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.
Read more about this topic: Interest
Famous quotes containing the words interest in, interest and/or mathematics:
“Parents do not give up their children to strangers lightly. They wait in uncertain anticipation for an expression of awareness and interest in their children that is as genuine as their own. They are subject to ambivalent feelings of trust and competitiveness toward a teacher their child loves and to feelings of resentment and anger when their child suffers at her hands. They place high hopes in their children and struggle with themselves to cope with their children’s failures.”
—Dorothy H. Cohen (20th century)
“Science is feasible when the variables are few and can be enumerated; when their combinations are distinct and clear. We are tending toward the condition of science and aspiring to do it. The artist works out his own formulas; the interest of science lies in the art of making science.”
—Paul Valéry (1871–1945)
“I must study politics and war that my sons may have liberty to study mathematics and philosophy.”
—John Adams (1735–1826)