🔎 The "after-tax" shortcut: multiply by (1-t)

Suppose you have an income of $100K, and you are taxed at 35%. What is your after-tax income?

Your tax bill will be 35% × $100K = $35K. Therefore your after-tax income will be:

$\text{after tax income} = \$100\text{K} - 35\% × \$100\text{K} = \$65\text{K}$

More generally, with earnings E and tax rate t,

$\text{after tax income} = E - t × E$

By factoring out the E, we get a shortcut we will use whenever we calculate taxes:

$\text{after tax income} = E - t × E = E × (1-t)$

Bottom line: Whenever we need to estimate the impact of taxes, we just multiply by (1-t). We will use this both for corporate and personal taxes.

Returning to the original example, 1-t = 35%, the after-tax income is $100K × 65% = $65K

You can think of the 1-t = (65%) as the percentage of the income that you get to keep.

$=(13,000 - 8,300 - 1500) (1-40\%) + 1500 + 0 - 1125 = 2295$