When the Back of the Napkin can be Worth Millions

cashnapkinWhat’s with Mr. Money Mustache and all his funny-business math? 

When you read the criticisms that sprout up around the web, you’ll often see people nitpicking over the accuracy of some of the numbers I present in these articles. You may even find yourself doing some of the nitpicking in your own mind.

You might feel that the assumed inflation rate or investment returns are wrong, or the bicycling data should be shown per mile rather than per hour. People even devote entire website discussions over the perceived inaccuracies in my recollection of how we saved for retirement.

“MMM uses fuzzy math and hand-waving!”, they say. Then they go off and feel better, feeling they have disproved the Tenets of Mustachianism and thus freed themselves from making any changes to their lifestyle.

This accusation is right – I do make up some fuzzy math at times. I’ll throw all kinds of unrelated formulae into the mixing bowl, estimating the dollar-value of being more sexy, or the annual cost of being a complainypants, and multiplying it all by an annual compounding rate pulled from my own hindquarters.

But although the equations are unusual, they can still be very useful. Because it turns out that life itself is very fuzzy, subject to incredible random variation and the splendid irrationality of human nature itself. In a world where you can take over entire countries using weaponry as gentle as an Optimism Gun, how can you argue that your own personal expenditures will invariably inflate at exactly the same rate as the Consumer Price Index?

So today, we are going to learn about why making your best wild-assed estimates (as seen on this blog) can still be massively more productive than making no estimates at all. And in fact, with the right practice and principles, the wild estimation can prove to be much more accurate than you would originally dare to assume.

Let’s use my friend Mark’s story as an example. Mark lives near me in Longmont, but he works far, far away in South Denver, doing some type of high-tech surveying work. It’s about 40 miles each way. As part of the job, he occasionally needs to drive on dirt roads, so he has decided he needs a high-clearance vehicle. But he also has two kids and a wife, so he wants something with four doors and lots of room. Here in America, this sort of wish list often leads to the Ford F-150 pickup, a spectacularly big truck with a very small cargo bed, big cabin, huge engine, and heart-attack level of fuel consumption. It’s the best-selling vehicle in the country.

So Mark visits the dealership, kicks the tires, and the dealer amazingly offers him the deal of a lifetime. The “regular” price is $45,000 or so, but just for Mark, this special model will be sold for only $29,000 with low-interest financing and a low downpayment.  Score, right? Oh yeah, and we’ll roll the $5,000 of taxes and dealer and registration fees into the loan for you.

This is where Mr. Money Mustache would come screeching into the dealership on his bike, with Fuzzy Math guns blazing.

“Mark, you damn fool! This truck is going to depreciate about $25,000 over the next 10 years. Your insurance will be $10,000 higher than it would have been driving an older car over that period. Gasoline at 15,000 miles a year will cost you $18,000 more per decade than it would to fuel a normal car. All told, you are wasting over $60,000 every 10 years with compounding, just by choosing this ridiculous truck over something like an equally capable, much-better-handling 2003 Subaru Outback wagon or maybe a Honda CRV. And that’s before factoring in about $100 grand in commuting costs you could save by moving closer to work or getting a closer job!

See, the standard shopper thinks, “Leather seats, big engine, room for the kids. Sold!”. When instead he needs to be thinking “A hundred and sixty thousand dollars!? I don’t even have a grand in my checking account! Maybe I need to buy something other than this truck”.

Although you could nitpick over the estimates I took at his insurance costs or the future price of gas, if you did, you would be missing the point. Just being in the right ballpark would have allowed me (and Mark) to avoid a potential $100,000 mistake. Avoid just 5-10 of these over a lifetime, and you’ve made the difference between “Broke” and “Retired”.

For most of us, even mundane financial decisions can lead to dramatically different outcomes. But you can’t always see those outcomes in advance if you’re down on the street making decisions with your emotions in the driver’s seat.

It is well known that most consumers, and even some of the newer arrivals to this blog, make shopping decisions emotionally. Meanwhile, I’ve always behaved more like a Vulcan (or an engineer, which is closely related), attempting to apply some logic to each purchasing decision. One reader even critiqued this blog‘s approach*, pointing out that not everyone thinks like an engineer.

But that is exactly my point: to build wealth efficiently, you should act a bit more like an engineer – trying to let go of emotions and put more logic and basic arithmetic into your decisions. You need to learn to do a bit of engineering on your own finances.

The reason is that at moderate incomes, the margin between poverty and wealth, middle class and kickass**, is very narrow. Spend most of your money and you’ll be almost-broke forever. Spend just a bit more and you’re bankrupt. Cut it down by just a factor of 2, and you’re financially independent in under 17 years. Cut it in 4 and you’re free in about 7. But without doing the numbers, trying to accomplish this is like trying to swish a basketball from an airplane.

You don’t need a fancy degree or even a scientific calculator to handle the basics. You just need to be willing to try your best to figure out how much something is going to cost you over time. Even if your numbers aren’t perfectly accurate, this is far better than the cautious person’s result of not trying at all. And here are a few guidelines to make your job easier.

  • Define the best and worst case scenarios. This will give you a range of possible outcomes, and you know the right answer is somewhere in there. Then take your best guess for the numbers, and use that as your guide. Example: Building this deck will take me between 8 and 16 hours. Doing the work myself will save me the $1000 the contractor had bid, so my pay rate will be between $125 and $62.50 per hour. Since even the worst case is quite good, I will do the work myself.
  • Use a search engine to quickly find scientific data or statistics instead of anecdotal evidence. The recent bike safety article is an example of this: Anecdotally, I feel like biking is perfectly safe, since I do it every day and never get hurt. But instead of using my own experience, I looked up official statistics and found that bike accidents do occasionally happen, allowing for more accurate decision-making.
  • Always try to figure out your per use costs. This leads to shocking revelations, like how upsizing to a 7-passenger vehicle might cost you $1000 per hour for the amount of time you actually spend carrying 7 passengers.  In my case, this decision making process has forced me to consider selling my construction minivan next year.
  • Divide annual savings by the money spent to get a return on investment figure. If it’s higher than 10%, you have found a smoking good life optimization and need to put it into action. Solar panels, tankless water heaters and LED light bulbs often do well when you evaluate them this way.
  • To calculate a weekly expense compounded over ten years, multiply the price by 752 (so a light restaurant habit can easily be $100,000 per decade)
  • For a monthly expense, multiply by 173
  • Be Reassured: approximate math and educated guesses can be deceptively accurate. This is because you tend to make random errors on both sides of the right answer. These random errors tend to cancel each other in the equation and you end up roughly right. I’ve seen this over and over again in my house building, fitness, investment, and spending guesses over the years. It’s not an exaggeration to say that my wild-ass guesses are the reason I was able to retire at 30, and they’re still coming through for me today. They may sound bizarre to the uninitated, but they’re not really all that bad.

Earning more money is often best accomplished with emotions – make people feel good about working with you, and they’ll want to pay you more. 

But actually keeping this money in your life requires a bit more hard-nosed practicality.

You can do both.



* To the Pressing Pause guy, I need to offer a bit of a rebuttal. I am of course aware that the battle for frugality is an emotional one rather than a logical one, silly. That’s why so many 350+ posts on this blog are philosophy-oriented. If it really were just about math and spreadsheets, you’d only need one post with a few equations in it, and everyone would say “Aaah! Early retirement it is, then!”.

But people can be made to trust the statistics, if we present the case well enough. Examples include the safety of airplanes,  investing in stocks, donating to distant charities, voluntarily paying taxes, and even believing in currency itself, as explained in the post about good old-fashioned trust.

** That Middle Class to Kickass post is often subject to its own nitpicking of the same type. People often complain, “Middle class!? The imaginary people in this article are making $140,000 a year – that’s super-duper-upper-income!”

Which is again missing the point: the concept of frugality and an efficient lifestyle costs becomes even more important as you move down the income scale. If you don’t like to read about what cutting cable TV does to a $140,000 budget, see what magic it does to a $25,000 budget instead. To figure it out, just bust out your calculator and do your best to run the numbers. You’ll love the results.


  • Wyatt June 24, 2013, 9:36 pm

    I am an engineer…..what you call your back of the envelope or wild ass guessing is what we call “using rational significant figures”. “aka sigfig”

    You never report a result number down into the 0.0000 range unless your assumptions and measuring equipment is also that good. We engineers find value in significant digits and # of decimal places, it tells you as much about the result as the result itself!

    Many people abuse this and report answers with every decimal that is given on the calculator, this is wrong and makes people THINK you have a higher level of certainty than is rational.

    Also, many stores make prices messy, not round and with lots of cents to try to stop people from calculating the usefulness in their head…..don’t let them trick you! Round up and quick compute like MMM is telling you! It still returns a valid result.

    I wish more people would be comfortable doing this level of math, its very powerful!

  • Josh June 24, 2013, 9:54 pm


    Dude, you’re blowing my cover.

    At the corporate level, these same concepts in “fuzzy math” are more often used to make large financial decisions than the exacting calculations of a tax professional. And the people who make these estimations that allow quick decision making with a frugal mindset are paid in the 6-figure salary realm. If these approaches to finance are highly valuable for large corporations, it certainly can be scaled down to the personal income level.

    This kind of financial management is my area of study, and the future career I am gearing toward. People tell me I’m pursing education way early in my career; I’m thinking I’ll retire before I hit what they think is the mid-point. That is, of course, if you don’t blow my cover….

  • Kruidig Meisje June 25, 2013, 2:12 am

    I find that marketing is a force.
    A force to be reckoned with, although it usually works in unperceived, pervasive ways. And considering the amount of marketing people are exposed to, it is pretty logical they have to make a big mental leap from their current (marketing infused) thinking to MMM’s conceptual and stoic thinking.
    And (psychology has scientifically proven that) people don’t like change, they are not designed for it. They can handle it, but preferabbly in emergencies only. And feeling your soft skin on a massive beautifull couch in a lovely large home filled with luxury goods has no mental connection to an emergency.
    So I applaud MMM for every person he CAN persuade to think differently. But it might take quite some bits (time, blogposts, and other thingiees) before a majority of the marketing infested crowd (i.e. US, Europe and the richer people in BRICs) is considering his thinking seriously. Adaption is a step behind that. Might take, let’s say, 10 years of a hugely popular TVshow, which in blogterms would be…. eeehhh… help me anybody, can’t find the conversion factor on the net…..

  • TJ June 25, 2013, 7:12 am

    Hey MMM,

    Thanks for the math shortcuts. They’re great. There’s one I’ve been trying to back search for on the blog that I can’t seem to find. It’s the one where you look at an expense, and say, ‘ok, in retirement, I need X portion of my nest egg to fund this expense’. (assuming an average return in index funds or similar)

    Do you remember the post(s) I’m talking about?

    I remember it being shocking and a useful way to think about expenses, but can’t find the post or the shortcuts used.


    • Elizabeth June 25, 2013, 6:56 pm

      I think MMM assumes a 4% safe withdrawal rate, which means that $25 is needed to safely take out $1 each year (since $1 is 4% of $25). So all you would need to do is calculate the annual cost of the expense, and then multiply by 25.

      As an example, say you have a $120 a month cable bill. That comes out to 12 x $120 = $1,400 annually. As 25 times the annual cost is 25 x $1,400 = $36,000, you would need an additional $36,000 in savings to cover the cable bill.

      Is that what you mean?

      • Derek @ MoneyAhoy.com June 26, 2013, 5:23 am

        That sounds correct to me. It is 25X the cost assuming 4% withdrawal each year.

  • Matt June 25, 2013, 7:45 am

    From another engineer…how many piano tuners are there in New York City?


  • Matt F June 25, 2013, 9:57 am

    I think there is an important engineering point that could be added to this conversation in terms of “sensitivity analysis”. Basically, some rough calculations work so well because the final result of the equation may not change that much even with significant changes to certain variables (explaining for the non-engineers). This is based on the mathematical construction of the equation, but also from some variables having dependence on each other (you change one it changes the other). In retirement calcs, long term compounding interest rates are the only variable I can think of that has a big impact, but MMM’s power is that if you reduce your timeframe to 10 years, it is no longer very sensitive since there is less time for compounding!!!

    If you can understand the sensitivity of your calculations, then back of the envelope is very useful and powerful. This may be the reason that non-engineers get worried about this type of math since they can get suckered into things like 30% credit card interest rates because “over the next month that’s only like 10 bucks!”

    Thought I would throw that out there as a possible reason people do not trust quick calculations, but most people are just complainypants for sure.

  • Whitefox June 25, 2013, 10:01 am

    Just wondering, again, what’s the compounding rate we’re looking at here when I use those quick-calculation numbers?

    5%? 7%? I’m sure there’s some easy way to back-calculate this, but… xD

  • gnucashgun June 25, 2013, 10:25 am

    I once calculated on the back of a napkin that a pumpkin cannon I made would produce 10 tonnes of thrust! Unfortunately the older I get the more accurate Fermi equations become :(

  • Carla June 25, 2013, 10:58 am

    Speaking of fitness and projections, we need an update on that fitness graph Mr. Mustache!

  • Hilda June 25, 2013, 12:11 pm

    I am a big fan of mustachianism and I do think it could bring great improvement to life. But I do not think everyone can do it.
    Let me explain myself: people are very much interested in being admired and envied, and most of them are much more interested in other people’s opinions than with the real quality of their own lives.
    Some people due enjoy that long commute to work just to show the new car to the colleagues. It is really stupid, but that is how it works for many people.
    They get into debt just to pretend they belong in the “high society”.
    When I bought my house in a good but cheaper neighborhood, people at work would bug me saying I should move to a fancier one, even when I said I did not care about “fancy”. Now my house is paid for and I live confortably debt free, and these people are still paying a lot of money in expensive rented properties (rent in Brazil is very expensive, specially in Sao Paulo).
    I think those marketers do one hell of a job convincing people to throw money right into the toilet =/

    • Art Guy June 25, 2013, 3:28 pm

      Yes, its the habit of fitting in. Biking to work, at least in my experience does kinda impress people, but they would rather drive the Escalade, and they give really odd looks (Really? You bike to work…even in this heat?), They definitely dont admire or envy me.

      • Derek @ MoneyAhoy.com June 26, 2013, 5:21 am

        You’ll get the last laugh when you have thousands of extra bucks and can retire healthy years earlier!

        • Hilda June 26, 2013, 7:39 am

          I am serious. I got a lot of criticism, even from close friends because I don’t seem to “enjoy life” and “money is meant for spending”.
          You have to be a person that really do not care about other people’s opinions. I think this is the key to go down the road to early retirement.

          • Jimmie Jo June 26, 2013, 8:38 pm

            Well, I certainly enjoy my commute more when I bike than when I drive. I even enjoy it enough that I spent $$$ on a proper commuting bike that makes it even more fun. I’ll wimp out and take the bus when the snow flies—it’s still less stressful than driving.

    • Doug June 28, 2013, 1:23 pm

      You make some good points, Hilda. Although I don’t get it at all, many people are more interested in impressing others than in doing what would work best for themselves. Many things I see, hear, or dates as I look at the calendar remind me of fun things I’ve seen or done because I didn’t have to work more to buy junk to try and impress people who probably don’t give a damn anyways. Oh yes, I do work at paid employment, but only intermittently and thus have more time for other pursuits.

      Last but not least I was born in 1960, was a teenager in the 1970’s and we were called the Me Generation because supposedly we were selfish and cared not about what anyone else thought. That describes me well, but what happened to the rest of this generation?

  • Trevor June 25, 2013, 12:25 pm

    Outstanding! Fantastic picturing you screeching into the car/truck dealership on your bike to save the potential buyer from themselves and the dealer. Keep up your good work in providing us with sensible, logical advice.
    A fellow MMM.

  • LMaS June 25, 2013, 3:29 pm

    I have always found napkins to be terrible for doing math, the pen is either too wet and soaks then tears the napkin, or too sharp and pokes and tears the napkin, maybe my napkins are too cheap ;)

    I appreciate your site (and your fuzzy math), but then again I’m just part of the choir you’re preaching to.

    Cognitive dissonance is simply too strong a force. As numerous complainypants have proven to you, it is no small feat to change someone’s mind using facts, especially with regards to things they believe strongly such as financial practices. And clearly many many people in America strongly believe in some pretty poor financial advice or the country wouldn’t be where it is.

    I know you are a punch-in-the-face-ologist, not a psychologist, but if your goal is 100% conversion to Mustachianism, perhaps there is room for some touchy-feely conversion methods (in moderation of course). I don’t know how, and perhaps that would be something all together different, like Goateeism… hmm. Although I do think it is a possibility that the Psychologist Industrial Complex has just convinced everyone in America that all their feelings and emotions are important to keep themselves in business, and lots of people could actually save lots of money if they just went to see the punch-in-the-face-ologists instead.

    • Miser Mom June 26, 2013, 6:47 am

      LMaS, I agree entirely with your first paragraph. I find that back-of-the-envelope computations to be vastly superior to back-of-the-napkin computations. (Besides, what are you doing with paper napkins, anyway? At home, any reasonably frugal person uses cloth napkins).

  • Jeff June 25, 2013, 3:34 pm

    Didn’t Warren Buffet say something like “It’s better to be approximately right than precisely wrong” ?

    Good advice. My car is 15 years old.
    The depreciation for each further year I run it is approximately zero.
    I last put fuel in it 3 months ago & it will have done over 700 miles before it needs more. At that time, the fuel will add about 20% to the value of the car.

    Considering the car is parked with no one in it for approximately 99% of it’s life, my choice of car is near to optimum.

    • Derek @ MoneyAhoy.com June 26, 2013, 5:13 am

      Hah, that’s a great quote!

      The gas tanking being full adding 20% to the value of the car really made me chuckle. I’m in a similar situation.

  • Daydreamsofearlyretirement June 25, 2013, 3:49 pm

    MMM, I have to agree with you 100%. This type of speculation is an incredible tool in motivating one self to make proper decisions, regardless of the accuracy of one’s projections, or even “daydreams.”

    My wife and I are both readers of your blog (thank goodness I married a fellow mustachian), and I made sure she read this entry immediately.
    She tends more towards a “stay in the present” type of mentality, and prefers not to speculate. Interestingly, she sometimes gets frustrated with my speculations. My talks of where we may be in 10-15 years (barring unforeseen disasters and assuming we maintain our savings rate) actually discourage her from making smart decisions in the present…by giving her an undesired level of comfort with our current financial situation.

    I showed her this not to argue that her mentality is wrong. In fact, her perspective has often done me a great service by making me think analytically about present decisions. I just thought you did a great job in explaining how this type of thing can be used as a motivational tool….and it helped me give her a little insight into why I frequently engage in this type of “daydreaming.”

    • Mr. Frugal Toque June 28, 2013, 8:47 am

      There were (apparently) some studies done regarding fitness and exercise – more specifically: how to get people to exercise. It turned out that emphasizing long term benefits wasn’t effective. People don’t go and exercise *right now* because they’re worried about heart disease 15 years down the road. They don’t stop smoking because they’re worried about lung cancer later in life.
      You can get people to exercise *now*, however, by emphasizing how good it’s going to feel in 30 minutes once the exercising is done. I’m not sure of the equivalent for smokers, but I’ve seen a short term diagram of the benefits of quitting (you’ll start to smell your food better in 7 days etc.)
      I suspect the same is true of personal finances. It might be hard to convince people of the awesomeness of early retirement when they’re in debt so deep they can’t even see it.
      Therefore, we also try to work on the idea of feeling better about not being such a consumer in the present day, of the power it will give you over yourself and how good it will be for the environment among other immediate benefits.

      • Daydreamsofearlyretirement June 28, 2013, 12:16 pm

        Great point. While I do use these daydreams as motivation (they seem to work on the big decisions…cars, houses, 401k contributions, etc…), my wife often has to rein me in on day to day decisions. She is better at focusing on the present and the immediate benefits of a decision. (she’s also in way better shape…speaking of your talk of exercise above…haha). I’ll definitely think of this as I make day to day financial decisions in the future.

      • Yukon Marianne May 27, 2014, 4:22 pm

        I’m not a numbers person (although I like science and I am super happy this blog is lousy with math-happy engineers) and rational, compelling numbers work is a bit of a trust deal. I’m not going to check and re-check anyone’s math. For me, the motivation and remembering to Act Mustachian isn’t numbers re-call, but re-training old unchecked thought processes. I’m prone to optimization paralysis…is this the best option? Will I regret this? well beyond the best thought:action ratio. So for me, what is helpful is a quick thought exercise for each crossroads (purchasing decision) like:
        1. Do I NEED this?
        2. Can I DIY/Hack this? (I’d love a forum for helpful creative hacks, sometimes it doesn’t occur to me to DIY something as the creative solution never popped up in my brain)
        3. Can I get it used?
        4. Would I rather buy this or 30 more minutes of freedom?

        Just to run though the Mustachian thought process consciously at each purchasing/lifestyle juncture until it becomes ingrained.
        Lather, rinse repeat. Until then, I still need a monthly budget to remind myself of the concept of limits and gauge progress.

  • Shilpan June 25, 2013, 9:42 pm

    And the worst part of this Ford-F150 saga is that it repeats itself every three years or so. I have a friend who loves a phone call from a dealership because they call him a great customer who pays on time monthly.

    So, he becomes a sucker every three year. Most of the depreciation occurs in the first three years. So, if you take that into account, his loss trajectory is much steeper than $60K every 10 years that you’ve projected.

    • Derek @ MoneyAhoy.com June 26, 2013, 5:11 am

      I’d be interested to see how much you lose over the course of a normal life owning the new car every three years say from age 25 – 65. It’s gotta be somewhere in the neighborhood of $500K after you account for lost compounding if you were to invest the money!

  • Mola June 25, 2013, 10:44 pm

    Avoid just 5-10 of these over a lifetime, and you’ve made the difference between “Broke” and “Retired”.

    This strikes me as terribly true. Not even 40 yet and with no history of any unusually bad moeny handling my wife and i can still lament over actions we took that, had we not, we would be much closer to retirement now. Buying a house rather than renting and then the market tanking. Selling stock when the price was higher than paid but watching it go up another 300% after we sold. Spending $20,000 on house improvements that make it nicer but wont get us that back when sold. Buying a truck because we haul stuff and then calculating renting a home depot truck from time to time would have been a lot cheaper. Etc.

    If 70% accurate fuzzy math helps people avoid perfectly normal but also perfectly financially limiting decisions than bully for fuzzy math. I wish i would have been using the MMM fuzzy math 8 years earlier and id be done by now.

  • Mark June 26, 2013, 1:08 am


    Great site – I’ve been reading it with interest from the UK since finding it a few weeks ago.

    I’d like to ask a bit more about where the figures of 752 and 173 for weekly and monthly purchases come from. I understand that it must be regular payments with compounding interest, but I just can’t get the maths to add up.
    Something that shows me how to derive these figures would be much appreciated.

    Keep up the good work!

    • Mr. Money Mustache June 26, 2013, 10:19 am

      To get those figures, I just used a “future value calculator” formula (there are lots on the web), with a weekly/monthly payment of, say, $1.00, and a 7% interest rate.

      The calc then figures out what would happen if you invested that first dollar on the first week, started earning returns, added a second dollar the next week, etc., with all returns reinvested, and then looked at the value after 10 years of that goodness.

      With zero investment return, a weekly purchase would of course just multiply by 520 – the number of weeks in 10 years. Even that is still a pretty big number. But given that many people have high-interest debts (or the ability to invest in stocks, rental houses, or a bicycle), it is much more accurate to assume the money saved will be doing something useful – and I use 7% for this figure myself.

  • Sir_Mordred June 26, 2013, 3:02 am

    Beiing a moustacheee for decades I really enjoy reading your blog. Although from Germany many of your ideas do work out also east of the Atlantic. The confusing thing is that even the most ridicolous ideas from the US, like driving an huge SUV to bring your kids to Kindergarten, found their way to us. And an AUDI Q7 or BMW X5 (with our ridicolous high fuel prices) are a complete waste of big money, with very little real value.

  • desk_jockey June 26, 2013, 5:50 am

    I love a good SWAG… one car related story was when I was trying to talk a coworker out of a car purchase. It was a nice new sports coupe. My logic… I know what I make each month after tax, and I know what my very base cost of living for rent, electricity, water, and food is. Now would I really want to apply ever available extra dollar that I earn for just over one year to purchase of something whose main purpose is to carry me to/from the place where I earn a living? Rinse and repeat every 8 years and you’re working 1/8th of your adult life just to pay for your transport to work. (In my fuzzy math, the incremental cost of insurance, etc of the new car is balanced out by the fact that that car would have some residual value at the end of the 8-years).

    It was an early attempt at spend-significantly-less-than-you-earn proselytizing. Call it a moderate success as she put off the purchase for a year until the emotion once again took over.

  • Chris June 26, 2013, 7:39 am

    First let me say that I am a newbie to your page (tuned in through an ex-bf). I compliment and value your money saving tips and advice.

    This post is one of my favorites so far. And I feel that I am broadening my money saving logic. Just recently I decided to put vinyl siding on my home. Before I made the final decision I weighed the vinyl siding cost (about $2000). I determined that if I put the investment in my home with maintenance (vinyl as opposed to painting shingles which costs about $300 every three year), I would save about $1000 every three years and the added work of painting every three years. Which proves to me that the investment of siding not only will add value to my home but saves me time and money long term with maintenance costs.

    Thanks for the money tips and great articles.

  • Guitarist June 26, 2013, 10:12 am

    Maybe the fear of logic, facts, math, and facing the hard truth right in the eye in some people truly shows that not everyone is cut out to be an engineer. I see the world as you do, MMM. I may not be as strong-willed as you are, but I do boil things down to equations and compare the joy of instant gratification (and almost just as quick regret) with the joy of long term saving and planning.

    Does this mean I need to be more understanding of those who refuse to see what’s clearly in front of them?


  • Doug June 26, 2013, 2:23 pm

    Having an engineering background myself, as well as being a long time mustachian, I can really relate to this topic. I find myself often doing quick calculations sometimes on scrap paper and sometimes in my mind, about the economics of purchases. It just seems like common sense to me, like something you do without even seriously thinking about it like putting a seat belt or bike helmet on.

    However, not everyone does such thinking it through. An example that comes to mind was a conversation 3 years ago with a guy I worked with. He said he wanted a pick up truck for periodically hauling stuff around. I said that if you were only occasionally hauling stuff around it would be better to buy a trailer, as a good sturdy built trailer, the hitch, and accessories could be bought for $1000 or less and it would last for many years. I also said a truck isn’t economical if there is a low utilization factor, in other words if you only use it for hauling stuff once a week or less. Better off to buy a smaller more fuel efficient car, and use it to pull the trailer occasionally as required. He said, and I quote: A trailer, that’s gay! I don’t care about utilization factor, I want a truck! I think that sums up why some people are better at accumulating wealth than others.

  • Greg Reynolds June 26, 2013, 6:50 pm

    M, don’t apologize for your engineering approach. Just think of yourself as a Leonardo da Vinci engineer. Be a Renaisance Man. You’re not just improving the lives of anonymous individuals by your efforts, you’re saving a generation from a form of mind-slavery. Hope that thought doesn’t take away the fun!

  • GamingYourFinances June 27, 2013, 9:03 am

    Totally agree MMM! It’s all about decision making. The precision of the math needs to be weighed against the size of the decision.

    Being +/- $10k on a $100k decision is much different than being +/- $10k on a $20k decision.

    Life rarely provides 100% of the info, you just need to understand how your estimates effect the precision of the math.

    If being off by $10k on that $100k decision doesn’t actually effect the choice then why bother being more percise?!?

  • Strick June 27, 2013, 9:53 am

    The funniest is those that have it both ways (figure some variables so exactly and guess on others) and think the conclusion is conservative. The most frequent I see is someone taking their life expectancy out 3 SDs to ‘make sure they don’t run out of money’ but then assume a S&P 500 return of between 6 & 10 percent over the next 20 years. Its just funny to me someone would assume they might live forever but not that the S&P will return zero over the next 20 years.

  • Breezy June 27, 2013, 10:22 am

    I just ran some fuzzy numbers yesterday that I liked quite a bit. I’ve set aside about $10,000 for each kid and had been *hoping* not to have to use it for college. I calculated if I invested it in a Roth for them at the earliest possible age in Vanguard’s Wellesley Fund and earned its 10% lifetime annual return, and saw that that simple decision would leave them each with over a million dollars fifty years down the road — it doesn’t matter if the math’s a bit fuzzy — that’s a better use of the money than a semester or two of college! Not to say they won’t go to college because I don’t put this money toward it, but saying this particular goal/gift would have far longer implications.

  • Miki June 27, 2013, 10:28 am

    Honestly, even if you implement a fraction of the advice provided in this blog, you are in much better shape than most people. If some feel like it is more worth their time to complain and dismiss the theories presented here, then they must somehow be ok with the idea of handing over 50 hours a week of their lives to some entity that does nothing for them spiritually or emotionally. Be my guest, I say!

  • Rebecca June 27, 2013, 11:49 am

    I’m an old dog (61) and it’s too late to retire early BUT… I will be retiring without worry by excising many of concepts put forth in your blogs. I’ve been on my path to comfort for about 5 years and plan to retire in less than 5 more years.

    It took awhile but now my spouse is on board too. I keep a lot of inspirational quotes taped up where I see them daily and one that fits this article is from General Patton. “A good plan, violently executed now, is better than a perfect plan executed next week.”

    Just get started!

  • jestjack June 27, 2013, 1:24 pm

    What a timely article! Automobiles have really gotten expensive ….especially trucks,,,yet there seems to be no shortage of them. As for me, despite being a landlord and having plentu of need for a truck…the Ford Ranger i purchased 10 years ago works great. I’m hoping to get another 10 years! Will share that when I interview tenant candidates the big truck payment usually “sinks the ship”. These payments are unbelievable ….like $600-700 a month. I just don’t know what these folks are thinking,,,,,

  • Pam McCormick June 27, 2013, 1:38 pm

    OH I just had to make a comment this article hit the nail on the head! I have made many mistakes and I am a nurse not an engineer BUT math never lies it is what I love about it.IF only most of America would just open their minds and run the numbers.Thank goodness for young and those who will not just except the status quo..Very nice job Mr. M

  • Micheal June 28, 2013, 5:36 am

    I used fuzzy math to get my wife onboard with saving for early retirement quite by accident. Stats don’t have to be exact to make sense or have an impact.

  • Ed Mills June 28, 2013, 9:51 am

    I love this whole “fuzzy math” topic. It’s funny how people think I’m some sort of math genius because I have a six-figure retirement balance. Sure, I have my own spreadsheet, but most of my calculations are done on little pocket notepads. I find that putting numbers to paper helps me visualize the enormous possibilities that we have. Once I have a vision, I go to hammer-the-goal mode.

    I love the monthly expense rule of thumb. Just compared my phone-internet-cable expenses using the format. Currently, $40 internet + $8 Netflix + 5 Skype subscription + $3 Pandora = $56 a month * 173 = $9,688 over 10 years. Previously, $131 cable/internet + $32 Vonage = $163 * 173 = $28,199! That’s a difference of $18,511! Is it just me, or is fuzzy math sexy? Hell, fuzzy math makes me horny!

  • Wiggle June 28, 2013, 11:34 am

    I find you need to these calculations even if not exact because I’ve observed people sweeping things under the table when dealing with very big or small numbers or assumptions. One I see all the time is with new cars, someone will say “Well you know I can get 0% financing, the used car is gonna have more upkeep, I can get some discounts on features on the new, it’s gonna be almost the same price to just get a new car”. No, it’s not even close. People have this tendency to think “a bit plus a bit plus a bit equals alot” (where alot is the cost of the new car). This of course doesn’t work when the cost is like an order of magnitude a part but it’s one of those quirks with how people see finances. Have any of you observed this?

  • Nate June 28, 2013, 11:56 am

    I DO NOT agree that you should calculate your automobile cost by the hour. In my undergrad, I studied to be an accountant, and one of the princples of accounting is to use an accurate unit of measure.

    If you are going to own a car for a set number of years before disposing of it regardless of the hours or miles driven, then you use straitline cost by dividing purchase cost less estimated selling price by the number of time periods of use (month or year).

    If you are going to own a car until the wheels fall off, then you should be using the more accurate unit of measure which is miles. It is pretty predictable how many miles a car can be driven before it reaches its wearout period, and I use 200,000. After 200k, there can be major repair requirements that make the car un-economical and it is worthless for resale. If you keep it past this point, you are simply paying for variable costs but you can consider the extra milage as free when it comes to depreciation.

    By using miles, you can more easily use back of the envelope math for variable expenses (i.e. MPG of fuel use, 80k for tires, oil/fluid intervals, etc…).

    Once you find the per mile cost, you can allocate the cost to your own usage rate. Better yet, many other people have done this math using miles, and because the calculation is applied consistently across the cars they are analyzing, you can see which cars are more expensive relative to the other choices. Only things like machinery and tractors make sense when using hours.

    At the end of the day, even though you are using an incorrect measure, the fact that you use one makes you better off than suffering the consequences of unseen expenses. My 2000 volvo S40 sits in the garage waiting for emergencies while I commute 21 miles each way on my bike every day (rain or shine, hot or cold) simple BECAUSE I know the cost of each mile.

  • George June 28, 2013, 5:41 pm

    about “the cycling data should be per mile rather than per hour”

    Just curious about the bicycle safety article, why there is there no mention of Jeffrey Rosenthal’s “Struck by Lighting” book?

  • Patrick June 28, 2013, 8:21 pm

    And -POW! How ya like me now?

    Yeah man, any math beats the snot out of NO math. Uhh…. helllo?

    I get down to the gnats ass because I enjoy it, but when you’re out in the world and just reviewing things in your head, there’s all sorts of ways to rock a bit of analysis.

    The deal is, you’ve got to be constantly questioning the assumptions. Helps to be able to bust some back o’ the napkin skillz.

    Classic post, brother.

  • nomoreuntdebt July 1, 2013, 9:28 am

    Swishing a basketball from an airplane:


    MMM, your hyperbolic exaggerations aren’t nearly far-fetched enough.

  • CincyCat July 2, 2013, 12:14 pm

    OK – I just applied the “min / max” estimating approach to the check engine light in my car. I had already scheduled an appointment with a mechanic to check it out, when I remembered that some auto parts stores can diagnose check engine lights for free. I took my 10-year-old car up the street to a local parts store, and discovered that O2 sensor #2 had gone bad, which is not uncommon. Based on the parts sales guy’s explanation of how to replace it, I figured it would take between 30 minutes & 2 hours for me to do the repair. I ran the numbers and I definitely come out ahead by changing it myself. Wish me luck!

  • frank July 18, 2013, 2:32 pm

    Lets see.. emigrated to the USA in 1997.

    Took out a 160K mortgage.. Almost no savings.
    Combined income (at the time $130K including rental income).
    Made double payments on house (using all rental income).

    Fast forward to 2013
    Mortgage paid off (took less than 7 years)
    Total assets about $1.6M
    Total income about $165
    Planning to retire in 1 to 3 years, Wife want to continue working and gets great medical bennies
    Expect a pension from the UK of about $25k in 8 years time.

    The only reason I want to wait to retire is cus I’m not sure I have “quite” enough yet, plus the work i interesting at the moment.

    The plan would be to live off the rent and the wife’s income (about 45k) and not touch the stash which should be worth about 2.5 to 3M in 12 years.

    House expenses (plus cheap paid for cars) is about $12k.. We should be able to do this.

  • Lydia Pack September 4, 2013, 4:56 pm

    OMG, I’m just a baby moustache an from New Zealand. But today I had a call from one of the American timeshare companies saying I had ‘won’ a trip to Florida (of which I was still paying flights and $728+ in fees). In New Zealand we don’t really seem to have these slick salespeople and deals coming through (in fact it was the first time I’d had one about a timeshare).

    I was just amazed by the slickness of the telephone operators. Their script was worked out to an absolute tee, first building trust by getting you to write down their name and travel I’d number, describing the holiday in detail, and only giving you a hint that there might be costs involved, laughing and making little self depreciating jokes as they go along. Sounding like your best buddy. It must be soul destroying to do their job knowing that they’re essentially conning people, but I’m sure they convince themselves of their own rhetoric just to be able to do the job.

    When I realised it wasn’t a good thing I told them ‘no’ and they had so many fallbacks, like you don’t have to use it for 16months, or we will just sign you up and you have a 30 day cool down period etc. Wow, no means no here. So I finally got off the phone after firmly saying no a few more times,

    I was just astounded at the level of slick salesmanship there. I don’t know how Americans resist such convincing sales scenarios all the time. It would take quite a level of willpower and I take my hat off to American mustachions having to deal with this each day.

    I did the back of the napkin calculations on this and ‘winning’ this trip would have cost me over $4,500 not including interest costs and I’m sure other fees along the way.

    Long live the moustache!

    • Mr. Money Mustache September 4, 2013, 5:49 pm

      Wow, a pretty crazy story!

      Another one of our American powers is hanging up the phone – you don’t have to firmly say ‘no’ several times, you just press the red button on the telephone, which ends the conversation with no fuss.

      Note: these sales calls are generally just a punishment for people who are 15 years late to dropping the land line… telemarketers don’t call mobiles nearly as much.

  • jonlemon October 13, 2013, 2:26 pm

    For those who like making guestimates:

    Santos (2009). How many licks?: Or, how to estimate damn near anything.

  • Ian Turner November 13, 2013, 7:25 am

    A counterpoint to this argument: http://blog.givewell.org/2011/11/10/maximizing-cost-effectiveness-via-critical-inquiry/

    “When information quality is good, you should focus on quantifying your different options; when it isn’t, you should focus on raising information quality.”

  • derek March 6, 2014, 10:46 am

    Actually that is where I find the value in this website, how to structure the rough calculations without going on and on ad nausium about the details. I used to think the money sense guide to saving for retirement was useful. Now I see it is not nearly as bad assed as i thought.
    So I cranked the savings up, replaced a 4×4 with a subcompact and think of expenditues in different terms. Behaviour modification with reinforcement by habit and support by ongoing articles.
    A wonderful recipe for effectiveness. I am grateful for the work you do and the differences you make in many many lives
    MMM articulates the strategy for FI insimple terms, while poking fun at our sense of self importance. I laugh, I pause, I rething, I adjust. I prosper.

  • Todd Goodman July 3, 2014, 2:38 pm

    I was just curious about one thing. If you get 25 times annual spending, keep costs low, live off of the dividends, what happens if we go through another 2008? You could see how that stash could dwindle fairly quickly. Cut it in half immediately, live off of it, what happens when your stash gets ransacked?

    • Mr. Money Mustache July 3, 2014, 7:58 pm

      To see the answer to what happens in that situation, look at what has happened in the years since 2008: stocks recovered back to higher-than-ever levels, dividend yields dipped a tolerable amount temporarily during the crash, and those of us who lived through it (myself included, as I was 3 years into retirement in 2008) are better off than ever!

      • St4n July 3, 2014, 11:31 pm

        +1 MMM!

        I can’t remember where I found the details, but I did look into this once before…

        Yes, the S&P 500 (and most other large-cap, developed world stock indices) dropped by a little over 50% from peak to trough. Nerves of steel would find that alarming! If I remember rightly, the market started looking iffy in 2007. Traders spent almost a year chewing their fingernails, but it wasn’t until later in 2008 that many holders capitulated and the market tumbled. I get less stress doing 9-5.

        The alternative is to be boring: Long-term buy and hold. Live off of your dividend income. Stop buying the daily newspaper, turn off the TV and leave your income paying index-tracker to do its work. Going back to the facts…

        If you look at the average yield of the S&P 500 over the same period, it almost doubled. This indicates your dividend (cash) income would barely have changed. If you collected $40,000 in dividends in 2007, you would have collected about the same in 2009. At the very worst, in 2008 you would have taken a hit of less than 10% of your income and by 2010, the quarterly ‘payrise’ had resumed in earnest.

        Now back to the grindstone, to grow my ‘stache and put the preaching into practice…

  • Josh September 26, 2014, 12:16 pm

    I’m wondering if this awesome might have some thoughts for me. (If it should be in the forum, let me know):

    I was tempted to list my name as “Mark” like the character in the story simply because my clown-car ways have bit me in the ass this year. I purchased a brand new $40,000 GMC pickup in February 2014 mostly because I hate my job and wanted something nice to drive on the way to work (the psychology of my clown-car-ness). After I started reading MMM in July ’14, I realized what a huge mistake I had made. Forgive me because my Mustachian muscles are still growing, but how do I correct this mistake? After doing some napkin math of my own, it seems my family would be way better off if I sold the pickup now even if I lost $8,000 – $10,000. What does this fine community think of the following logic:

    Sell new pickup at a worst case scenario of $32,000. (There’s no debt on this vehicle)
    Purchase a smaller, fuel efficient family car for $10,000.
    Invest the difference of $22,000 in Vanguard index fund OR pay towards mortgage. (We have no other debt and savings and retirement accounts are being added to regularly).

    In spite of the loss on the pickup, growth of the $22,000 difference over a 10 year period more than makes up for the loss of selling it now, right? So I should totally dump it?

    • Mr. Money Mustache September 26, 2014, 3:36 pm

      Holy shit yes, you should sell that ridiculous truck! You aren’t “losing” $8000, you are GAINING $32,000. Or preventing the cruel world from locking in the $40,000 loss for good. I am happy for you!

      Luxury trucks (and cars) are some of the fastest depreciating things in the universe – get that hot potato out of your hands before you turn around and find it’s worth $1500. Small cars (even though still money-losers) do much better. My $9000 used car bought 6 years ago is still worth over $6k (and running flawlessly while it gets us around at 40+ MPG). $500/year depreciation versus $8k or more for the typical large truck!

  • dave September 26, 2014, 6:17 pm

    My 20 year old honda civic with 430,000 Km on it runs great still and I am going to go for another winter here in Ontario Canada with it.

  • szofter December 23, 2014, 3:40 am

    “If you don’t like to read about what cutting cable TV does to a $140,000 budget, see what magic it does to a $25,000 budget instead. To figure it out, just bust out your calculator and do your best to run the numbers. You’ll love the results.”

    I totally second this one. Although I haven’t watched TV in years (regardless of its budgetary consequences, I simply got bored with it), the same applies to bike commuting and many more. I’m a college student in Budapest, Hungary, working part-time, earning the equivalent of cca. 300 dollars each month (note that prices are much lower here than in the US, but it’s still a pretty low earning). I used to commute by public transport, even though I love biking. The public transport pass for a year costs approximately $180 here. Buying a good bike second hand costs no more than that – but if I use the bike for 3 years (which is a ridiculously short useful life for a bike), the annual cost is $60. Even if I do repairs, upgrades and stuff like this for $40, I’m 80 bucks richer every year. If I divide the price of the bike by a higher number of years, let’s say by 5, and manage the repairs and stuff on $20 or less, I’m in the $110-130 range each year. That’s 10 bucks each month – and, as we know, a millionaire is made at 10 bucks at a time. And all this compared to a student’s pass; an adult’s pass costs almost three times as much, adding another $300 to the annual savings. And then I haven’t even mentioned driving.

  • EarningAndLearning June 8, 2017, 10:00 am

    As a non-engineer, non-analytical type, until I started reading this blog, I never considered the precise cost of things like my daily cup of coffee made at home, or driving to my job, or my dog! Inspired by MMM’s & the commenters’ fuzzy math (which I confess sometimes leaves my head spinning & I’m not sure I’m really following everything) I now do my own fuzzy math on SO many things in my life & it helps guide my spending decisions (usually to stop spending as I have been). What an eye-opener fuzzy math has been for this non-numbers person, so keep it up!

    I used to wonder where all my money went, and regarded my bank account and Visa bill with fear, and used to avoid looking at it, for weeks and sometimes for months on end. I called myself an ostrich with her head in the sand when it came to finances. Now, inspired by MMM, I know where all my money goes: I chart my monthly spending in a spreadsheet & look daily at my online bank account & watch my mortgage diminish with glee. :) Your blog has literally changed the way I look at money & spending it & keeping track of it.

    So thank you & keep up those calculations!

  • Party of 7 July 14, 2018, 10:18 am

    I always thought the 2 best things about the Tightwad Gazette were:
    1. She showed you how to do the math.
    2. The success stories. Life-changing, tear-jerking stories of real people.

    Similarly the best things about MMM:
    1. Actually doing the math.
    2. The optimism gun brings financial hope.
    3. Wisdom & wit of comments. (Rx for a happy life: Read MMM everyday until you LOL. Apply it.)
    4. Glimpses of life-changing success

    I’ve been using graph paper to analyze since 4th grade. But I’m not nearly as advanced in spreadsheets as many of you. But I thank MMM for showing us the power of math in real life. (Math “Knowledge is Power!”) You are changing lives with math and optimism. No small thing.


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