Maclins Rate of Return - Reading 9 EOC 13

[The Song of the]

The Maclin’s require an annual outflow from their portfolio to cover ongoing expensis. They need 26,000 annually after tax. Their tax rate is 40%.
My entry for rate of return:
PV = 1,235,000
FV = 2,000,000
PMT = 43,333 [=26,000/(1-.4)]
t = 18
gives a necessary return of 5.59%
The actual answer uses PMT of 26,000 to get a calculated return of of 4.427% and then gets the after tax rate of return from: 4,427/(1-.4) = 7.38%. With 7.38% being the answer for return.
It’s not clear to my why this is done after the calculation instead of included with it. Any thoughts?

 

[S2000magician]

“All capital gains and investment income are taxed at 40%.”
Your method taxes only the portion they withdraw; their method taxes everything.

 

[The Song of the]

S2000, very much appreciated. Thanks!

 

[S2000magician]

My pleasure.