I am answered based on the last update but there still are not enough numbers to actually figure this out, but we can look at the moving parts and do some back of the envelop calculations.
The first question is $150k your AGI or your total income?
From the way you are using this number in your formulas I think you intend this to be total income, since that is what you use in figuring out the percentages. However AGI is what you use in the tax tables. Your worst case AGI would be if you just took the standard deduction of $6300 for a single person.
Your AGI: $143,700
Your Tax: $33,273
Percentage of total income: 22.1%
This is still a big chunk, but since you said you are paying 40% that leaves 18% unaccounted for. From that we can back figure your state tax rate as
- 4.9% (social security)
- 1.45% (Medicare)
= 11.65% (State and Local)
This means that you are paying $17,475 in local taxes! You need to be itemizing! this would change you AGI calculations to be:
Your AGI: $132,525
Your Tax: $30,144
Percentage of total income: 20%
I know this breaks the original local taxes calculation, these are all made up numbers anyway and this just shows where the described example is leaving $2k on the table for the tax man. You work with the pretend numbers you have and not the pretend numbers you wish you had.
Now, if you want to hit that magic 13% there are still a few things you can do from this point, you still need to shed $10,644 dollars of tax which is $38,014 in pretax dollars. My first suggestion would be to max out the 401k at $18,000 for someone under 50. This will change your calculations like this:
Your AGI: $114,525
Your Tax: $25,104
Percentage of total income: 16.7%
Ooh, so close! Only 3.7% away, have you considered home ownership? A mortgage in the area of $200k at 4% would include $7,820 in interest payments the first year.
Your AGI: $106,705
Your Tax: $22,914
Percentage of total income: 15.3%
If you have your heart set on reaching 13% you still need to identify $3,450 of deductions. This is not so much that you could not make a cash donation to a charity contributing to a tax advantaged health care account to make up the difference. You could also consider marriage and/or acquiring dependents to bring your tax bill down further.