za3k > finances > how to retire for infinity years

This is the first in a short series of articles. This will be by far the longest (and therefore the least interesting). But it's the one that people ask me about the most, so I figured I'd get it out of the way.

I retired at 31, which is pretty unusual. And I get asked about it a fair deal (and even more people want to ask but are too polite). So I wanted to go ahead and answer "how did you retire early?". The basic answer is

There's a good chance you're imagining you need to make six figures a year, spend about what you are already minus the frills, and basic subtraction means you'll have enough to live on until you're dead. All three guesses are wrong.

Once you read the article, you might think "well, I don't really want to be retired at 30 or 40". At least not with the sacrifices it requires. That's fine, you know what you want. Or, you might do the math and realize you can't retire early. Either way, I still recommend the rest of the articles. They're 80% about normal stuff like how to save money. I just go a little further than most people.

I'm going to walk you through retirement math in today's first article, because until you see the math, you will think the remaining 20% of my later advice is insane.

Finances innately need math. Financial rules of thumb are bullshit, and only numbers actually work.

Most finances, hopefully including the rest of these articles, only need addition, subtraction, and maybe multiplication. This article, and this one alone, we're doing interest calculations (division and multiplication). That means, you invest $100K per year, at 4% interest, you need to know you make $4K every year. You can use a calculator to follow along if you want, you only need the answers, not any deep grasp. But you should check if what I'm saying is true. Never take financial advice on authority or faith. The footnotes have the really advanced math for the really advanced skeptics, but you can skip them if you're not a math person.

The math

That's it, that was the basic math. Now you can retire in 10 years, no matter how old you are. Just make $70K every year, spend $20K, and wait. And don't have the stock market collapse.

Well, there is a caveat. You need an additional safety margin, even if the stock market doesn't collapse. You probably want to retire in 12 or 15 years, at 35. Here's why:

To summarize, if you live on $20K/year, and work at $70K/year, you can retire indefinitely in theory, after 10 years (maybe at 32). In practice, add a safety margin (maybe 34 or 37). Now you're secure against random stock market problems, and you make more money over time.

Well, what if you're not making $70K and spending $20K? I'll walk you through the general formula. You need to know three numbers

The rough4 estimate is that you can retire in: 25 * expenses / (income - expenses) = 25 * 20K / (70K per year - 20K per year) = 500K / 50K per year = 10 years. Substitute your own numbers to find out your own situation.5

Now let's say you make $50K/year, and spend $40K/year. The same math says it will take you 25 * 40K / (50K-40K) = 1,000K / 10K = 100 years to retire. You will never be able to retire indefinitely; you'll die first. That is a huge difference between those two examples! We'll talk about that in a second, and how to best reduce the number of years. But first, what gives? That's a pretty typical person, right? Why is everyone not starving on the street at 80?

Normal retirement

In practice of course people do spend a lot of what they make and then retire. There are many reasons.

If you're retiring at 30, almost none of the above apply to you. You need to get by on savings, no external support. You don't get a 55% mortality discount on retirement, you get a measly 15% discount. You probably don't have much in your standard retirement account, and even if you do, you can't access it for another 35 years. You don't get medicare (though you may get medicaid). You don't get social security. Expect no social support. If people see a healthy 50-year old go broke from poor retirement planning, they should tell you to get a job. I would.

Retiring early

Returning the the topic of the retirement formula, we can see that there are exactly two numbers that affect you. How much you make (income), and how much you spend (expenses). Making a lot of money is good. But not spending money is at least as important. Imagine you made a lot, say six figures ($100K) but spent $50K per year. It would take you 25 years to retire. Not bad! What if you wanted to retire faster? If you spend $25K per year instead, you can retire in 8.3 years. If you make $200K instead, you can retire in 8.3 years. Both are equally good. You can halve your expenses, or double your income. They have the same effect.789

To me, that's 16 years of my life I get back. If I make twice as much, I can get 16 extra years to do anything I want, instead of working a job I kind of tolerate. If I spend half as much (remember, for my whole life, not just until I retire!) I get 16 extra years. That's a huge chunk of time. How much would you pay to live 16 extra years? And I get those years now, when I'm healthy and energetic. Prime years. I would do a lot of things10 to live 16 extra years however I want. Changing my job or spending is just a no-brainer. And the reality is that for most people, it's more than 16 years--it's going from retiring at 65, to retiring at 40 or 30. 25 or 35 years, that's a massive chunk of your life.

Of course, this assumes the value of time when you're at work is next to nothing compared to free time. That's actually how I feel11. If you don't, if you think it's only a bit better, then it's not as amazing. But basically, do the math. 15 years is a HUGE chunk. Even if it's just 10% better, having every day be 10% better for 15 years is still a huge impact.

It could be someday I'll change my mind, of course. I could go back to work. I could decide I don't want to live on $20K into my 50s, or have kids and need to change my plans. But there's nothing really irreversible involved. You're just saving up some extra money and not spending as much. No big deal to have some extra cash if you go back to work, right?

Now you've heard why I think it's really important to spend half as much, or save twice as much. Because it can get you 15 or 25 or 35 years (or 8 hours a day of them!). Way more important than you might have thought without the math.

For most people, finding a job that pays twice as much is very hard. Spending half as much is also very hard. Which is easier depends on your situation.

How to make more money really depends on your field of work, and to some extent where you live. On the other hand, people generally save money the same way--everyone has the same basic expenses. So I'm going to focus on teaching you how to save money in later articles. That doesn't mean it's a better plan. It's just the one I can teach.

  1. This is very conservative. Since it's founding in 1957, the S&P 500 on average made 7% yearly over inflation. 

  2. Which I am 100% in favor of. Get cracking on that science. 

  3. Why 25? 25 is (1/0.04). You need 25 times any amount to make it at 4% per year. Want $100 per year? Invest $2500 at 4% per year. 

  4. The rough estimate assumes you don't invest until you retire. If you invest all your money the whole time, you can retire in 25 * ln(1+E/(I-E)) years. Good luck! You may need a calculator. For anyone who wants the derivation: 

    > S(0)=0
    > S'(t)=0.04*S(t)+I-E
    ...differential equations, too hard so ask Wolfram Alpha...
    > S(t)=25*(I-E)*(e^0.04t-1)
    ...algebra, solve for S(t)=E/0.04...
    t=25 * ln(1+E/(I-E))
  5. Actually, the sitation is a little better, because you make money from investments before you retire, which I haven't take into account. If you're spending a small fraction of your income like in the first example, the exact4 and rough formulas give similar answers (within a couple years). 

  6. What about in between? As a reminder, we're making $50K and spending $40K each year. -If you plan to retire at 65 and die at 8012, you need 15 years of savings. That would be $600K ignoring interest, but it's actually $451K13. -If you plan to retire at 40 and die at 8012, you need 40 years of savings. That would be $1600K ignoring interest, but it's actually $798K13. -If you plan to retire at 30 and die at 8012, you need 50 years of savings. That would be $2000K ignoring interest, but it's actually $864K13. -If you plan to retire at any age and live forever2, you need infinity years of savings. That would be $infinity dollars (!) ignoring interest, but it's actually $1,000K. That's surprising! We might expect that with twice the money, you could retire for 30 years, but it's actually not true--you can retire indefinitely. Focusing on this magic cutoff point was, to me, a huge deal. 

  7. I would have expected the relevant numbers here to be savings (income minus expenses) and expenses, but I was wrong.  

  8. The effect is not anything easy and constant. It doesn't remove the same number of years, or the same fraction of years, each time. Too bad, huh? 

  9. Actually, this is a small lie. We're assuming that you don't make interest before you retire again. I haven't done the math if you do. 

  10. Still not exercise, though. Just you know, eating boogers. 

  11. I'm the kind of person who just fundamentally dislikes being told what to work on what someone else cares about, for 8 hours a day, 5 days a week. Why would I want that? I got my own shit I want to do. I've never had a job I liked even close to the weekend afterwards14. I have felt passionately about projects! I've felt like they're my life's purpose. I've been paid to do work. But so far, I've just never found any overlap between my passions and paid work. I wanted to retire early exactly so I can spend my life on what I'm passionate about. 

  12. Not, you know, that people plan to die at 80. They don't circle a date in their calendar. But you have to know how long you'll be retired to plan financially. Actually, living to 100 can turn into a financial problem! This is part of how insurance got started.  

  13. The equation here is 25 * E * (1 - e^(-0.04 * years)) 

  14. If you're considering whether to retire, take a month off. Then take a year off. If you're going stir-crazy after either, maybe don't retire. If after a year, you think "ugh, I have to go back to work?" both before and after your first month back? Start working out the math. That said, if I had the option to work 6 months out of every year, I would consider it.