The math doesn't work out

[somebody8198]

I have to say, after thinking through a lot of the math that gets sold on FIRE forums, I don't think this works as well as I would like it to. Please check this and let me know if I'm missing something big.

So assuming I get 7% return on investments annually on average and you earn a decent $100k/year income. After taxes you can invest maybe $35,000 per year into investments which is about 50% of your take-home pay. Assume that you have to live on this single income, you are unmarried, and you live in an urban area. Let's say you start with $100,000 in your investment account just to keep things simple.

Compounding at 7% annually, the money would double in about 10-11 years. With a $35,000 contribution each year this works out that you'll double your initial balance in about 3 years, then double it again 5-6 years later, then again 6-7 years after that. It will still end up taking 15 years to get to $1 million at which point you could withdraw 3% and the account will continue to grow.

Except that withdrawal amount is not accounting for inflation! You can't live on 50% of your original take home pay 15 years ago. You will need much more. For example, if in this scenario you can live on $20,000 a year (which is pretty frugal if you're making a $100k/year salary and living in an expensive city), you would need $31,000 in 15 years to equal that same purchasing power. All so you can enjoy living a lower middle class lifestyle and eating discount canned food the rest of your life.

Am I missing something? I cannot work out a way that retiring early makes any sense at all when I actually do the math.

[dude]

I think the "math" as typically shown holds the numbers constant for ease of understanding. Of course, in real life, you are going to get wage increases, promotions, etc.  The key is to invest the difference and hold your standard of living constant (in real dollars).  I think the math works itself out pretty reasonably with that assumption.

[CoderNate]

I think you answered the question yourself when you said you assume a 7% rate of return, but you're only withdrawing 3%.

[undercover]

I think you answered the question yourself when you said you assume a 7% rate of return, but you're only withdrawing 3%.

No, he's talking about something different. He's saying the math that estimates WHEN you can retire is more complicated than savings rate, and he's right. "Withdraw 3% while your investments return 7%" is what takes inflation into account after you're retired. The "Shockingly Simple Math" post by MMM and the site he references (Networthify.com) do not take into account spending increases as a result of inflation. In my opinion it's not really worth doing so, because it's all highly estimated anyway. But I don't think it would be hard to incorporate that detail into a new calculator, it's just no one has done it yet for whatever reason.

OP, you're still missing the big picture. I personally don't use calculators because my life isn't one big calculation (well it is, because I don't believe that anything is random, but that's a different story) - I know I'll change over time. The most important takeaways from the blog is to live well below your means and invest diligently. Focus on increasing income and decreasing expenses and you'll be fine either way. The amount of time it takes is honestly a pointless thing to even worry about. You're right in that these and other forums get way too caught up in the math and "retirement" part of things - but those are not the key takeaways of the blog.

I will say that your scenario doesn't exactly make sense though - 3% of $1M is $30k, which is $1k shy of your estimated $31k. And if you're spending $20k then where is the extra $15k going during the accumulation phase assuming half of your take home pay is $35k? Some of that $15k will go to expenses per year if inflation indeed does hold steady at 3% a year, but this is still a mystery based on your post.

The lifestyle you live is up to you. For me it isn't so much about retiring as it is FU money aka "FI". I have no idea why people get so caught up in the "RE" part. It's not like you're hopes and dreams as a human just go away because you suddenly have lots of money - but it sure is nice to get to a point where you aren't dependent on doing something you hate or just want a change from. So it's a terrible excuse to say that just because a simple little calculator isn't all inclusive, being FI isn't worth it.

[tobitonic]

The lifestyle you live is up to you. For me it isn't so much about retiring as it is FU money aka "FI". I have no idea why people get so caught up in the "RE" part. It's not like you're hopes and dreams as a human just go away because you suddenly have lots of money - but it sure is nice to get to a point where you aren't dependent on doing something you hate or just want a change from.

Very well put.

[MandyM]

I think you answered the question yourself when you said you assume a 7% rate of return, but you're only withdrawing 3%.

I will say that your scenario doesn't exactly make sense though - 3% of $1M is $30k, which is $1k shy of your estimated $31k. And if you're spending $20k then where is the extra $15k going during the accumulation phase assuming half of your take home pay is $35k? Some of that $15k will go to expenses per year if inflation indeed does hold steady at 3% a year, but this is still a mystery based on your post.

This.

The "simple math" of FIRE makes a lot of simplifications and assumptions (e.g. pay increases keep pace with inflation, spending pre-FIRE resembles spending post-FIRE), but to figure out your own personal case is more involved that then scattered example that you are using. Are you questioning the savings rate vs working years comparison? Or the post-FIRE spending/safe WR math? Those are two big, fairly different questions.

 

[FIPurpose]

I think you answered the question yourself when you said you assume a 7% rate of return, but you're only withdrawing 3%.

No, he's talking about something different. He's saying the math that estimates WHEN you can retire is more complicated than savings rate, and he's right. "Withdraw 3% while your investments return 7%" is what takes inflation into account after you're retired. The "Shockingly Simple Math" post by MMM and the site he references (Networthify.com) do not take into account spending increases as a result of inflation. In my opinion it's not really worth doing so, because it's all highly estimated anyway. But I don't think it would be hard to incorporate that detail into a new calculator, it's just no one has done it yet for whatever reason.

OP, you're still missing the big picture. I personally don't use calculators because my life isn't one big calculation (well it is, because I don't believe that anything is random, but that's a different story) - I know I'll change over time. The most important takeaways from the blog is to live well below your means and invest diligently. Focus on increasing income and decreasing expenses and you'll be fine either way. The amount of time it takes is honestly a pointless thing to even worry about. You're right in that these and other forums get way too caught up in the math and "retirement" part of things - but those are not the key takeaways of the blog.

I will say that your scenario doesn't exactly make sense though - 3% of $1M is $30k, which is $1k shy of your estimated $31k. And if you're spending $20k then where is the extra $15k going during the accumulation phase assuming half of your take home pay is $35k? Some of that $15k will go to expenses per year if inflation indeed does hold steady at 3% a year, but this is still a mystery based on your post.

The lifestyle you live is up to you. For me it isn't so much about retiring as it is FU money aka "FI". I have no idea why people get so caught up in the "RE" part. It's not like you're hopes and dreams as a human just go away because you suddenly have lots of money - but it sure is nice to get to a point where you aren't dependent on doing something you hate or just want a change from. So it's a terrible excuse to say that just because a simple little calculator isn't all inclusive, being FI isn't worth it.

Small correction here, the post on "shockingly simple math" does include inflation because the 4% safe withdraw based on the trinity study includes inflation in spending. But when you look at websites like firecalc, they adjust all numbers to be in present currency. MMM even states:

Assumptions:

You can earn 5% investment returns after inflation during your saving years
You’ll live off of the  “4% safe withdrawal rate” after retirement, with some flexibility in your spending during recessions.
You want your ‘Stash to last forever, you’ll only be touching the gains, since this income may be sustaining you for seventy years or so. Just think of this assumption as a nice generous Safety Margin.

[fattest_foot]

The part you're missing is that you're using 7%, but the CAGR of the S&P has been about 10% historically. "7%" is used as an after-inflation return.

That is, unless you think that in the future, the market will only earn 7% before inflation; and you might be right. There are other factors to consider, like the fact that inflation isn't actually running at 3% anymore and hasn't for a while.

If you really dig into the numbers though, you'll realize that until you get closer to 7 figures, it's your contributions that make up the bulk of your portfolio and the earnings in the market are mostly irrelevant.

[JordanOfGilead]

I want to know two things from the OP.
1) Why do you assume that you can only maybe save 50% of your take-home pay, especially at 100k gross? My gross is 65k and my "savings" (actually going toward pre-mmm debt payments currently) rate is over 60% of my take-home.
2) Why on earth would a single adult with no pets or dependents NEED $35k/year and still consider it a mustachian lifestyle? I have a wife and two pets (cat - 18lbs, dog - 65lbs and growing) that all take up considerable resources and we still only spend maybe 20-25k/year on living expenses, and that includes our mortgage payments AND we are a seriously wasteful household ...

[BBub]

Using your savings/return assumptions it works out fine if you:
a. Use a 4% SWR instead of 3%
b. Use 2% inflation instead of 3%

Beginning with $100k, adding $35k for 15 yrs @ 7% ROR = $1,155,419

$1,155,419 x 4% SWR = $46,217

PV of $46,217 at 2% inflation rate for 15 yrs = $34,134

That's pretty close to your $35k ann spending.  Maybe it'll take 15 yrs + a few extra months to get to $35k.  That's not a wide enough margin to declare BS, in my opinion.

Of course the outcome will change if you change the inputs to suit your own temperament or expectations (i.e. lower SWR, lower returns, higher inflation).  That doesn't make the math flawed.

[BBub]

By the way, MMM does address inflation in the shockingly simple math by using a 5% ROR to account for inflation.  His underlying assumption is that the nominal return is 7% and the real return is 5%.  Using your numbers:

$100k beginning value, $35k annual PMT, 5% ROR, 15 yrs = $963,143

963,143 x 4% SWR = $38,525 inflation adjusted.

The end result is slightly different because this scenario accounts for inflation annually instead of my previous post where the final number was simply discounted once.  But either method puts you well within striking distance of your $35k inflation adjusted spending requirement.

[somebody8198]

I think you answered the question yourself when you said you assume a 7% rate of return, but you're only withdrawing 3%.

No, he's talking about something different. He's saying the math that estimates WHEN you can retire is more complicated than savings rate, and he's right. "Withdraw 3% while your investments return 7%" is what takes inflation into account after you're retired. The "Shockingly Simple Math" post by MMM and the site he references (Networthify.com) do not take into account spending increases as a result of inflation. In my opinion it's not really worth doing so, because it's all highly estimated anyway. But I don't think it would be hard to incorporate that detail into a new calculator, it's just no one has done it yet for whatever reason.

OP, you're still missing the big picture. I personally don't use calculators because my life isn't one big calculation (well it is, because I don't believe that anything is random, but that's a different story) - I know I'll change over time. The most important takeaways from the blog is to live well below your means and invest diligently. Focus on increasing income and decreasing expenses and you'll be fine either way. The amount of time it takes is honestly a pointless thing to even worry about. You're right in that these and other forums get way too caught up in the math and "retirement" part of things - but those are not the key takeaways of the blog.

I will say that your scenario doesn't exactly make sense though - 3% of $1M is $30k, which is $1k shy of your estimated $31k. And if you're spending $20k then where is the extra $15k going during the accumulation phase assuming half of your take home pay is $35k? Some of that $15k will go to expenses per year if inflation indeed does hold steady at 3% a year, but this is still a mystery based on your post.

The lifestyle you live is up to you. For me it isn't so much about retiring as it is FU money aka "FI". I have no idea why people get so caught up in the "RE" part. It's not like you're hopes and dreams as a human just go away because you suddenly have lots of money - but it sure is nice to get to a point where you aren't dependent on doing something you hate or just want a change from. So it's a terrible excuse to say that just because a simple little calculator isn't all inclusive, being FI isn't worth it.

This is a hypothetical scenario, not my exact personal finances. But I have found myself that I bump up against a certain threshold of savings rate (for me, it's around 60%) at which point I find that I'm not just cutting out wasteful consumer spending but actually living an increasingly crappier life. For example, I like going to the gym and taking martial arts classes. I could add another few % to my savings rate by cutting out the gym and just doing pushups in my small apartment, but I would be miserable (and not nearly as fit). Still even with 60% I'm in the 99.999th percentile for a personal savings rate, so I find it hard to justify being miserable and bored for years just to have a little extra money in retirement.

Now I understand that this is the argument a lot of people use to justify not properly saving for retirement – "just live your life!", "you only live once!", etc. – and that's not what I'm advocating. I'm just saying that at some point, for me, the equation flips and spending a little more to have a decent life that I don't hate begins to make more sense.

FWIW, I spend about 31-34% of my take home pay. Probably 25-28% is absolute survival necessities (rent, groceries, home supplies so I'm not living in squalor) which I could scrape down to 15-20% or lower if I had to (e.g., by moving to a shared apartment in a cheaper part of town, which would double my commute). Of the remainder, a little bit goes into entertainment (seeing friends, going to plays and movies) and a bit goes into irregular medical costs which I unfortunately cannot control or anticipate. I'm really not a spendthrift!

[runningthroughFIRE]

It isn't about having a little extra money in retirement, or depriving yourself.  If you are truely happy spending the little extra to take gym classes then go for it - the point is to challenge your expectations of what really makes you happy, and (usually) people realize that they don't need to burn all their resources to do so.  You seem to have lived both ways, and made the informed decision that you are happier taking martial arts classes.

I see additional money saved as time taken off my working-because-I-need-the-money career, not having more money in retirement.  Unless you're building in a safety margin, money leaves the equation once you're FI and have 'enough'.

[zephyr911]

Except that withdrawal amount is not accounting for inflation!

Am I missing something? I cannot work out a way that retiring early makes any sense at all when I actually do the math.

YES.

You're missing that the 7% DOES account for inflation.

/thread

[undercover]

Small correction here, the post on "shockingly simple math" does include inflation because the 4% safe withdraw based on the trinity study includes inflation in spending. But when you look at websites like firecalc, they adjust all numbers to be in present currency. MMM even states:

But OP is referring to expenses inflating by 3% every year during the accumulation phase, not after you're living off your investments. The usual “how long do I have until I can retire/life off my investments” calculators do not take this into account. MMM would need to state that he assumes income will increase by inflation or at least an amount to cover the additional expense. You won’t need your income to increase by 3% necessarily to cover a 3% increase in expenses per year since there should hopefully be a wide gap between the two.

FWIW, I spend about 31-34% of my take home pay. Probably 25-28% is absolute survival necessities (rent, groceries, home supplies so I'm not living in squalor) which I could scrape down to 15-20% or lower if I had to (e.g., by moving to a shared apartment in a cheaper part of town, which would double my commute). Of the remainder, a little bit goes into entertainment (seeing friends, going to plays and movies) and a bit goes into irregular medical costs which I unfortunately cannot control or anticipate. I'm really not a spendthrift!

Well, no one here honestly cares about your savings rate or what you do with your money, that’s up to you. It's still true, regardless of which calculation you perform, that savings rate is all that matters. In your case, if you aren't happy with an extremely high savings rate at your income, then raising income is the only solution. Math is math. And most of the math people do here are rough calculations - meaning yes, there are tons of variables that aren’t taken into account. I do agree that it’s unwise to assume that your income will keep pace with inflation - because it historically hasn’t - but you can definitely do your own math however you think it will work for you. Any small increase in income per year will still make the calculations you’re looking at more and more feasible.

[MidWestLove]

one question on your math - what exactly are you allocating for taxes? if I am reading it correctly, it is extremely high (30k out of 100k)? No way that is the case in US.  or are you accounting for before tax deductions (401k/403b/etc) and then no counting them in savings rate?

[Eric]

So your expenses increase with inflation, but your salary doesn't?  There's your problem!  That's why most of us just use real numbers and don't try to add inflation into everything. 

[zephyr911]

Small correction here, the post on "shockingly simple math" does include inflation because the 4% safe withdraw based on the trinity study includes inflation in spending. But when you look at websites like firecalc, they adjust all numbers to be in present currency. MMM even states:

But OP is referring to expenses inflating by 3% every year during the accumulation phase, not after you're living off your investments. The usual “how long do I have until I can retire/life off my investments” calculators do not take this into account. MMM would need to state that he assumes income will increase by inflation or at least an amount to cover the additional expense. You won’t need your income to increase by 3% necessarily to cover a 3% increase in expenses per year since there should hopefully be a wide gap between the two.

YES.

You're missing that the 7% DOES account for inflation.

/thread

[somebody8198]

So your expenses increase with inflation, but your salary doesn't?  There's your problem!  That's why most of us just use real numbers and don't try to add inflation into everything.

I would not count on it, no, given the type of job market we have these days. I'm hoping my salary will increase another 50-60% over the next few years as I move into higher positions but this is very much not a guarantee.

[runningthroughFIRE]

Deflation could occur and your expenses could go down in the future, too.  I wouldn't count on it, given the economy these days, but this is very much not a guarantee.

[Eric]

So your expenses increase with inflation, but your salary doesn't?  There's your problem!  That's why most of us just use real numbers and don't try to add inflation into everything.

I would not count on it, no, given the type of job market we have these days. I'm hoping my salary will increase another 50-60% over the next few years as I move into higher positions but this is very much not a guarantee.

Really?  I don't know about you, but in my 20 years of working I've gotten at least a few promotions.  Increasing at the rate of inflation should be the minimum projection, with most people far exceeding that.

Either way, that's the assumption to the math.  It doesn't make sense to inflate everything but your salary.