I'll assume $200k is before tax. I'm single filing in Kansas. The only deductions that I will allow myself are the standard deduction and one personal exemption. Federal Taxes use 2014 data. State Taxes use 2013 data. I'll ignore inflation.
Tax Calculation:
Social Security Tax = $7,254
Medicare Tax = $2,900
Federal Taxable Income after standard deduction and one personal exemption = $189,850
Federal Income Tax = $46,508.75
This is above the Alternative Minimum Tax.
Kansas Taxable Income after standard deduction and one personal exemption (using 2013 data) = $194,750
Kansas Income Tax (using 2013 data) = $9,257.75
Annual After Tax Income = $134,079.5
Annual Expenses = $15,000
Monthly Savings = $9,923.30
I'll determine my savings goal by using a 3.5% SWR at $15,000 per year, adding $200k to buy a house outright on the day of retirement, and adding a 10% buffer to that total.
Savings Goal = $691,428.60
Using historic S&P 500 data from 1950 to the end of 2013 and assuming no transaction costs or expense ratios and a 100% equities allocation, I find the following about the years to the savings goal. (NOTE: using this data without adjusting for inflation is problematic since the above numbers are in 2014 dollars, but I don't really feel like adjusting the numbers right now):
Average = 5 years and 6 months
Minimum = 3 years and 8 months
25th percentile = 4 years and 8 months
Median = 5 years and 2 months
75th percentile = 6 years and 3 months
Maximum = 9 years and 7 months
If saving started after 8/1/2009, then the saving goal would not yet be met. These years were not included in analysis.