Depending on your age, this might or might not be more reflective of rational utility. Obviously, if your rational expectation of remaining life expectancy is less than 33 years, then unless you are desiring to leave some part of capital as estate after your death, applying the 3% rule rather than D-R/R will tend towards over-valuation of present time devoted to work towards savings. So, for example, since I am 51 and my optimistic expectation of life expectancy might be another 40 years:Fish said: This lacks the investment part of modern FIRE in assuming a real return of 0%, meaning FI is achieved through one's own eventual death.
$250,000 in savings/40 years= $6250/year
$250,000 X (.03) =$7500/year
$250,000 X (.04) =$10,000/year
$250,000 X (.025) =$6250/year
So, not too much difference between calculating one way or the other. However, if my current health and/or family history led me to believe that 20 years was a better estimate for life expectancy then:
$250,000 in savings/20 years=$12,500/year
$250,000 X (.03) = $7500/year
$416,667 X (.03) =$12,500/year
So, if my yearly expenses were $12,500 and my current income was $25,000, I might needlessly work an extra (416,667-250,000)/12,500= 13 years out of the slim remnant of years left to me, before choosing to retire if I was applying the 3% rule rather than death clock calculation with assumption of overall 0% return. Since my expectation is that I will likely be able to collect at least $500/month in early withdrawal SS benefits starting at age 62, and my current expenses are not much above that level, my clock is set at only 11 years, so it makes very little rational sense for current me to favor future me by saving money towards time, except to the extent that I want to set a chunk aside for a specific project that requires it. IOW, my current rate of semi-retirement leisure is directly determined by my rate of semi-employment pay with little benefit to be derived from compound interest. Given a 40/hour work week , 50 week/work year, and $8000 yearly expenditure, and $20/hr pay rate, each hour of work will purchase me 4 hours of leisure, but nary a penny more (sigh.) In fact, it is likely that my most rational behavior would be to greatly favor current time spent towards maintenance/improvement of health/fitness over current time spent making/saving money, since it is unlikely that 36 hours/week would ever be optimal and more than 4 hours/week would likely be optimal.
Thanks for posting that equation!