What interest rate is needed for $1000 to double after 10 years if compounded continuously?

.0693

To find this, use the equation A = Pe^rt

This is because it is being compounded continuously rather than a set time.

Use what is given to set up a formula as so:

2000 = 1000e^10r

2000 is put in as it is double of 1000. To solve for r, or the rate, divide both sides by 1000, leaving you with this new equation.

2 = e^10r

In order to get rid of e, you need to do the inverse which is ln or natural log. ln(2 is equal to .693147806

So your new equation can be of variations of that, but I used this one:

.693 = 10r

Now, divide 10 on both sides to get:

r = .0693

Hope this helps!

other answer is correct. i had used the radius of the radius somehow. a website: