Question

investment how long would it take to double your principal in an account that pays 6.5% annual interest compounded continuously

Answer 1

The formula for continuously compounded interest is the following:

$A = Pe^{rt}$

Where $A$ is the resulting amount, $P$ is the initial amount, $e$ is the mathematical constant (2.718...), $r$ is the interest rate (percentage), and $t$ is the time in years.

Since you are looking to double your money, you can use any value for $A$ and $P$, as long as $A$ is twice $P$. This gives you the following equation:

$2 = e^{0.065t}$

Solving for $t$ will give you your answer.