"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! 

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.