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Definition of e

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

In this comic the teacher Miss Lenhart is asked by the student Hairy to explain what the constant e actually means.

The 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 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". 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 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.[citation needed]

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.