[namdnay]

When calculating the capital needed to live off the interest, you need to subtract inflation from the interest, as 1000$ will be worth less and less every month. What you need to survive is "equivalent to 1000$ today", not "1000$".

[IanCal]

The safe withdrawal rate of 4% (or whichever figure you pick) already includes inflation.

The rule is supposed to be that you have a high probability of withdrawing $X per year, each year, adjusting for inflation, where $X is 4% of your initial starting sum.