Question

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?

Answer 1

It would take 10.7 years.

The formula for continuously compounded interest is:
$A=Pe^{rt}$
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:
$A=Pe^{0.065t}$

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

Divide both sides by P:
$\frac{2P}{P}=\frac{Pe^{0.065t}}{P} \\ \\2=e^{0.065t}$

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

Divide both sides by 0.065:
$\frac{0.6931471806}{0.065}=\frac{0.065t}{0.065} \\ \\10.7\approx t$

Answer 2

Answer:

11 years

Step-by-step explanation: