You also need favorable stock returns. I think there’s a reason that financial freedom is a recent phenomenon, and that’s due to the stock market’s performance since 2009. It’s obvious the author has only been investing during this long bull run. He pays lip service to market drops, but doesn’t understand how frightened people get when their net worth is suddenly half what it was six months ago.
A reason I believe 4% is reasonable, especially for myself and for Mad Fientist readers, is because early/semi retirees will have much more flexibility than the retirees that the Financial Mentor is writing for. You’ll notice in his article that he references $2.5 million and $3.3 million nest eggs in his article. I hate to make another assumption but I assume people with nest eggs that large most likely have much higher expenses and more financial obligations (i.e. bigger mortgages, boat loans, expensive habits, etc.) so it may be harder to adjust their lifestyles when the economy changes. For me, however, if I start withdrawing 4% from my portfolio but then the market tanks, I’ll be able to move somewhere where the cost of living is less and potentially pick up part-time work that I enjoy so that I can withdraw less from my portfolio during the downturns.

I agree with FS. I hope my $1M number is too high but it’s not unreasonable. According to the Department of Agriculture study last year the average family with an combined household income of greater than $107,000 will spend on average $372,000 to raise a child to age 18. Add in $250k of college costs (before inflation) and you’re already over $600,000 for the average. This average doesn’t include private school costs. I hope to send my children to public school but private school tuition around here is $40,000+/year if the public schools aren’t good enough. Without kids we would have a 3 bedroom house, with kids we had to go with a 4 bedroom. Adding that 4th bedroom here adds about $400,000 to the price of the house and $8,000+ extra in property taxes annually. And we haven’t gotten to any extras yet. I was fortunate enough to travel internationally with my family growing up and I want to provide that experience to my children. I believe that is valuable but it also costs thousands per year.
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The doctor or lawyer, for instance, could use her or his income to invest in a medical start-up or buy shares of medical companies he understands such as Johnson & Johnson. Over time, the nature of compounding, dollar cost averaging, and reinvesting dividends can result in her or his portfolio generating substantial passive income. The downside is that it can take decades to achieve enough to truly improve your standard of living. However, it is still the surest path to wealth based on the historical performance of business ownership and stocks. 
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