How much $ is needed to never have to work again?

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You cannot just subtract your rate of withdrawal from your rate of return.

Do you see why?


If not compare two scenarios:
1)the stock market drops 40% one year and increases 100% the next
2)the stock market gains 10% one year and increases 10% the next

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any sort of uncertainty about returns or withdrawals makes calculating this get really complicated .. in a model with risk, simulating your uncertainty to come up with a reasonable number will probably be easier than any sort of derivation.