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:
“Just as the French of the nineteenth century invested their surplus capital in a railway-system in the belief that they would make money by it in this life, in the thirteenth they trusted their money to the Queen of Heaven because of their belief in her power to repay it with interest in the life to come.”
—Henry Brooks Adams (1838–1918)
“The prairies were dust. Day after day, summer after summer, the scorching winds blew the dust and the sun was brassy in a yellow sky. Crop after crop failed. Again and again the barren land must be mortgaged for taxes and food and next year’s seed. The agony of hope ended when there was not harvest and no more credit, no money to pay interest and taxes; the banker took the land. Then the bank failed.”
—Rose Wilder Lane (1886–1968)
“In mathematics he was greater
Than Tycho Brahe, or Erra Pater:
For he, by geometric scale,
Could take the size of pots of ale;
Resolve, by sines and tangents straight,
If bread and butter wanted weight;
And wisely tell what hour o’ th’ day
The clock doth strike, by algebra.”
—Samuel Butler (1612–1680)