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The mathematical constant ''{{w|e (mathematical constant)|e}}'' is known as Euler's number. It is typically demonstrated in terms of compound interest. Here, Miss Lenhart seems to be setting up such an example, but in a typical Lenhart style she is actually asking her student to give her money. | The mathematical constant ''{{w|e (mathematical constant)|e}}'' is known as Euler's number. It is typically demonstrated in terms of compound interest. Here, Miss Lenhart seems to be setting up such an example, but in a typical Lenhart style she is actually asking her student to give her 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% | + | 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, 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. | + | 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 $10.6 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. | ||
