First a couple paragraphs for me to lay out my understanding and then my actual question.
It is often reported that one can estimate how much they need for retirement by taking their current expenses and multiplying by 25. This comes from the idea of a 4% safe withdrawal rate which is related to a historical real rate of return on investments of 4% which arises from a 7% return less 3% for investment.
My understanding is that you start with a nest egg of a certain amount. You start off withdrawing 4% of that nest egg. Each year it appreciates by 7% and you withdraw your original 4% (of the principal) plus an additional 3% (of the total withdraw amount) each year to compensate for inflation. Long term, the net result is that this can reach a sort of steady state where the nest egg is essentially never depleted meaning there is enough there for retirement.
All of the above makes good sense to me. My question is about the validity of using my current expenses to predict even my initial expenses during retirement in light of inflation between now and the start of retirement.
Suppose my current expenses are $40,000. The 4% rule would indicate a required nest egg of $1,000,000. However, suppose it would take 20 years to save that up. Well assuming 3% inflation per year that $40,000 of spending is now $72k of spending which would require a nest egg of $1.8 million by the 4% rule.
The question is do I need to adjust my current spending amount for inflation at the beginning of retirement to accurately determine how much I need for retirement?
I'm coming from a math background so I'm very comfortable with any math/formulas and I prefer to think about things in those terms. Also, I really there are many simplifications in the model I'm presenting (largely I'm assuming no variability of any of the parameters with time) but I'm just trying to get a sense for how the numbers work in the simplest model and then I can think about how variability would affect things in real life afterwards.
This may be a duplicate of I'm trying to figure out a formula for when I'll be able to retire at any given month but my question here is a little more specific and direct.