Question

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

Answer 1

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

`A=Pe^(rt)`

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

`A=P(1+(r)/(m))^(t)`

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.