Question 1153394
How long does it take for an investment to double in value if it is invested at 16​% compounded monthly question mark  Compounded​ continuously?
<pre><b><u>MONTHLY:</b></u>
{{{matrix(3,3, A, "=", P(1 + i/m)^(mt),
A/P, "=", (1 + i/m)^(mt),
2, "=", (1 + .16/12)^(12t))}}}
{{{matrix(1,3, 12t, "=", log ((1 + .04/3), (2)))}}} ----- Converting to LOGARITHMIC  form
{{{highlight_green(matrix(1,9, "t,", or, time, "=", (log ((1 + .04/3), (2)))/12, "or", "appr.", 4.360987255, years)))}}}
She's WRONG, AGAIN!!
The <b><u>RULE of 72</b></u> ALSO demonstrates that it should be about 4.5 years!


<b><u>CONTINUOUSLY:</b></u>
{{{matrix(3,3, A, "=", Pe^(rt),
A/P, "=", e^(rt),
2, "=", e^(.16t))}}}
{{{matrix(1,3, .16t, "=", ln (2))}}} ----- Converting to LOGARITHMIC (Natural) form
{{{highlight_green(matrix(1,9, "t,", or, time, "=", ln (2)/.16, "or", "appr.", 4.332169878, years)))}}}

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?
</pre>