Editing 2768: Definition of e

{{comic
| number    = 2768
| date      = April 26, 2023
| title     = Definition of e
| image     = definition_of_e_2x.png
| imagesize = 571x186px
| noexpand  = true
| titletext = Yeah, my math teacher back in high school set up the system to try to teach us something or other, but the 100% rate was unbelievably good, so I engineered a hostile takeover of his bank and now use it to make extra cash on the side.
}}

==Explanation==
{{incomplete|Created by 2.718 BANKERS - Please change this comment when editing this page. Do NOT delete this tag too soon.}}
The mathematical constant ''{{w|e (mathematical constant)|e}}'' (also known as Euler's constant) is typically demonstrated in terms of compound interest. Here, Miss Lenhart seems to be setting up such an example, but is actually asking her student to deposit money.

The constant ''e'' can be described {{w|E (mathematical constant)#Compound interest|in the context of compound interest}}. For a bank account that pays interest at a rate of 100% per year, and that interest is paid ''n'' times a year and compounded, then a $1 deposit will grow to $1 * (1 + 100%/n)^n after a year. As ''n'' approaches infinity (continuous compounding), the amount approaches ''e''  dollars. In the comic, minutely compounding is used as an approximation of continuous compounding; here ''n'' = 365 * 24 * 60 = 525,600, and the resulting amount would be $2.718279.

As such, one would expect Miss Lenhart to say in panel 4 something like "you'll have ''e'' dollars". But it turns out she's just charging $1 for answering the question of what ''e'' is. The supposed interest rate the teacher can earn off this deposit is so high that the $1 principal will grow to over $22,000 in ten years, $485 million in twenty years, or $10.6 trillion in thirty years.

In the title text, a {{w|Takeover#Hostile|hostile takeover}} is an acquisition of a company against its management's wishes, by simply buying up its shares from its shareholders. A bank offering accounts with an {{w|APY}} of 172% is certain to go bankrupt almost immediately, making it a very bad investment. Banks earn money by lending at a higher rate than they pay on deposits, but it is illegal to charge such high interest rates on loans, and no one would take them anyway. Therefore the bank will lose huge amounts of money on deposits while earning essentially no revenue. The speaker is effectively buying out the bank in order to drain it of its own funds, which is both illegal and financially pointless. Alternatively, their plan may be to buy 51% of the stock, then attempt to extract a majority of the bank's reserve funds through huge high-interest deposits, which is still not profitable, since banks hold only a small fraction of deposits in reserve, and their market capitalizations (the cost of buying all the stock) are much higher than their total reserves. Even if for some reason this bank had a very high reserve ratio, and this tactic could somehow be profitable, it would still be illegal, effectively robbing the other 49% ownership of its equity through deliberately bad management.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[Hairy is seated at a classroom desk, with Miss Lenhart standing in front of him, and a chalkboard behind her.]
:Hairy: Can you explain what the constant ''e'' actually ''means''?
:Miss Lenhart: Sure.

:Miss Lenhart: I have a bank account that pays 100% annual interest, compounded every minute.

:Miss Lenhart: If you deposit $1 now,

:Miss Lenhart: I will answer your question.

[[Category:Comics featuring Hairy]]
[[Category:Comics featuring Miss Lenhart]]
[[Category:Math]]

{{comic discussion}}