 + 0.1 * 0.98)^20
 
I just compared what’s relevant. Of course for multiple periods you raise the bracket to the power of n
 
cpk123 wrote:
your formula is absolutely WRONG Mr Frank.
It is [(1+r)(1-T)]^n
1 $ become 1 + R at the end of year.
the entire (1+R) gets taxed @ T so (1+r)(1-T) is what 1 $ becomes at the end of 1 year.
at the end of N years => [(1+r)(1-T)]^n
Click to expand...
May I know why my formua is wrong?
From intuition, it shows tax deducts the principle directly. [(1-T)+r(1-T)]^n
From math, [(1+r)(1-T)]^n= [1-T+r-rT]^n=[1-T+r(1-T)]^n
 
i missed the brackets. Your formula is ok. However it is a long way of going about it.
would you do for a 10% return, 2% tax….
(1.1 * 0.98)^20
or
[(1-T)+R(1-T)]^n
(0.98 + 0.1 * 0.98)^20
 
Thanks. Yes, the curriculum one is quicker for calculation. But I think [(1-T)+r(1-T)]^n is more intuitive, no?
 
not sure what you are fighting the intuition for.
1 $ grows to (1+r) due to r% return.
and then tax is applied to the entire amount.
so what is left = (1+r)(1-t)
and this continues on for n years
so [(1+r)(1-t)]^n
 
Not yet… Hope will not be killed by a new beast…
 
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