information:filtering, structural:summarization, structural:reformatting
In the history of mathematics

It is thought that Jacob Bernoulli discovered the mathematical constant e by studying a question about compound interest. He realized that if an account that starts with $1.00 and pays say 100% interest per year, at the end of the year, the value is $2.00; but if the interest is computed and added twice in the year, the $1 is multiplied by 1.5 twice, yielding $1.00 × 1.5 = $2.25. Compounding quarterly yields $1.00 × 1.25 = $2.4414..., and so on.

Bernoulli noticed that if the frequency of compounding is increased without limit, this sequence can be modeled as follows:

where n is the number of times the interest is to be compounded in a year.