*Senior 3 lessons in "Compound Interest" * Bernoulli discovered the constant e<http://en.wikipedia.org/wiki/E_%28mathematical_constant%29>by studying a question about compound interest <http://en.wikipedia.org/wiki/Compound_interest> which required him to find the value of the following expression (which is in fact *e*): [image: \lim_{n\to\infty} \left( 1 + \frac{1}{n} \right)^n]
One example is an account that starts with $1.00 and pays 100 percent interest per year. If the interest is credited once, 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 compounding monthly yields $1.00×(1.0833...)12 = $2.613035.... Bernoulli noticed that this sequence approaches a limit (the force of interest <http://en.wikipedia.org/wiki/Compound_interest#Force_of_interest>) for more and smaller compounding intervals. Compounding weekly yields $2.692597..., while compounding daily yields $2.714567..., just two cents more. Using n as the number of compounding intervals, with interest of 100%/ n in each interval, the limit for large n is the number that came to be known as *e*; with *continuous* compounding, the account value will reach $2.7182818.... More generally, an account that starts at $1, and yields (1+R) dollars at simple interest<http://en.wikipedia.org/wiki/Interest#Simple_interest>, will yield *e*R dollars with continuous compounding.
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