Question 207170
<font face="Garamond" size="+2">


The formula for continuous compounding is *[tex \Large A = Pe^{rt}]


where *[tex \Large A] is the balance on *[tex \Large P] dollars invested for *[tex \Large t] years at *[tex \Large r] rate of interest (expressed as a decimal) and *[tex \Large e] is the base of the natural logarithms (approx. 2.718), so for your first problem:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A = 2000\ \cdot\ e^{0.06(1)}]


Get out your calculator.  As a check on your work, 2000 at 6% simple interest would have a $2120 balance after a year.  Continuous compounding is going to be larger, but not by a whole lot -- certainly less than $2125.  For the second problem, substitute 2 in the place of the 1 in the exponent on *[tex \Large e].  Your answer should be somewhere between $2247 and $2255.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
</font>