I'm missing some basic fundamental concept here. It'd be great to know a simple explanation for the effects of inflation in the Multiply by 25 rule... I see sources that say this accounts for inflation already, and others that say you need to consider the effects of inflation.

i.e. if I want 25k in passive income, I'd need roughly 625k invested.

But if I look at a source like this:

https://www.thebalance.com/budgeting-for-retirement-454001Simplified to exclude social security and other sources of retirement income, the guide has you account for inflation first, THEN multiply by 25... yielding drastically different numbers, obviously. In their example, I'd take my 25k, and if I wanted to retire in 10 years, I'd multiply that by 1.48 (per their table, step 5).. then multiply by 25 in step 7.. yielding $925k, instead of the 625k not accounting for inflation. If I wanted to retire in 25 years the number is obviously much, much higher (1.7 million).

So... what's the correct method for determining how much is needed to save (annually, let's say; periodically) if I wanted to retire in a certain number of years? Is it just two names for the same thing (625k in today's dollars, 925k in dollars 10 years from now..).

When I look at an IRA calculator, for example, that tells me that with 11k annual contributions, 7% return, over 25 years will yield me 378k.. and I use the 4 percent rule to figure out how much I could withdraw.. that would mean ~$15k annually.. in future dollars 25 years from now?, so I'd need to think of it in terms of my future expenses (15k/2.67(from 25 years inflation in thebalance.com's table)=5700 in today's dollars..?

I know if I was to retire right now, 625k would lead to the 25k in passive income over time, but how does one calculate over periods of time? Here's a question posed in the comments section regarding this exact thing, and MMMs response (his response is really what I'm just looking for some clarification on):

http://www.mrmoneymustache.com/2012/05/29/how-much-do-i-need-for-retirement/Dan: So does that magic number you multiply by 25 apply to today’s money? Say for example I calculate that I’d need 600k for the retirement following the 4% rule, but what if it would take me 10 years to save that? Does that mean my goal would be basically 600k adjusted for inflation? (600×1.03^10) assuming my expenses stayed the same (in real money, not nominal)?

MMM: Yes, you can pretty much ignore inflation with this way of calculating things. Because your rate of spending will automatically rise with inflation (and of course drop with optimization). So in general, if you take your most recent year’s spending, make any adjustments to cover things like health insurance, travel, transportation or other things in your future budget, and multiply that by 25, that’s your retirement nest egg guideline.