I found the imputed rent data on MMMs spending most helpful to show the real difference between paying off a house pre-FIRE or having a mortgage/renting during FIRE. Not necessarily the intention of showing it, but I found it quite eye-opening.
Same here. In my case, if I keep a mortgage payment in perpetuity (currently $600/mo), my stash would need to be substantially larger, by order of $180,000 to support that $600/mo mortgage expense using the 4% withdrawal rule. Or pay it off pre-FIRE and it's done.
That's the type of thinking that makes one FIRE much later than necessary (by paying off their mortgage). :)
Because in the one comparison (keeping the mortgage), you're funding the mortgage payment in perpetuity, even though it's going to go away at some point, at which point you'll have an extra $600/mo, or $7200/yr over the other scenario. Certainly not apples-to-apples.
Think about it this way: what is your mortgage balance? THAT'S the extra amount you'd need to save (and you'd do it by, whenever you'd go to prepay your mortgage, investing it instead, so it wouldn't take any longer to save that extra amount than it would to pay off your mortgage, and it might take shorter cause of compounding). That extra money sitting in stocks, earning you money, instead of sitting in house equity, earning you nothing, causes you to come out ahead, and means you can FIRE quicker.
Read more here: http://forum.mrmoneymustache.com/investor-alley/paying-off-mortgage-early-how-bad-is-it-for-your-fi-date/
Paying off your house slows your FIRE date versus leaving the mortgage and investing the money you would use to pay off the mortgage. Just think if it as needing to save: 25x my non-mortgage expenses PLUS my mortgage balance. When your stache equals that, you can FIRE (rather than the "25x my total expenses, including mortgage" you were thinking of).
Hope that helps. :)
Just to pile in on this mortgage discussion, I'll mention that we have two of them (homeowner and rental property) and they'll be paid off when I'm nearly 80 years old.
I have a 12-year spreadsheet tracking the return of taking a mortgage at 5.375% and investing the cash into a small-cap value fund, while making the mortgage payments from my pension and our investments. Even after blundering into the Great Recession (sequence of returns risk) the investment is still comfortably ahead of the 5.375%... even though since then we've refi'd down to the current 3.625%.
Let's do a thought experiment: If the U.S. government pays you a monthly inflation-adjusted annuity of approximately 2x your mortgage payment, and you can get that 30-year fixed-rate mortgage at 3.625%, would you borrow the money and invest it in the stock market? Long-term CDs? Or would you sleep more comfortably at night with a paid-for home?
One of those decisions is risk-taking math while the other is the behavioral financial psychology of loss aversion. Both are perfectly valid. Since I already have an annuitized income from one of the world's most trusted sources (or one that can at least print money) then I feel that I have the loss-aversion part covered and can take a little risk.