No calculus is required. After guessing the marginal tax bracket, only algebra is needed. For example, assuming 2018 brackets and standard deduction, let "w" be the withdrawal amount:Bongleur wrote: ↑Sat Feb 17, 2018 9:53 pmYou can imagine that if you retired into a 0% bracket, but needed $100,000 -- do some guesses as to the future bracket schedule & see how much money you would pay in taxes -- and remember that you need the entire $100,000, so you would be withdrawing more to cover the taxes. Which is also taxed at the highest bracket rate... ad infinitum. Ah, Calculus...

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```
Single
14,089.50 Tax on 82,500 [top of 22% bracket] = 10% * 9525 + 12% * (38700 - 9525) + 22% * (82500 - 38700)
w - (w - 12,000 - 82,500) * 0.24 - 14,089.50 = 100,000
0.76w + 22,680 - 14,089.50 = 100,000
0.76w = 91,409.50
w = 120,275.66
Joint
8,907 = tax on 77,400 [top of 12% bracket] = 10% * 19050 + 12% * (77400 - 19050)
w - (w - 24,000 - 77,400) * 0.22 - 8,907 = 100,000
0.78w + 22,308 - 8,907 = 100,000
0.78w = 86,599
w = 111,024.36
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```
Single Joint
------ -----
Rate: ord income bracket 1 10% 10%
Rate: ord income bracket 2 12% 12%
Rate: ord income bracket 3 22% 22%
Rate: ord income bracket 4 24% 24%
Floor: ord income bracket 2 9,525 19,050
Floor: ord income bracket 3 38,700 77,400
Floor: ord income bracket 4 82,500 165,000
Non-SS Ordinary Income 120,276 111,024 <-- found with Goal Seek
Adjusted gross income 120,276 111,024
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```
Deductions plus Exemptions 12,000 24,000
Taxable Income 108,276 87,024
Taxable: ord income bracket 4 25,776 -
Taxable: ord income bracket 3 43,800 9,624
Taxable: ord income bracket 2 29,175 58,350
Taxable: ord income bracket 1 9,525 19,050
Tax: ord income bracket 4 6,186 -
Tax: ord income bracket 3 9,636 2,117
Tax: ord income bracket 2 3,501 7,002
Tax: ord income bracket 1 953 1,905
Total tax 20,276 11,024
After tax income 100,000 100,000
```