Write a sentence or two to explain the difference between interest compounded continuously and interest compounded monthly.

Answer:Both type of compounded interest are different, they behave different and they are represents by different functions.A continuous compounding is modelled by the function [tex]A=Pe^{rt}[/tex]Which represents an exponential growth, which is the important thing about interest compounded continuously, you can see this as a not discrete compounding.On the other hand, an interest compounded monthly can be seen as a discrete compounding, which has a simple interest rate. This type of compounding interest is modelled by the function[tex]A=P(1+\frac{r}{m})^{t}[/tex]This interest has compound periods in a certain number of years, if it's monthly compound, that means there are 12 compound periods in one year. This characteristic is not presents in the first case.