How long will it take for an investment that is earning 12.0% interest (compounded continuously) to double in value? (pt = p0ert)

Formula of continuous compounded interest is:

A=P.e^(rt), where A is the amount generated after t years, P is the principal amount you deposit at the bank, e=2.718 (constant), r= interest rate
and t the time in years
In short they are asking, at an interest rate of 12% (or 0.12), after how many years (t=?) A becomes 2P

2P=P.e^(0.12t)==> 2= e^(0.12t)

ln2 = (0.12t).lne or lne=1 & ln2  = 0.693 ==>0.693/0.12 =t & t=5.776 years

The answer is part a: use