MONTHLY:

 ----- Converting to LOGARITHMIC  form

She's WRONG, AGAIN!!
The RULE of 72 ALSO demonstrates that it should be about 4.5 years!


CONTINUOUSLY:

 ----- Converting to LOGARITHMIC (Natural) form


There it is!!! THAT'S ALL!! 
These people are writing complex "NOVELS," and still end up with a WRONG answer. Don't they know anything about mathematics? Most likely NOT! 
How can doubling take over 34.6 years, compounded MONTHLY - according to someone who doesn't seem to have a clue - but takes 4.33 years when compounded continuously?

2A = ,


where "n" is the number of months.


Divide by A both sides


2 = ,   or, equivalently


2 = .


Take log base 10 from both sides


log(2) = n*log(1.013333)


n =  = 52.3 months = 4 years and 5 months (rounded as required).    ANSWER