Question

what's the main difference between continuous compounding and exponential growth, and why does my text book say that it is better to express growth rates as if they are continuously compounded? What's the advantage---both give outrageous estimates to "what if" scenarios. ...?

Answer 1

The big advantage to using continuous compounding to express growth rates is it avoids the problem of asymmetry in growth rates:

For example, if we use the normal definition and $100 grows to $105 in one time period, that's a growth rate of $105/$100 - 1 = 5% But if $105 decreases to $100, that's a growth rate of $100/$105 - 1 = -4.76%

The problem of asymmetry is those two growth rates, 5% and -4.75% are not equal up to a sign.

But if you use continuous compounding the growth rate in the first case is ln(105/100) = 0.04879.
And the growth rate in the second is ln (100/105) = -0.04879.
Those two growth rates are definitely the negative of each other.