How long would it take to double your principal in an account that pays 6.5% annual interest compounded continuously? round your answer to one decimal place?

It would take 10.7 years.

The formula for continuously compounded interest is:
[tex]A=Pe^{rt}[/tex]
where P is the principal, r is the interest rate as a decimal number, and t is the number of years.

Using our information we have:
[tex]A=Pe^{0.065t}[/tex]

We want to know when it will double the principal; therefore we substitute 2P for A and solve for t:
[tex]2P=Pe^{0.065t}[/tex]

Divide both sides by P:
[tex]\frac{2P}{P}=\frac{Pe^{0.065t}}{P} \\ \\2=e^{0.065t}[/tex]

Take the natural log, ln, of each side to "undo" e:
[tex]\ln{2}=\ln{e^{0.065t}} \\ \\0.6931471806=0.065t[/tex]

Divide both sides by 0.065:
[tex]\frac{0.6931471806}{0.065}=\frac{0.065t}{0.065} \\ \\10.7\approx t[/tex]