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The Shockingly Simple Math Behind Early Retirement

Here at Mr. Money Mustache, we talk about all sorts of fancy stuff like investment fundamentals, lifestyle changes that save money, entrepreneurial ideas that help you make money, and philosophy that allows you to make these changes a positive thing instead of a sacrifice.

In addition, the Internet presents us with retirement calculators, competing opinions from the mainstream media, financial doomsayers, unpredictable inflation, and a wide distribution of income and spending patterns between readers.

I reviewed my own path to age-30 retirement in “A brief history of the ‘Stash“, then I did a hypothetical calculation using two average teacher salaries to show how long it would take them to retire in “The Race to Retirement – Revisited“.

Because of this torrent of information, people tend to become overwhelmed and say things like,

“Yeah, good for you Mr. Money Mustache, but how can I possibly know when I’ll have enough to retire myself, with a completely different lifestyle?”

Well, I have a surprise for you. It turns out that when it boils right down to it, your time to reach retirement depends on only one factor:

Your savings rate, as a percentage of your take-home pay

If you want to break it down just a bit further, your savings rate is determined entirely by these two things:

How much you take home each year

How much you can live on

While the numbers themselves are quite intuitive and easy to figure out, the relationship between these two numbers  is a bit surprising.

If you are spending 100% (or more) of your income, you will never be prepared to retire, unless someone else is doing the saving for you (wealthy parents, social security, pension fund, etc.). So your work career will be Infinite.

If you are spending 0% of your income (you live for free somehow), and can maintain this after retirement, you can retire right now. So your working career can be Zero.

In between, there are some very interesting considerations. As soon as you start saving and investing your money, it starts earning money all by itself. Then the earnings on those earnings start earning their own money. It can quickly become a runaway exponential snowball of income.

As soon as this income is enough to pay for your living expenses, while leaving enough of the gains invested each year to keep up with inflation, you are ready to retire.

If you drew this on a graph, it would not be a straight line, it would be nice curved exponential graph, like this:

years_to_retirement

Working years vs. Savings Rate (screenshot from networthify.com)

If you save a reasonable percentage of your take-home pay, like 50%, and live on the remaining 50%, you’ll be Ready to Rock (aka “financially independent”) in a reasonable number of years – about 16 according to this chart and a more detailed spreadsheet* I just made for myself to re-create the equation that generated the graph.

So let’s take the graph above and make it even simpler. I’ll make some conservative assumptions for you, and you can just focus on saving the biggest percentage of your take-home pay that you can. The table below will tell you a nice ballpark figure of how many years it will take you to become financially independent.

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.

Here’s how many years you will have to work for a range of possible savings rates, starting from a net worth of zero:

Savings Rate (Percent)Working Years Until Retirement
566
1051
1543
2037
2532
3028
3525
4022
4519
5017
5514.5
6012.5
6510.5
708.5
757
805.5
854
90under 3
95under 2
100Zero

It’s quite amazing, especially at the less Mustachian end of the spectrum. A middle-class family with a 50k take-home pay who saves 10% of their income ($5k) is actually better than average these days. But unfortunately, “better than average” is still pretty bad, since they are on track for having to work for 51 years.

But simply cutting cable TV and a few lattes would instantly boost their savings to 15%, allowing them to retire 8 years earlier!! Are cable TV and Starbucks worth having two income earners each work an extra eight years for???

The most important thing to note is that cutting your spending rate is much more powerful than increasing your income. The reason is that every permanent drop in your spending has a double effect:

  • it increases the amount of money you have left over to save each month
  • and it permanently decreases the amount you’ll need every month for the rest of your life

So your lifetime passive income goes up due to having a larger investment nest egg, and it more easily meets your needs, because you’ve developed more skill at living efficiently and thus you need less.

If want to retire within 10 years, the formula is right there in front of you – simply live on 35% of your take-home pay**, which is approximately what I did without even realizing it during my own younger years. The only reason Mustachians will remain a rare breed, is because this article will never appear in USA Today. (Or if it does, people will be too busy complaining about how it can’t be done, rather than figuring out how to do it)

 

*If you want to play with the (rather basic) spreadsheet I made to generate this table, you can download it in OpenOffice format (.ods) here: Retirement Savings vs. Years

** definition of take-home pay: gross income minus all taxes. Remember to add back in any 401k or other savings deductions to the paycheck you see, since these are really part of what you are “taking home” – you just happen to be saving it automatically.

Note on how to track spending: we do almost all spending using the best rewards credit card I can get my hands on, and the rest by automated bank debit (checks or cash only for things that strictly require it, like Craigslist purchases). So at the end of the year just need to review the online statements for card and bank.

Recently this has been revolutionized by signing up for an account at Mint.com. Same basic idea, but it lets me see up-to-the-minute spending that is automatically categorized into nice pie charts, etc. If a figure looks surprisingly high, you can click in to see the detailed transactions in the various accounts that were added together to make that category. Quite futuristic.

  • Cruz is growing a mustache September 5, 2014, 2:01 pm

    Done with all of 2011 posts!!! Slowly but surely becoming a knowledgeable mustachian.

  • MeanyGoat September 25, 2014, 2:07 am

    The math is always so obvious but the road to early retirement is paved with temptation! We are just bombarded with advertising all the time and then there is peer pressure and of course bad habits. In the end many of our Frugal Savings end up being thwarted by hidden spending. The human brain plays tricks on us and we all have our weak spots and blind spots. If you really want to retire early, as I have but only at 57!!, then you need to identify these “Frugal Blindspots” which are holding you back. It could be your pet dog which costs over $1500 a year or it could be that you always insist on buying top brands rather than generic products. Explore this topic in more depth by checking out this article http://www.meanygoat.com/frugal-blindspots/ and you will find that you can really start to cross off the years to your early retirement!

    • Bob Werner September 25, 2014, 8:31 am

      Nice point on the pets. I was reading in the forum and there was one guy worried about his student loans. Yet he was spending something like $100 a week on doggy daycare. Amazing! He just couldn’t figure out how to save money.

      Of course there is always the theory that dog ownership extends life by 2 years, but I find walking and not having to scoop up shit more fun.

  • aleksandar December 16, 2014, 3:58 pm

    HEllo we are all on the same page so let me translate this article to you, its simple you save you retire early.the more you save earlier you retire and all calculations are SOOOO different from country to country ,city to city or even person to person so each of us should find his/her way of becoming FI and even the reality of retiring is individual.for me is working 4 days 5 hours in my private dental clinic and making average salary (500$/MO)(and yes that is maximum dental salary in my country, and yes i own it)and enjoying the time with my family the rest of the week.I am debt free with savings (noting to invest it in in my country, shitty economy) and most important RETIRED IN MY MIND!!!!

  • Rob January 31, 2015, 1:44 pm

    MMM – Thanks for the blog – I recently read almost all of them since you started in 2011!

    I was hoping someone can clear this up for me. Do you include retirement savings (i.e. IRA, 401k) in your total savings percentage? I understand the rule of thumb is to have 25 times your annual spending before reaching FI, but should that include retirement savings (IRA, 401k) that you cannot touch until age 59.5?

    Between my wife and I, we are investing 20% of our income into our 401k and IRAs. I’m trying to calculate my savings rate and I have two figures: one at 40% (not including 401k/IRA) and one at 60% (which includes 401k/IRA). Which one would I use that corresponds to the “savings chart” in the blog post?

    • Paul February 27, 2015, 11:45 am

      Of course you count your retirement savings as part of the total.

      • Erich February 27, 2015, 12:27 pm

        Paul,
        I think rob asked because his assumption is that the money can’t be touched until he’s 59.5, and presumably his FI goal is prior to that age. I’m in Canada so I don’t know the rules for 401k, but in Canada you can take money out of your RRSP (equivalent) any time, you are just taxed at your income level for doing so. I believe I’ve heard there are withdrawal penalties in the USA, but someone else would need to comment on that.

  • Earlyretiree February 24, 2015, 4:49 pm

    I love you MMM. Really. Your blog just resonates truth in simplicity and common sense.

    I’m 34 and have been semi retired for about 4 months now and it’s really nice. I can’t imagine going back to work again full time. Yuck! I worked so hard getting here because I disagree so strongly about the whole 9-5 mantra. I could do my work in 4 hours but had to stay another 4 each day when I had things I wanted to be doing. Anyhow, I now work 2-3 days a week. But one of those days is playing in a band so that’s just fun usually. The other day or two I do lawn mowing and I actually enjoy it because I’m my own boss! So cool. Now I feel more natural and relaxed and have time to do things around the house that need doing. At first I was a bit bored but not anymore!

    By far the biggest thing that’s allowed us to do this is: low debt. Then, we kept a few investments that average 6% a year and have savings that will last a long time.

    Simple!

  • Hrishikesh March 21, 2015, 4:05 am

    Thank you so much for the sharing this wealth of analysis and experience in a blog !

    I noticed quite a few statements in assorted articles about how living in a developed country (U.S, Canada… ) is helps early retirees. I an 35 years old, living in India, with a salary that can give me a living standard of what $120K in the U.S would. My saving percentage is about 60 %, mostly in stocks.

    My question is about how high inflation affects the surprisingly simple retirement math ? India records about 8 % inflation in some basic commodity prices.
    Buying a house for a passive rental income may not be fruitful either – Real estate is expensive and the rental yields are as low as just 20 % of the mortgage payments the purchase would entail.

  • Laurent March 30, 2015, 8:51 am

    Dear MMM,
    I have started a similar process in France, and though there are websites in France addressing personal finances and financial independance, none I know of discuss early retirments and frugality, in a fun and graphic way as you do! Keep the good work!
    I have 2 questions about the % saving vs duration of remaining working years:
    1/ the graph illustrates perfectly how increasing savings has an exponential effect on retirment age, however people do not kepp the same salaries over years. Does the graph takes into account a salary increase of let’s say 2% per year, with all this extra cash invested, and then at retirement the montlhy income is the salary – investments at initial time point?
    2/ The % of saving is investments / wages or investments / (wage+incomes from renting house, dividends, etc)?

    Thank you very much in advance for your answers!

    Laurent

  • Wade April 9, 2015, 8:28 am

    Thank you for this great information. I’m going through all of your posts from the beginning and they are great.

    I am confused about one thing that I haven’t figured out yet. When you say saving a certain percentage of your income will let you retire in a certain amount of year, is that based on a certain salary or just assuming that you will live at the same spending rate when retired?

    Assuming all numbers are take home pay, if you make $100K and save 50% that means you can retire in 17 years and still live on 50K\year. Is this correct?

    I guess writing it out helps it make a bit more sense. The only real variables are how much you want to live off of in retirement and if you can save that much each year for the number of years the chart shows.

    Thanks for letting me work that out in my writing. :)

    Wade

  • Kevin April 15, 2015, 5:56 pm

    This article is really helpful and motivates me to cut down my spending!

    I was wondering how realistic is the assumption of 5% investment returns after inflation during your saving years. I know that you mentioned that in the S&P500 index, the median ROIC is around 7%. That means to get this 7% return on investment for your savings, one has to invest all of its savings in an indexed fund. Is that a reasonable thing to do? I am new to investing myself and I would think one would probably have an asset allocation of putting only a portion of money into their indexed fund and put another portion of money into a more conservative investment (e.g. T-bills).

    I would love to hear what everyone thinks. Thank you!

  • Eskimo April 19, 2015, 8:32 pm

    Hi there! First time posting. Early retirement has been my goal ever since the day I started working. What a pleasant surprise to stumble upon this “secret society” of people who think alike!

    I have a couple of questions:

    1) Regarding the 4% rule, does anyone know if it takes taxes into consideration? Taking money out of my investments, be it in the form of dividends or capital gains, invites the tax man to my door. I’ll need to withdraw between 5 to 6% in order to get my 4% spending money. With that in mind, my stash actually needs to be 25-30 times of my pre-tax spending.

    2) When tallying the amount of your stash, do you make a distinction between your regular savings and retirement savings? Besides tax considerations, withdrawing from retirement savings before the age of 59 1/2 incurs a penalty. It makes me wonder if I should include my non-retirement savings in my stash at all when deciding the timing of my retirement, since I’m planning to retire well before 59 1/2 but do not want to incur the penalty. Any thoughts?

  • Andrew May 2, 2015, 6:05 pm

    I love this concept. Since the link to the Excel document didn’t work, I recreated one with the assumptions laid out in the post. I get the same answers as to how many years it would be when comparing to the table, however, it doesn’t seem that the 4% withdrawal rate takes into account income taxes that would have to be paid when retired. Does this calculation assume all retirement income is coming from non-taxable accounts?

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