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I was pretty conservative in my calculations, figuring a pretty high inflation rate (5%) and a pretty low investment return rate (8%), but I figured it's better to over-estimate what we'll need than to under estimate. If you believe these figures will be different, then you'll come up with very different results.

Using historical data to test portfolio withdrawal survival the number is only 4% for a 30 year withdrawal not running out of cash and about 3.8% for the ending balance to be the same as the starting balance. This is a bit higher than you estimate but not by much. Now this would survive the worst time periods in the historical record but most time periods are not the worst and the probability is high (though not guaranteed) that your portfolio after 30 years would be quite a bit larger than at the start.

This would cut your stash down to $1.47M if you aim to keep the start and end values the same as the worst case.

http://rehphome.tripod.com/moresafe.html

Hyperborea
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