Sunday, January 14, 2024

"Index, A History of the" by Dennis Duncan had me laughing out loud!

 I don't remember what compelled me to pick up and buy this book but I'm glad I did. Index, A History of the by Dennis Duncan had me laughing out loud earlier today.  If you're wondering what on Earth could be amusing much less hilarious about a book about the history of indexing (and page numbers, a relatively modern development that made indexes possible), I encourage you to read the book yourself. 



Nonfiction books didn't have indexes until sometime in the 17th century, and even then, most didn't. (Why novels don't have indexes, I'll never understand, but they sure could use them, especially long Russian novels spanning generations with characters that can be referred to by one of three names!)  When indexes first appeared, many people looked at them with disdain and horror. What would prevent someone from going directly to the index, reading only what was needed or wanted, and skipping everything else? Wasn't that a form of intellectual laziness, even theft, that might make us all dumber? The same sorts of questions asked when Ask Jeeves then Yahoo! and Google appeared: why would anyone read anything when it could be looked up instantly by anyone? 

Obviously, people still read books and by some measures, we read more than we ever did; we are probably better readers because we can instantly get a one-sentence summary of a historical figure or place mentioned in a book or - better yet - learn the pronunciation and definition of a strange word we've never encountered before. 

But hostility to the index was so fierce that its enemies weaponized it, adding unauthorized indexes to books written by people they wanted to ridicule. 

I will spare you the details of the pissing contest between Charles Boyle and Richard Bentley (but they are amusing). Suffice it to say that when Boyle's supporters wanted to ridicule Bentley, they inserted an index into a book, allowing users to turn to a specific page to know instantly about such important Bentley flaws as, 


His egregious dulness, p. 74, 106, 119, 135, 136 ... 

His Pedantry, from p. 93 to 99, 144, 216

His Appeal to Foreigners, p. 13, 14, 15

His familiar acquaintance with Books that he never saw, p. 76, 98, 115, 232. 


According to the author (of the Index, A History of the), if you turn to each of these page numbers, you really would find descriptions of such things. 

The mock index was most effectively weaponized against a man named William Bromley, who wrote as a young man a book about his Grand Tour of France and Italy, something so clichéd at the time (because everyone was doing it) that he wrote it anonymously, stating only that it was written by "A Person of Quality." 

Fast forward 13 years when Bromley was running for office. 3 days before the election, a second edition of this terrible book appeared, this time with an index. 

And what an index! Its entries were used to highlight idiocies and tautologies in the text that otherwise might have gone unnoticed. 


Naples, the Capital City of the Kingdom of Naples, p. 195. 

Carpioni a Fish in the Lake di Guarda, by the Similitude of the Fish and of the Name, the Author much questions if they are not the same with our Carps, p. 50. 


He lost the election; ridicule inspired by the index pointing readers to his imperfect text no doubt played a decisive role. 

Tory satirists used the same weapon against a Whig opponent Joseph Addison, issuing an edition of his Remarks on Several Parts of Italy with the same caustically-spirited index with entries such as, 


Uncultivated Plants rise naturally about Cassis. (Where do they not?), 1

Same us'd as an Adjective Relative without any Antecedent. Send him back to school again. 20

The Author has not yet seen any Gardens in Italy worth taking notice of. No matter. 59

Water is of great Use when a Fire chances to break out. 443


You don't need to have read the book to get these jokes. I imagine someone reading these out loud à la Monty Python while everyone burst out laughing which made me burst out laughing as well. OK, it's not as funny as a dog pooping C4 making the trash can blow up on Reno 911! but it's pretty damn close! 

Perhaps the moral of the story might be not to write books about Italy when you're young; they might come back to haunt you when you are older... thanks to the index! 

Friday, January 12, 2024

How to Calculate Compounding in Your Head - How much must you save each month to have $1 million in 40 years?

 Compounding must be one of the most difficult operations to do in your head which is unfortunate because it is also so important. We vastly underestimate how much something grows when it compounds over time because of compounding's difficulty. What our brains cannot grasp on the fly tends to be ignored or misunderstood. 

But there are ways of doing compounding in your head that are not quite as difficult as you might think. 

It helps if you work with a particular growth rate often. 10% per year, for example, is particularly easy because it can be found in Pascal's Triangle.  If you know that row 4 of Pascal's Triangle is 

 1 4 6 4 1 

Then you know that every dollar compounded at 10% a year compounds in 4 years to 


  1×$1 + 4×$0.10 + 6×$0.01 + 4×$0.001 + .1×$0.0001

 =   $1.4641


$10,000 compounded at 10% a year will grow to $14,641 in 4 years. 

Note that if there were no compounding, if someone you lent money to paid you 10% interest on the $10,000 principal each year then paid back the amount borrowed, you would have $10,000 + $1,000×4 = $14,000. 

Compounded growth, in this case, gave you $641 beyond what you would have with simple growth, where the growth is not itself growing.  This is what makes it so difficult to anticipate. If you know that 4 years of compounding 10% interest gives you 6.41% more - over half a year's additional interest - it doesn't help you anticipate how much more you will have in 10 years of compounding at 10%... $10,000 compounded for 10 years at 10% a year grows to $25,937 and change. This is now $5,937 more than simple interest over that time period would have yielded. Put another way, compounding for 10 years at 10% is the same as growing at 10% simple for 15.937 years. You get an extra 5.937 years of simple 10% return after 10 years versus only 0.641 years additional at 4 years. 

Put another way, by increasing your time invested by 150%, you increased your total return by 343%. 

And as you continue, the gap itself between a longer and shorter investment period itself compounds and at a rate that is counterintuitively large. 


So how do you do compounding in your head if you don't have Pascal's Triangle? 

One way is to memorize the doubling time associated with a given rate of return. For 10%, that time is about 7.2 years, something you can calculate in your head using the Rule of 72: 


  Doubling time in years = 72 ÷ % growth rate per year 


Note that for 10%, you don't divide 72 by 0.1 but 10. 

7.2% is particularly convenient because it has a doubling time of 72 ÷ 7.2 or 10 years. And, to make life particularly easy, 7.2% is the long-term after-inflation total return of the United States stock market over the very long run. So take whatever you have invested in stocks today and, if you leave it alone and don't tinker, in 10 years, you should have doubled your purchasing power. Note that the dollar amount will be even greater but when you take inflation's growth over that decade, its spending power would have doubled. 

Most of us invest over our working lifetimes - regular dollar amounts each year. Every $1 a year invested at 7.2% a year will give you a portfolio worth $14 in a decade. 

This is because the first $1 doubles and the last dollar invested - the one invested in year 9 - grows only to $1.072 (7.2%×1 year). Every dollar in years 2 through 9 grows somewhere in between these extremes.  The average dollar grows 40%, as it turns out. 

This allows you to do the most difficult compounding problem in your head - how much must you invest each year to have a portfolio with $1 million of spending power in today's dollars? 

You simply make a table for each decade, starting with the simplest amount, $1 invested each year. 

Years 1-10:  $1 a year grows to $14.         

Years 11-20:  $14 at the start of decade doubles to $28. 

                   $1 a year adds another $14 for a total of $42 

Years 21-30: $42 doubles to $84. 

                   $1 a year adds another $14 for a total of $96 

Years 31-40: $96 doubles to $192. 

                   $1 a year adds another $14 for a total of $206. 


Phew! If you don't want to work this out each time, you could just remember the amounts you will have at the end of each decade: 

  10 years    $14 

  20 years    $42

  30 years    $96 

  40 years  $206


Notice something about this series: like all compounding values, its growth per decade in dollars seems to accelerate from +$14 to +$28 to +$54 to +$110 the final decade. The doubling of the portfolio swamps the effect of the amount added each decade, an effect that you may have experienced later as retirement approaches and you feel less motivated to keep making contributions since they have a shrinking impact on a portfolio much larger than when you started. 

Someone who starts such a systematic plan at age 21 would have $206 in today's money in at age 61 for every dollar invested each year. 

So, to answer the question of how much is needed to have $1 million, its a matter of simply scaling that $206 to get $1 million: 


If $1 per year compounds to $206 in 40 then 

   $x per year compounds to $1 million... 


 $1m / x = 206 / 1 

 x = $1m / 206 =  $4,854, rounding off 


So, if you invest $4,854 each year in your 401-k or IRA and get 7.2% a year on average for the next 40 years, you will have $1 million of today's purchasing power. 

That's just $186.69 per paycheck if you get paid every 2 weeks* or just $13.34 a day. 

And, to periodically check if you're on target, you can crunch the numbers in your head! 



* Actually, a little less. The $14 per decade assumes that you make the entire contribution in one lump sum each year.  You must invest  less per year if you spread your contributions out over the year, something especially true if you are investing into a mutual fund or ETF whose value fluctuates frequently. 

Saturday, December 30, 2023

Fact-checking "SO YOU THINK YOU KNOW EVERYTHING?" List of Facts

SO YOU THINK YOU KNOW EVERYTHING?
A friend on Facebook posted a list of interesting facts with the admission that "I haven't fact checked these but for those of you wanting to spend the holiday time doing something" which I took as a challenge...

Challenge accepted! What follows is a list of each claim, its truthiness rating, a brief discussion and - in most cases - a credible-appearing online source.

A dime has 118 ridges around the edge. TRUE: yacenter.org

A cat has 32 muscles in each ear. TRUE: source

A crocodile cannot stick out its tongue. TRUE: dawn.com

A dragonfly has a life span of 24 hours.

FALSE: "How long do Dragonflies live? Is it true that they only live for one day? ... No insect has a lifespan of only one day – even mayflies (not closely related to dragonflies) live for several months underwater as larvae before emerging as winged adults. Adult mayflies may only live for a day or so as they are dedicated 'breeding machines'. They cannot feed as adults as most species don’t have any functional mouthparts." - British Dragonflies.org

A goldfish has a memory span of three seconds. FALSE: https://www.livescience.com/goldfish-memory.html....

A "jiffy" is an actual unit of time for 1/100th of a second.

TRUE: https://en.wikipedia.org/wiki/Jiffy_(time)....

A shark is the only fish that can blink with both eyes.

NOT SURE: no fish blinks in the way we do but sharks have protective membranes that can cover their eyes when attacking prey. https://brainly.in/question/25827598....

A snail can sleep for three years.

TRUE: https://naplab.com/guides/how-long-do-snails-sleep/....

Al Capone's business card said he was a used furniture dealer.

TRUE (or certainly repeated often across multiple websites): factsbee

All 50 states are listed across the top of the Lincoln Memorial on the back of the $5 bill.

FALSE: Only 26 states are listed on the $5 bill. "When the Lincoln Memorial was constructed the names of 48 states were engraved on it. The picture of the Lincoln Memorial on the $5 bill only contains the names of 26 states. These are the 26 states that can be seen on the front side of the Lincoln memorial which is what is pictured on the $5 bill." - https://en.wikipedia.org/wiki/United_States_five-dollar_bill

Almonds are a member of the peach family.

FALSE: "A nut is defined (among other things) as being the seed of a fruit. The almond is frequently, but incorrectly, said to be a member of the peach family. The almond is not a member of the peach family, but rather it is a member of the Rosaceae (Rose) family. The peach also is a member of the Rosaceae (Rose) family." - Quora

They belong to the same genus, however: https://www.isaaa.org/.../cropbiot.../article/default.asp....

An ostrich's eye is bigger than its brain.

TRUE: https://homework.study.com/.../is-an-ostrich-s-eye-bigger...

Babies are born without kneecaps. They don't appear until the child reaches 2 to 6 years of age.

TRUE: https://www.encyclopedia.com/.../is-it-true-that-babies.../

Butterflies taste with their feet.

TRUE: https://www.floridamuseum.ufl.edu/.../butterfly.../....

Cats have over one hundred vocal sounds. Dogs only have about 10.

TRUE: https://www.annexvet.com/fun-facts-feline-companions/...

"Dreamt" is the only English word that ends in the letters "mt".

TRUISH: there are 5 words ending in mt but all of them are variations of the "dreamt" theme: outdreamt, daydreamt, redreamt, undreamt, and dreamt

- https://www.thefreedictionary.com/words-that-end-in-mt

February 1865 is the only month in recorded history not to have a full moon.

- FALSE on 2 counts: February 10, 1865, had a full moon and there are other months that had no full moon, including February 2018. -https://www.wral.com/story/4470081/

In the last 4,000 years, no new animals have been domesticated.

FALSE: the timeline of domesticated animals on this webpage shows many examples of domesticated animals more recently than 4 thousand years ago: https://www.visualcapitalist.com/the-domestication-of.../.

If the population of China walked past you, in single file, the line would never end because of the rate of reproduction.

TRUE: although I could only find repeats of this claim, it can be demonstrated mathematically. 1.43 billion people live in China as of 2023. If a line of people is shuffling forward at 2 miles per hour (a good clip for a line) with a distance of 1 foot between each person, then 1 person will pass you every second, 60 in 1 minute, and 3,600 every hour. It would take over 397,000 hours for the entire population of China to pass you, or 16,541 days, or 45 years.

So if there were no births or deaths among anyone in line, it would take 45 years for everyone in China alive today to walk past you.

But the population is growing at about 0.5% a year - some in line will die, others will drop out to have a baby then get back in line, but the line will grow by over 7 million a year. This adds 81 days to the length of the line when converted from people to time needed to count them. But remember that this is just one year. Because it takes 45 years to count those in line now, even if we ignore compounding and simply add 81 days every year, by the time we get to what would have been the end of the original line, we will have a line requiring 3,645 additional days to count (81 days per year × 45 years), or another decade, during which additional people would be born. Throw in compounding and your task of counting everyone would never end because the population would grow faster than you can count them all.

If you are an average American, in your whole life, you will spend an average of 6 months waiting at red lights.

TRUISH: AAA estimates 4.7 months for someone who commutes regularly from age 15 to 75. https://finance.yahoo.com/.../ll-spend-much-life-waiting...

It's impossible to sneeze with your eyes open.

FALSE: this seems based on the incorrect idea that if you sneeze with your eyes open, you will pop your eyeballs out of your head. You won't and you can easily train yourself to sneeze with your eyes open if you desire. There are other reasons to keep your eyes shut when sneezing but none involve popping eyeballs. - https://www.self.com/story/sneeze-eyes-open

Leonardo Da Vinci invented the scissors. FALSE: he may have improved the scissors but didn't invent them. https://homework.study.com/.../did-leonardo-da-vinci....

Maine is the only state whose name is just one syllable. TRUE: Maine is also the only state with a single state neighboring it and it produces 90% of all toothpicks.

https://www.visitmaine.net/maine-facts-trivia/....

No word in the English language rhymes with month, orange, silver, or purple. TRUE: "There are many words that have no rhyme in the English language. "Orange" is only the most famous. Other words that have no rhyme include: silver, purple, month, ninth, pint, wolf, opus, dangerous, marathon and discombobulated." - https://www.flocabulary.com/rhymeswithorange/....

Our eyes are always the same size from birth, but our nose and ears never stop growing. TRUE with a caveat: https://www.flushinghospital.org/.../truth-or-myth-our.../

Peanuts are one of the ingredients of dynamite. TRUISH: peanuts make glycerol, used in dynamite, but peanuts aren't essential to making dynamite. - https://www.irishtimes.com/.../peanuts-can-be-explosive....

Rubber bands last longer when refrigerated. TRUE: https://www.j-flex.com/why-do-rubber-bands-last.../....

"Stewardesses" is the longest word typed with only the left hand and "lollipop" with your right. TRUE: "'Stewardesses,' 'reverberated,' and 'lollipop' are the longest words that can be typed using only one hand on a keyboard. 'Skepticisms' is the longest word that alternates hands. The longest word that can be typed using the top row only is 'typewriter.'" - https://www.ocala.com/.../09/playing-with-words/31222392007/

The average person's left hand does 56% of the typing. TRUE: https://www.discovermagazine.com/tech.../the-curse-of-qwerty

The cruise liner, QE2, moves only six inches for each gallon of diesel that it burns.

FALSE: The QE2 at 20 knots, her average cruising speed, covered about 125 feet per gallon, which works out to an average 45 mpg fuel efficiency for each of the 1900 souls on board.

https://www.roblightbody.com/qe2-fuel-economy.html....

The microwave was invented after a researcher walked by a radar tube and a chocolate bar melted in his pocket. TRUE: his name was Percy Spencer and the year was 1945. https://invention.si.edu/.../431-percy-spencer-microwave....

The sentence: "The quick brown fox jumps over the lazy dog" uses every letter of the alphabet. TRUE: https://www.nycgovparks.org/.../quick-brown.../history....

The winter of 1932 was so cold that Niagara Falls froze completely solid. FALSE: it froze but not completely. Water always flowed. https://www.niagarafallshotels.com/.../does-niagara.../....

The words 'racecar,' 'kayak' and 'level' are the same whether they are read left to right or right to left (palindromes). TRUE: no source needed - can be verified through inspection, but here you go: https://rtac.org/Strange.html....

There are 293 ways to make change for a dollar. TRUE: https://maa.org/frank-morgans-math-chat-293-ways-to-make...

There are more chickens than people in the world. TRUE: 19 billion chickens outnumber us 3:1. That's not that surprising - people are large, complex organisms, apex predators thanks to technology and our huge brains and opposable thumbs. As a rule, apex predators are outnumbered by smaller organisms on which they feed, usually by many orders of magnitude, increasing as the organism in question shrinks in size. There are far more insects of just about any variety than there are people and the mass of all those insects is similarly larger. https://www.hgtv.com/.../13-fascinating-facts-about...

There are only four words in the English language which end in "dous": tremendous, horrendous, stupendous, and hazardous. FALSE: although this claim is repeated often on the Internet, a simple query of a Scrabble word finder disproves it by generating other examples:

palladous, uropodous, amadous, molybdous, apodous, decapodous, and vanadous.

- https://wordfind.com/ends-with/dous/

There are two words in the English language that have all five vowels in order: "abstemious" and "facetious." FALSE: there are actually 32 such words, according to a list given in Wikipedia. https://en.wiktionary.org/.../Category:English_words_that...

There's no Betty Rubble in the Flintstones Chewables Vitamins. FALSE: after a grassroots campaign, Betty Rubble was added in 1995. https://en.wikipedia.org/wiki/Flintstones_Chewable_Vitamins

Tigers have striped skin, not just striped fur. TRUE: https://www.nathab.com/blog/why-do-tigers-have-stripes/

TYPEWRITER is the longest word that can be made using the letters only on one row of the keyboard. FALSE: the solution using Python is quite interesting. At least 3 other words are longer: rupturewort, proprietory, and proterotype.. https://jasonstitt.com/longest-top-row-word-not-typewriter

Winston Churchill was born in a ladies' room during a dance.

FALSE: Winston Churchill himself dodged some rumors about his birth with the quip, "Although present on the occasion, I have no clear recollection of the events leading up to it." But Snopes concludes:

Winston's mother may have been attending a dance when she went into labor and delivered him in the palace where the dance was held, but he wasn't actually born until more than 24 hours later, long after the dance had ended and all the guests had departed. And the room where the birth took place wasn't a ladies' bathroom at all but ordinary living quarters temporarily pressed into service as a place to store coats, as can be seen in photographs of Blenheim Palace. The confusion may stem from the fact that 'cloakroom' is sometimes employed as a euphemism for 'lavatory' in the UK, but in this case 'cloakroom' was clearly used in its literal sense.

            https://www.snopes.com/fact.../winston-churchill-born-dance/

Women blink nearly twice as much as men. TRUE: "Spontaneous blink rate was significantly larger in women than in men (19 vs 11 blinks per minute)." - https://pubmed.ncbi.nlm.nih.gov/18565090/

Your stomach has to produce a new layer of mucus every two weeks; otherwise it will digest itself. TRUE but misleading: your stomach is essentially a bag of acid used to begin the process of breaking down food and killing any bacteria that came along for the ride. It produced a gallon of hydrochloric acid a day to accomplish this task. Yes, the mucus lining the stomach protects the epithelium from caustic burns from the acid but it isn't literally true that the stomach would digest itself if the mucus layer wasn't replenished. It could be damaged, even destroyed, but this isn't what most of us think of when someone says "digest itself." - https://biologydictionary.net/digestive-system-fun-facts/


You're welcome!


Friday, February 19, 2021

Medical School is Well Worth the Cost

Bottom Line Up Front: 

The financial benefits of a medical school education are far greater than the costs. 
$5.3 million: lifetime benefit of a medical degree. 
$255,000:  Medical school cost estimated from someone with $300,000 of total debt.
$20.78: extra lifetime income generated by every dollar invested in medical school education.
2078%: lifetime return on investment. 
9 to 1: medical school payoff if true cost were as high as a $510k. 

All estimates of the cost of education are greatly exaggerated because they ignore costs of living that everyone must pay whether a student or not. 
$54,880: private college sticker price per year.
$26,820: what the average family actually pays.
$13,700: the true cost of a year of private college above living expenses.

Taxes reduce but by no means eliminate the advantage of pursuing medical education. 

3.33x: how much more than a college graduate the average medical school graduate earns
6.6x:  how much more in federal taxes the medical school graduate will pay.
$3,592,516: 40-year marginal benefit after taxes of a medical education. 
$140.88: medical education return per dollar over 40 years 




The New York Times ran a depressing article profiling some of the 8% of medical school graduates who do not match with a residency training program. This forced gap year results from the failure of residency training programs to expand to accept an increasing number of medical school graduates.
Someone reading the article might walk away with the impression that this is a tragedy. Someone profiled in the article had amassed $300,000 of debt but didn't match. The tone of the article seemed to imply that she had made a colossal mistake.
As painful as her situation must be, as much as she must be disappointed, it is highly likely that she is more inconvenienced than ruined.  She can regroup, do something with this gap year that she didn't plan on, perhaps change the programs or even the specialty to which she applies (some are far more competitive than others).  Someone with an M.D. can do a wide range of jobs that pay decently while waiting.
$300,000 of debt sounds extraordinary. Even by today's standards, it is high - the average medical student graduates with almost $200,000 of debt, versus just below $30,000 for the average 4-year college graduate.  The additional debt medical school adds averages $170,000.
Behavioral finance makes clear that we are exquisitely sensitive to how numbers are presented. We are relatively oblivious to small daily expenditures - $9 a day at Starbucks, for example, but shocked when the number is annualized: $3,285.  If we paid for coffee the way we pay for college and medical school, in one massive 8-year total, that $9 a day would translate to $26,280!  And that's just coffee!
Although we should work to reduce the total cost of education, especially in service professions such as medicine from which all of society benefits, my fear is that someone considering medicine might be frightened away by this high initial lump sum cost.
And that would be a mistake since it presents 8 years of costs disconnected from a lifetime of massive benefits, financial and nonmonetary.
Medical school is an investment and like any investment can be evaluated by analyzing expenses versus income.  A physician working full-time will earn $300k easily in 1.5 years, so this is the first way to view $300k: an investment that pays for itself every 8 months. Few investments offer that sort of return.
Another way is to divide lifetime earnings by startup investment. A resident graduating at 30 has earned a good chunk of the initial cost already if paid $60,000 per year [1] x 4 years = $240k.  The median physician income was $206,500 in 2019 [2]  Half made more, half made less, but the range is much tighter than in other professions.
Let's round off to $200,000 per year.  A medical school graduate who completes training and works until age 70 will work 40 years, earning $8 million.  Add in the $240,000 earned during training and you get a total of $8.240 million.
Divide 8.240 million by 300k and you get 27.5, meaning a medical student who accumulated $300k of debt can expect to generate over 27 times this amount in her lifetime.
Put another way: the cost of medical education is only 3.6% of the eventual payoff.
These calculations ignore many variables.  Most notably, debt is not the full cost of education, only the portion that had to be financed. But even doubling cost estimates to twice net debt gives a business startup cost of about 7%. Not bad at all.
The next simplification is that 100% of income is attributed to medical training. Obviously, the 99% of Americans who aren't physicians earn something; a fair analysis would subtract this something from what a physician earns to generate marginal income, the additional amount someone who paid for college and medical school earns over someone who paid for neither.
The average (median) high school graduate earns $30k.
The median college graduate earns just below $60k.
So a $200k per year income for a physician should subtract $30k as the median expected income if they didn't spend $300k for college and medical school to get $170k per year as the additional annual income payoff from a college and medical school education. 
We could try to isolate the cost and payoff of medical school alone by comparing physician earnings with college graduate earnings. Since the average college graduate starts out with $30k of debt and the average medical school graduate has almost $200k, let's apply this relative proportion to someone with $300k of total debt to determine what proportion is from medical school. If  $200k total debt for a medical school graduate minus $30k debt for a college graduate implies that medical school adds another $170k debt on average.  This means that the proportion of total debt represented by medical school is $170k / $200k or 85%.  85% of $300k is $255k, giving us a refined cost-benefit analysis:

Lifetime expected physician earnings: $8.240 million.

Lifetime expected earnings of a college graduate who starts work at age 21 and works until age 70:  49 years x $60k per year = $2.94 million. [3]

Marginal income attributable to medical degree: 

  $8.240 million physician earnings

- $2.94 million

= $5.3 million.

The lifetime benefit of a medical degree is therefore $5.3 million, the additional amount you would earn with an MD versus with only a college degree.

Medical school cost: $255k

Would you buy a business for $255k expected to make you $5.3 million over your lifetime?  That depends, of course, on what other options are available, but medical school seems a great one.

Every dollar invested in medical school returns $20.78 of extra lifetime income, an 2078% return on investment. By contrast, every dollar invested in the stock market over the same period will grow to $16 [4] - and the stock market is a great investment!

As a percentage of total return on investment, $255k represents only 4.8%. Even doubling the debt to get a $510k true cost estimate gives you an investment that pays off 9 to 1. Few things in life do that.

Often ignored when computing mind-blowing educational costs is the fact that much of the cost of education involves expenses everyone must pay whether in school or not.  Using College Board data, a year at a private college with an average sticker price of $54,880 for which the average family ends up paying $26,820 includes an average of $13,120 of room and board, also known as food and shelter.  College might be the only time when your total cost of rent, utilities, and food averages only $1,000 a month.  Back those expenses out and the true cost of education - even at a private college - is only $13,700.[5]

To illustrate, imagine that you graduate from college and can choose between taking a job paying $50,000 a year or spending a year at graduate or medical school.  It is probable that the worker must pay twice as much for rent, utilities, and food: $2,000 x 12 = $24,000.  The employee also faces a tax bill of $10,492 ($4,295 federal, $3,825 FICA, $2,372 state)[6]; the student pays no taxes.  At the end of the year, the worker's total starting costs before entertainment, vacation, or other luxuries, is $34,492.
This is actually greater than the TOTAL $26,820 the average college student pays for living expenses AND college tuition.  At the end of a year, the worker has $15,508 net after the basic cost of living and taxes.
The student has a year of education under her belt and only paid $13,700 net ($26,820 average minus $13,120 room and board) for that real asset (economists consider education a real asset no different than a home or car). 
Even including a year of lost income, after taxes and the higher living expenses living off-campus, the true cost of a year of education is $29,208.

The bottom line is that there is no cost-free option. To live costs money. None of us has a "burn rate" of zero.  We should only consider the amount education costs BEYOND this baseline cost of living.

 

Taxes and Death
Taxes lower the relative benefit of a medical degree but by no means eliminate it.  Because our tax code is progressive, meaning each marginal dollar is taxed at a higher rate, a worker making less money will keep a higher proportion of gross earnings.  A physician earning 3.33 times the average college graduate will pay 6.6 times as much in federal taxes and 4 times as much in state (Georgia) taxes. [8]  However, since no tax rate is 100%, you are always better off after taxes earning more than less.

Let's apply taxes to the $5 million that a physician will gross on average over a 40-year work life.
A $200,000 income in 2021 generates $63,936.60 in total taxes ($40,811 in federal taxes, $11,753.60 in FICA, and $11,372 in Georgia state taxes), for an after-tax income of $136,063.40.  
Someone earning $60,000 pays $13,749.50 in total taxes ($6,187.50 federal, $2,972 state (Georgia), and $4,590 FICA) for a net income of $46,250.50.
The physician pays 32% of income in total taxes, including FICA; the worker earning $60,000 pays 23%.  The result of this 39% greater proportional tax bite for physicians is a reduction of the higher income advantage: when taxes are taken into account, the annual benefit of a medical education drops over a third from $140,000 gross to $89,812 net.

But this still works out to a 40-year marginal benefit of $3,592,516 for that medical education that cost $255,000, a return of $140.88 for every $1 invested.  [7]

 

Medicine Offers So Much More than Financial Compensation
Of course, we should not choose a career based on money alone. A career in medicine offers enormous additional benefits that are difficult to monetize.

Your work is far more likely to be perceived as meaningful and societally useful both by you and others. This can sustain you through difficult days.

A medical degree opens all sorts of doors to interesting work unavailable to others.

You work closely with human beings and form powerful relationships. You see people get better. Many will thank you.  That feels good.

You never have to explain what you do for a living or why you want to do it. Although this is a weak reason, it's still a positive.  
You learn about and deal with the most fascinating machine out there, one all of us have a selfish interest in: the human body.  Everyone has a body and everyone wants to be healthy.

You help make the world a little better place. Even if you don't always succeed, you are on the side of those who are suffering. You know that you are not causing more suffering than you are alleviating.

You get the awesome privilege of being invited to the most sacred of spaces: births, deaths, and everything in between.

Your work might be difficult but rarely boring.

You realize early on that nothing cures or even ameliorates the common cold.

You can follow healthcare news and help your friends and family know that almost all fantastic medical claims and fads are nonsense.

You will find out how surprisingly heavy a human arm is.

You will get very comfortable with the elderly, the morbidly obese, and those suffering terrible addictions, trying to smoke through a trach tube.

Secretions, gurgling liquid noises, pus, blood, and smells won't bother you much. You will learn how to stick a needle in just about every body cavity and part.  You will become adept at drawing blood, starting an IV, and getting an arterial blood gas.

You will resuscitate someone who has stopped breathing or whose heart has stopped.

You will learn how to have some of life's most difficult conversations.

You will never get used to dying children. But you will also see how resilient and healthy most kids are.

You will always wear your seat belt and never smoke.

You will be surrounded by colleagues who are bright and motivated to help others.  You might even marry one (I did)!

You will meet people from all walks of life, strangers you never would have met, who will open up to you because they trust you, sharing with you the most intimate details of their lives. This will give you an insight into the human condition and how people live that few jobs will. It is no coincidence that so many great writers were physicians (Arthur Conan Doyle, Chekhov, Somerset Maugham, Walker Percy, even Michael Creighton).

You will learn and apply basic rules of logic, inference, and probability in real-time to make calls with limited information. By doing so repeatedly, you will be both humbler and more aware of the limitations of human knowledge. You will learn to avoid snap judgments and sidestep cognitive pitfalls.

You will approach and lay hands on conditions that fill others with dread and be with people whose personal choices might be killing them yet learn to suspend judgment and help them change their trajectory.

You will approach the end of your career knowing that you did some good. Not everyone can say that (honestly) about their work. This isn't a criticism of others but a recognition that most jobs are soul-crushing and most people lead lives of quiet desperation, as Thoreau so eloquently put it.

In the end, you pay so little and are paid so much for such priceless experiences.

 

 

[1] https://www.glassdoor.com/Salaries/medical-resident-salary-SRCH_KO0,16.htm $62,297 is the national residency average pay.
[2] https://money.usnews.com/careers/best-jobs/physician/salary

[3] 49x = 50x - x, so 49 x 60k = 50 x 60k - 60k = 3 million- 60k = 2.940 million

[4] using 7.2% per year after inflation total return from the stock market, close to the long-term average per Jeremy Siegal using 250 years of data presented in his book, Stocks for the Long Run.  7.2% is a convenient number since it doubles an investment every decade.  A 40-year investment therefore grows at by 24 or 16x.

[5] https://www.collegedata.com/resources/pay-your-way/whats-the-price-tag-for-a-college-education  According to the College Board, the average private college has a sticker price of $54,880 on average; in-state public colleges cost less than half that: $26,820.  Although few pay this sticker price, tuition and fees average $37,650 for a private college to $10,560 for an in-state public college.  The rest - between 40-65% - are essentially the costs of living, especially food and shelter.  Average room and board ranges from $11,620 to $13,120 for public versus private colleges, which means that a hungry 18-year-old can be sheltered and fed for only $1,000 a month, a deal she is unlikely to find beyond a college campus.  This discounting of food and housing offsets somewhat the ever-rising cost of tuition, but the net effect is to overstate the cost of a year of college.

[6] https://www.taxformcalculator.com/state-tax/georgia.html   Assumptions: single, no deductions or dependents, Georgia state resident.
[7] https://www.taxformcalculator.com/state-tax/georgia.html  This assumes that the physical files as a single payer without any deductions at all, a highly unlikely scenario.  It also treats FICA withholding as a cost which is only true in the short term. Social security deductions from your paycheck are used to calculate your benefits upon retirement - the more you contribute, the more you will receive.  Social security "taxes" really should be viewed as compulsory retirement contributions to a plan that offers a modest positive return as well as disability insurance and a lifetime pension that increases each year with inflation.  One's actual return can vary greatly depending on how long you work, how early you start withdrawing, and how long you live beyond that, but even for high income taxpayers who have other private savings, social security income in retirement is not insignificant.  For simplicity, I treated it as a cost, which it is on a short-term (before ages 65-70.5), cash flow basis. 
[8] One advantage of a higher income is that social security withholding cuts off after $142,800 (in 2021), meaning that $57,200 is not subject to FICA.  The net result is that the TOTAL tax bite of the higher earner is brought down to 4.65 times that of the lower earner; however, social security probably should not be considered a tax (see previous end note).

 

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