2768: Definition of e - Revision history

172.71.31.104: too wordy originally

2024-10-11T13:47:39Z

too wordy originally

172.69.79.139: /* Explanation */

2024-10-02T08:23:56Z

‎Explanation

172.70.42.129: /* Explanation */

2024-08-26T06:04:37Z

‎Explanation

Jkshapiro: /* Explanation */ Simplify the explanation of the title text. It was getting pretty overgrown.

2024-04-10T02:26:53Z

‎Explanation: Simplify the explanation of the title text. It was getting pretty overgrown.

Peregrine: Doesn't look like a plain fist to me; definitely one or more digits raised. Context suggests it's a single finger to signify "one".

2024-02-25T15:04:22Z

Doesn't look like a plain fist to me; definitely one or more digits raised. Context suggests it's a single finger to signify "one".

162.158.158.125: /* Explanation */ Deleted paragraph about illegally high interest rates and payday loan companies, which seems to have confused banks crediting interest to their depositors and lenders charging interest to their borrowers.

2023-12-28T22:38:17Z

‎Explanation: Deleted paragraph about illegally high interest rates and payday loan companies, which seems to have confused banks crediting interest to their depositors and lenders charging interest to their borrowers.

162.158.187.66 at 03:47, 16 October 2023

2023-10-16T03:47:05Z

Xurkitree10: /* Explanation */

2023-07-22T09:50:16Z

‎Explanation

172.69.34.132: /* Explanation */ payday loans

2023-05-20T23:14:10Z

‎Explanation: payday loans

172.69.162.142: /* Explanation */ -americanisms

2023-05-08T04:04:01Z

‎Explanation: -americanisms

@@ Line 16: / Line 16: @@
 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 (527,040 for leap years with 366 days), and the resulting amount would be $2.7182792…, less than one part per million different from that of a straight multiplication by ''e'' (which is 2.7182818…).
-As such, one would expect Miss Lenhart to say in the last panel something like "you'll have ''e'' dollars in a year". It is not clear if Miss Lenhart sees the growth of the deposited amount as answer enough to explain ''e'' or if she's just charging $1 for answering the question of what ''e'' is. The supposed interest rate the teacher can earn off this deposit, alone, is so high that the $1 principal will grow to over $22,000 in ten years, $485 million in twenty years, or $10.68 trillion in thirty years.
+As such, one would expect Miss Lenhart to say in the last panel something like "you'll have ''e'' dollars in a year". The joke here is that she instead uses the normal beginning phrase ("If you have $1...") and turns it into a charge to answer the question ("I will answer your question.")
 In the title text, Randall remembers that his high school teacher, like Miss Lenhart in the comic, had a bank account that paid 100% annual interest. This is an extremely high rate, and a bank that is able to offer it must have a very lucrative source of revenue. Therefore, he bought the bank, via a {{w|Takeover#Hostile|hostile takeover}}, in order to gain direct access to that source, and now uses it as a source of supplementary income. It is unlikely that this story is true.{{cn}}

@@ Line 18: / Line 18: @@
 As such, one would expect Miss Lenhart to say in the last panel something like "you'll have ''e'' dollars in a year". It is not clear if Miss Lenhart sees the growth of the deposited amount as answer enough to explain ''e'' or if she's just charging $1 for answering the question of what ''e'' is. The supposed interest rate the teacher can earn off this deposit, alone, is so high that the $1 principal will grow to over $22,000 in ten years, $485 million in twenty years, or $10.68 trillion in thirty years.
-In the title text, Randall remembers that his high school teacher, like Miss Lenhart in the comic, had a bank account that paid 100% annual interest. This is an extremely high rate, and a bank that is able to offer it must have a very lucrative source of revenue. Therefore, he bought the bank, via a {{w|Takeover#Hostile|hostile takeover}}, in order to gain direct access to that source, and now uses it as a source of supplementary income. It is unlikely that this story is true.
+In the title text, Randall remembers that his high school teacher, like Miss Lenhart in the comic, had a bank account that paid 100% annual interest. This is an extremely high rate, and a bank that is able to offer it must have a very lucrative source of revenue. Therefore, he bought the bank, via a {{w|Takeover#Hostile|hostile takeover}}, in order to gain direct access to that source, and now uses it as a source of supplementary income. It is unlikely that this story is true.{{cn}}
 It is also plausible that the title text is Miss Lenhart explaining how she acquired the bank to set up her account there, and that she regularly charges people $1 for trivial services, such as explaining concepts to her students.

← Older revision		Revision as of 06:04, 26 August 2024
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	In the title text, Randall remembers that his high school teacher, like Miss Lenhart in the comic, had a bank account that paid 100% annual interest. This is an extremely high rate, and a bank that is able to offer it must have a very lucrative source of revenue. Therefore, he bought the bank, via a {{w\|Takeover#Hostile\|hostile takeover}}, in order to gain direct access to that source, and now uses it as a source of supplementary income. It is unlikely that this story is true.		In the title text, Randall remembers that his high school teacher, like Miss Lenhart in the comic, had a bank account that paid 100% annual interest. This is an extremely high rate, and a bank that is able to offer it must have a very lucrative source of revenue. Therefore, he bought the bank, via a {{w\|Takeover#Hostile\|hostile takeover}}, in order to gain direct access to that source, and now uses it as a source of supplementary income. It is unlikely that this story is true.
		+
		+	It is also plausible that the title text is Miss Lenhart explaining how she acquired the bank to set up her account there, and that she regularly charges people $1 for trivial services, such as explaining concepts to her students.

	==Transcript==		==Transcript==

@@ Line 18: / Line 18: @@
 As such, one would expect Miss Lenhart to say in the last panel something like "you'll have ''e'' dollars in a year". It is not clear if Miss Lenhart sees the growth of the deposited amount as answer enough to explain ''e'' or if she's just charging $1 for answering the question of what ''e'' is. The supposed interest rate the teacher can earn off this deposit, alone, is so high that the $1 principal will grow to over $22,000 in ten years, $485 million in twenty years, or $10.68 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 in some jurisdictions 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 off-comic speaker is effectively buying out the bank in order to drain it of its own funds, which is financially pointless, and may also be illegal. 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 usually still be illegal, effectively robbing the other 49% ownership of its equity through deliberately bad management.
+In the title text, Randall remembers that his high school teacher, like Miss Lenhart in the comic, had a bank account that paid 100% annual interest. This is an extremely high rate, and a bank that is able to offer it must have a very lucrative source of revenue. Therefore, he bought the bank, via a {{w|Takeover#Hostile|hostile takeover}}, in order to gain direct access to that source, and now uses it as a source of supplementary income. It is unlikely that this story is true.
 ==Transcript==

@@ Line 35: / Line 35: @@
 :Miss Lenhart: I have a bank account that pays 100% annual interest, compounded every minute.
-:[In a frame-less, and very slim panel, Miss Lenhart is shown holding a hand up in a fist.]
+:[In a frame-less, and very slim panel, Miss Lenhart is shown holding a hand up with one finger raised.]
 :Miss Lenhart: If you deposit $1 now,

← Older revision		Revision as of 22:38, 28 December 2023
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	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 in some jurisdictions 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 off-comic speaker is effectively buying out the bank in order to drain it of its own funds, which is financially pointless, and may also be illegal. 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 usually still be illegal, effectively robbing the other 49% ownership of its equity through deliberately bad management.		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 in some jurisdictions 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 off-comic speaker is effectively buying out the bank in order to drain it of its own funds, which is financially pointless, and may also be illegal. 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 usually still be illegal, effectively robbing the other 49% ownership of its equity through deliberately bad management.
−
−	In theory, a bank charging depositors such a high rate would be hugely profitable, but be illegal. However, payday loan companies have accomplished something similar by claiming to be charging fees, rather than interest.

	In the title text, Randall may have also just confused a couple of concepts. A bank offering a 100% rate (assuming somehow sustainably) would be an incredibly good place to open a checking or savings account, and a rational actor would shovel as much money as possible into such an account at this bank. Randall may have simply misused the term "hostile takeover," which would not yield any of the benefits of the 100% rate, as mentioned above, when he really meant to colloquially describe a scenario in which one would aggressively exploit the bank's 100% rate for one's own benefit. (A perhaps unintuitive aspect about banks that might have tripped up Randall is that "assets" in other contexts become liabilities for banks and vice versa. So customer deposits become liabilities upon which a bank would have to pay such an incredibly high rate, and loans, which are traditionally considered liabilities, are assets from which banks derive income.)		In the title text, Randall may have also just confused a couple of concepts. A bank offering a 100% rate (assuming somehow sustainably) would be an incredibly good place to open a checking or savings account, and a rational actor would shovel as much money as possible into such an account at this bank. Randall may have simply misused the term "hostile takeover," which would not yield any of the benefits of the 100% rate, as mentioned above, when he really meant to colloquially describe a scenario in which one would aggressively exploit the bank's 100% rate for one's own benefit. (A perhaps unintuitive aspect about banks that might have tripped up Randall is that "assets" in other contexts become liabilities for banks and vice versa. So customer deposits become liabilities upon which a bank would have to pay such an incredibly high rate, and loans, which are traditionally considered liabilities, are assets from which banks derive income.)

← Older revision		Revision as of 03:47, 16 October 2023
Line 23:		Line 23:

	In the title text, Randall may have also just confused a couple of concepts. A bank offering a 100% rate (assuming somehow sustainably) would be an incredibly good place to open a checking or savings account, and a rational actor would shovel as much money as possible into such an account at this bank. Randall may have simply misused the term "hostile takeover," which would not yield any of the benefits of the 100% rate, as mentioned above, when he really meant to colloquially describe a scenario in which one would aggressively exploit the bank's 100% rate for one's own benefit. (A perhaps unintuitive aspect about banks that might have tripped up Randall is that "assets" in other contexts become liabilities for banks and vice versa. So customer deposits become liabilities upon which a bank would have to pay such an incredibly high rate, and loans, which are traditionally considered liabilities, are assets from which banks derive income.)		In the title text, Randall may have also just confused a couple of concepts. A bank offering a 100% rate (assuming somehow sustainably) would be an incredibly good place to open a checking or savings account, and a rational actor would shovel as much money as possible into such an account at this bank. Randall may have simply misused the term "hostile takeover," which would not yield any of the benefits of the 100% rate, as mentioned above, when he really meant to colloquially describe a scenario in which one would aggressively exploit the bank's 100% rate for one's own benefit. (A perhaps unintuitive aspect about banks that might have tripped up Randall is that "assets" in other contexts become liabilities for banks and vice versa. So customer deposits become liabilities upon which a bank would have to pay such an incredibly high rate, and loans, which are traditionally considered liabilities, are assets from which banks derive income.)
		+
		+	In fact, Randall wasn't confused or tripped up in any way and didn't misuse anything - the title text was just a silly joke based on taking the idea of 100% interest and pretending you could somehow take over the bank and take advantage of this rate for yourself, and calling it a "hostile takeover" is a humorous exaggeration.
		+

	The teacher who inadvertently sparked this action, male, was clearly not Miss Lenhart, who may be better at providing more memorable (if somewhat non-standard) lessons. And, as the speaker cannot even recall what the point was of the original mathematical example, it is possible that they have insufficient understanding of the numbers involved and why their attempt to profit will turn out to be ultimately illusory. A similar lack of successful education in the subjects of business and/or law could also likely come back to bite them, sooner or later.		The teacher who inadvertently sparked this action, male, was clearly not Miss Lenhart, who may be better at providing more memorable (if somewhat non-standard) lessons. And, as the speaker cannot even recall what the point was of the original mathematical example, it is possible that they have insufficient understanding of the numbers involved and why their attempt to profit will turn out to be ultimately illusory. A similar lack of successful education in the subjects of business and/or law could also likely come back to bite them, sooner or later.

← Older revision		Revision as of 09:50, 22 July 2023
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	==Explanation==		==Explanation==
−	~~{{incomplete\|Created by 2.718 BANKERS - Please change this comment when editing this page. Do NOT delete this tag too soon.}}~~
	In this comic the teacher [[Miss Lenhart]] is asked by the student [[Hairy]] to explain what the constant ''e'' actually means.		In this comic the teacher [[Miss Lenhart]] is asked by the student [[Hairy]] to explain what the constant ''e'' actually means.

← Older revision		Revision as of 23:14, 20 May 2023
Line 20:		Line 20:

	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 in some jurisdictions 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 off-comic speaker is effectively buying out the bank in order to drain it of its own funds, which is financially pointless, and may also be illegal. 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 usually still be illegal, effectively robbing the other 49% ownership of its equity through deliberately bad management.		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 in some jurisdictions 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 off-comic speaker is effectively buying out the bank in order to drain it of its own funds, which is financially pointless, and may also be illegal. 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 usually still be illegal, effectively robbing the other 49% ownership of its equity through deliberately bad management.
		+
		+	In theory, a bank charging depositors such a high rate would be hugely profitable, but be illegal. However, payday loan companies have accomplished something similar by claiming to be charging fees, rather than interest.

	In the title text, Randall may have also just confused a couple of concepts. A bank offering a 100% rate (assuming somehow sustainably) would be an incredibly good place to open a checking or savings account, and a rational actor would shovel as much money as possible into such an account at this bank. Randall may have simply misused the term "hostile takeover," which would not yield any of the benefits of the 100% rate, as mentioned above, when he really meant to colloquially describe a scenario in which one would aggressively exploit the bank's 100% rate for one's own benefit. (A perhaps unintuitive aspect about banks that might have tripped up Randall is that "assets" in other contexts become liabilities for banks and vice versa. So customer deposits become liabilities upon which a bank would have to pay such an incredibly high rate, and loans, which are traditionally considered liabilities, are assets from which banks derive income.)		In the title text, Randall may have also just confused a couple of concepts. A bank offering a 100% rate (assuming somehow sustainably) would be an incredibly good place to open a checking or savings account, and a rational actor would shovel as much money as possible into such an account at this bank. Randall may have simply misused the term "hostile takeover," which would not yield any of the benefits of the 100% rate, as mentioned above, when he really meant to colloquially describe a scenario in which one would aggressively exploit the bank's 100% rate for one's own benefit. (A perhaps unintuitive aspect about banks that might have tripped up Randall is that "assets" in other contexts become liabilities for banks and vice versa. So customer deposits become liabilities upon which a bank would have to pay such an incredibly high rate, and loans, which are traditionally considered liabilities, are assets from which banks derive income.)

@@ Line 21: / Line 21: @@
 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 in some jurisdictions 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 off-comic speaker is effectively buying out the bank in order to drain it of its own funds, which is financially pointless, and may also be illegal. 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 usually still be illegal, effectively robbing the other 49% ownership of its equity through deliberately bad management.
-In the title text, Randall may have also just confused a couple concepts. A bank offering a 100% rate (assuming somehow sustainably) would be an incredibly good place to open a checking or savings account, and a rational actor would shovel as much money as possible into such an account at this bank. Randall may have simply misused the term "hostile takeover," which would not yield any of the benefits of the 100% rate, as mentioned above, when he really meant to colloquially describe a scenario in which one would aggressively exploit the bank's 100% rate for one's own benefit. (A perhaps unintuitive aspect about banks that might have tripped up Randall is that "assets" in other contexts become liabilities for banks and vice versa. So customer deposits become liabilities upon which a bank would have to pay such an incredibly high rate, and loans, which are traditionally considered liabilities, are assets from which banks derive income.)
+In the title text, Randall may have also just confused a couple of concepts. A bank offering a 100% rate (assuming somehow sustainably) would be an incredibly good place to open a checking or savings account, and a rational actor would shovel as much money as possible into such an account at this bank. Randall may have simply misused the term "hostile takeover," which would not yield any of the benefits of the 100% rate, as mentioned above, when he really meant to colloquially describe a scenario in which one would aggressively exploit the bank's 100% rate for one's own benefit. (A perhaps unintuitive aspect about banks that might have tripped up Randall is that "assets" in other contexts become liabilities for banks and vice versa. So customer deposits become liabilities upon which a bank would have to pay such an incredibly high rate, and loans, which are traditionally considered liabilities, are assets from which banks derive income.)
 The teacher who inadvertently sparked this action, male, was clearly not Miss Lenhart, who may be better at providing more memorable (if somewhat non-standard) lessons. And, as the speaker cannot even recall what the point was of the original mathematical example, it is possible that they have insufficient understanding of the numbers involved and why their attempt to profit will turn out to be ultimately illusory. A similar lack of successful education in the subjects of business and/or law could also likely come back to bite them, sooner or later.