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To what extent is this accurate?
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The amount of money you save (and invest) isn't accurately depicted with this though. Living expenses don't necessarily grow with take home, if you keep lifestyle creep to a minimum.
So what this means is that if you make $100k and save $10k/year, if you start making $200k you can save the same $10k/year, plus the entire additional $100k after taxes (let's just say that's $50k+). So you doubled your salary but your savings went up 6x+.