The correct formula to calculate approximate time to FI-ERE

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lillo9546
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The correct formula to calculate approximate time to FI-ERE

Post by lillo9546 »

Hi there guys!
We know that there are various formula to calculate an approximate time to FIRE.
Like https://captainfi.com/saving-rate/ or https://www.mrmoneymustache.com/2012/01 ... etirement/ or https://www.reddit.com/r/financialindep ... rrent_net/

But, which would be in the ERE scenario, the correct formula/factors to calculate approximate time to FI-ERE?

jacob
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Re: The correct formula to calculate approximate time to FI-ERE

Post by jacob »

CaptainFI uses a linearization. MMM's article originally derived from chapter 7 in the ERE book. You'll find the full nonlinear equations there insofar you actually care for the math. Otherwise, just use the table or one of the apps, like https://networthify.com/calculator/earl ... awalRate=4 .

The best solution as an individual is to build your own spreadsheet that evolves networth, expenses, taxes, and active/passive income year by year. You can expand on this as much as you want. I believe iDave has the most complicated/comprehensive version on the forum. It's better to have a simple version you built yourself than trying to fit your situation into someone else's spreadsheet.

The diagrams and derivations are mostly useful for general statements about the entire range of savings rates.

lillo9546
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Re: The correct formula to calculate approximate time to FI-ERE

Post by lillo9546 »

jacob wrote:
Thu Jun 01, 2023 6:09 am

The best solution as an individual is to build your own spreadsheet that evolves networth, expenses, taxes, and active/passive income year by year. You can expand on this as much as you want. I believe iDave has the most complicated/comprehensive version on the forum. It's better to have a simple version you built yourself than trying to fit your situation into someone else's spreadsheet.
It would be nice to find the right one. Where could we find it?

jacob
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Re: The correct formula to calculate approximate time to FI-ERE

Post by jacob »

lillo9546 wrote:
Mon Jun 05, 2023 3:44 am
It would be nice to find the right one. Where could we find it?
The right one is the one you make yourself. This way you know how it works.

To get started make simple a spreadsheet using e.g. google sheets.
The columns are
year, networth, earned income, passive income, expenses

passive income(year) = networth(year)*0.03
networth(year+1) = networth(year)*1.05+earned income+passive income-expenses

You can play around with the 0.03 and 1.05 numbers.

The rest is left as an exercise for the reader.

lillo9546
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Re: The correct formula to calculate approximate time to FI-ERE

Post by lillo9546 »

jacob wrote:
Mon Jun 05, 2023 10:11 am
The right one is the one you make yourself. This way you know how it works.

To get started make simple a spreadsheet using e.g. google sheets.
The columns are
year, networth, earned income, passive income, expenses

passive income(year) = networth(year)*0.03
networth(year+1) = networth(year)*1.05+earned income+passive income-expenses

You can play around with the 0.03 and 1.05 numbers.

The rest is left as an exercise for the reader.
I've made this one, which I also use to track expenses and other stuff.
What do you think? (It's not complete) https://docs.google.com/spreadsheets/d/ ... sp=sharing

AxelHeyst
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Re: The correct formula to calculate approximate time to FI-ERE

Post by AxelHeyst »

Most people's spreadsheets will be idiosyncratic and difficult for anyone else to quickly evaluate. And then, no one else can tell you the most important thing about your spreadsheet, which is whether or not it makes sense to *you*.

When you open up your spreadsheet, does it tell you things you are interested to know about your finances? Is it easy for you to input information? Do you have to input the same information more than once? Are interesting ratios and conclusions buried or in obscure places?

Your spreadsheet makes only a little sense to me after looking at it for fifteen seconds... But almost no one's would. My spreadsheet probably wouldn't make sense to a quick look from you, either. This isn't an indication of a problem.

lillo9546
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Location: Italy

Re: The correct formula to calculate approximate time to FI-ERE

Post by lillo9546 »

whats the *1.05 for?

sodatrain
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Re: The correct formula to calculate approximate time to FI-ERE

Post by sodatrain »

lillo9546 wrote:
Tue Jun 06, 2023 8:09 am
I've made this one, which I also use to track expenses and other stuff.
What do you think? (It's not complete) https://docs.google.com/spreadsheets/d/ ... sp=sharing

I'm new to this and still learning, so It's really interesting to see other peoples sheets (OPS?!)

My first reaction was...wow that is very granular Income/CoL/Savings data! And then I thought the same thing about your budget categories. This is of course the "make what works best for you" comes in. I'm working thru my tracking categories still. Using Mint and then I transfer it into a sheet. Eventually I want to have so few transactions I can just enter everything by hand. (I met a guy who build a Google Form to record each transaction into his Google Sheet and thought that was pretty groovy. Not great for offline but thats prob. ok).

xmj
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Re: The correct formula to calculate approximate time to FI-ERE

Post by xmj »

I agree that the best spreadsheet is the one you make yourself. There are many good templates on the interwebs, but after having found quite a number of glaring mistakes, my position became that the best way to have the correct one is to do it from first principles.

As to the correct formula to financial independence (extremely early or not), here is my derivation.

https://xmj.me/FIRE_Math.pdf

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