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:
“You will think me very pedantic, gentlemen, but holiday though it may be, I have not the smallest interest in any holiday, except as it celebrates real and not pretended joys.”
—Ralph Waldo Emerson (1803–1882)
“Governments which have a regard to the common interest are constituted in accordance with strict principles of justice, and are therefore true forms; but those which regard only the interest of the rulers are all defective and perverted forms, for they are despotic, whereas a state is a community of freemen.”
—Aristotle (384–322 B.C.)
“I must study politics and war that my sons may have liberty to study mathematics and philosophy.”
—John Adams (1735–1826)