How much will a day of FIRE cost today?

[meerkat]

I have a puzzle I'm trying to figure out but I'm not quite sure how to figure it out. The original idea was that paying for a cleaning service or lawn service will push our FIRE date back, but I was curious to figure out the hard numbers on how much it would push it back. Another way I was trying to think of it was that $X will equal one day of FIRE, since I've seen mention of that one or two times around here, but I'm not sure how to get to that number either.

Rough numbers [Edited to make then annual after the first couple comments]:
Average monthly annual spending is $51,600
Average monthly income is $87,840 (after taxes)
Savings rate: 41.25%
FIRE goal: One million in investments
Estimated monthly annual spending post-FIRE: $39,600

I was curious a few months ago and called around for quotes on a lawn service, they typically came in at $50/month if we promised to use them year round (we don't get snow so winter would be more like yard clean up rather than mowing). One thought I had was if we need a million for FIRE, then divide 1,000,000 by 365 to get how much we would need per day, but maybe that line of thought is wrong? Because that's not reflecting our actual FIRE spending. Basically I have the pieces but I'm not sure how to assemble it into a math equation.

[Saskatchewstachian]

I think I would just put it to a yearly cost. i.e. 50/month is 600/year. In order to support that cost indefinitely you need 600*25 so an extra $15000.

To get that $15000 strictly through savings you would need to work 15000/(7320-4300)= 5 extra months.

Realistically it would be less than that as over that 5 months you would have the 1,000,000 in assets appreciating as well. If the 1million gets 7% per year and it's a linear appreciation (huge guess). Then in the first two months of the year the 1,000,000 will appreciate by 7%/6=1.16% or $11,600 plus the two months of savings of $6,000 then you would have you $15,000 needed.

So for you it looks like an extra $50/month would be about 2 more months to FIRE.

[Linea_Norway]

You could calculate how much 50 dollars a month is per year (= 600) and then calculate rent over rent on that amount until you plan to FIRE. That is how much it will set you back.

About your 1 million to FIRE. The idea is to invest that into e.g. Index funds and take out 4% of the profit each year. On average you would expect an index fund to make 7% profit a year. The remaing 3% hopefully corrects for inflation. The million will stay and make more profit for you. This way it will not become less and you could live forever on it.

[MDM]

...paying for a cleaning service or lawn service will push our FIRE date back, but I was curious to figure out the hard numbers on how much it would push it back. 
...
Basically I have the pieces but I'm not sure how to assemble it into a math equation.

You might take a look at cell C63 on the 'Misc. calcs' tab in the case study spreadsheet.  Put your current situation into cells C47:C51, and cell C63 will give you the derivative of "time to FI" per additional $10K/yr savings, assuming your expenses decrease by $1 for every $1 of savings increase.

[neo von retorch]

Are you trying to figure out the cost of living financially independent, retired early for one day... or how much you contribute towards being FIRE each day between now and then (and thus, how many more days you have to continue to contribute through optional expenses?

Because the answer to the first question is clearly "annual expenses divided by 365 adjusted to inflation" but... it doesn't necessarily give you an accurate picture for the second question.

Assuming you have $200k saved and want $1000k, and you save $36,240 each year, you'd be 22 years from FIRE if the money wasn't invested... and you'd be saving about $100/day. So every $100 you spend would add one day of work. But all of this needs recalculated based on what you currently have saved, and how much you assume you'll get in investment returns.

[yachi]

Here are others with the same idea:
https://forum.mrmoneymustache.com/share-your-badassity/i-just-bought-2-days-per-year-of-free-life-indefinitely-363-to-go/

[meerkat]

...paying for a cleaning service or lawn service will push our FIRE date back, but I was curious to figure out the hard numbers on how much it would push it back. 
...
Basically I have the pieces but I'm not sure how to assemble it into a math equation.

You might take a look at cell C63 on the 'Misc. calcs' tab in the case study spreadsheet.  Put your current situation into cells C47:C51, and cell C63 will give you the derivative of "time to FI" per additional $10K/yr savings, assuming your expenses decrease by $1 for every $1 of savings increase.

Thank you, I'll check that out. I went through the case study spreadsheet not too long ago just to see where things stood so I might still have those numbers saved.

Here are others with the same idea:
https://forum.mrmoneymustache.com/share-your-badassity/i-just-bought-2-days-per-year-of-free-life-indefinitely-363-to-go/

Thanks, I couldn't remember exactly where I had seen that, I just knew it was somewhere around here.