Interest in 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 $1.00×1.5² = $2.25. Compounding quarterly yields $1.00×1.254 = $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.
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Famous quotes containing the words interest in, interest and/or mathematics:
“I am pleased to think of Channing as an inhabitant of the gray town. Seven cities contended for Homer dead. Tell him to remain at least long enough to establish Concord’s right and interest in him.”
—Henry David Thoreau (1817–1862)
“Consider the difference between looking and staring. A look is voluntary; it is also mobile, rising and falling in intensity as its foci of interest are taken up and then exhausted. A stare has, essentially, the character of a compulsion; it is steady, unmodulated, “fixed.””
—Susan Sontag (b. 1933)
“... though mathematics may teach a man how to build a bridge, it is what the Scotch Universities call the humanities, that teach him to be civil and sweet-tempered.”
—Amelia E. Barr (1831–1919)