Question

I am supposed to find how long it takes for an investment to double at an annual interest rate of 8.5%, compounded continuously. I know that e is supposed to turn into ln when you try to divide by t (or at least, I think), but how do you do this? Could someone offer an explanation? Thank you so much!!

Answer 1

you would start with

2 = 1(e^.085t) , the same formula you used in your previous post
It doesn't matter what amount you start with, on the left side you would have twice that amount, and then the amount can be divided, leaving my equation.

now take ln of both sides

ln 2 = ln (e^.085t)
ln 2 = .085 ln e, but ln e = 1
so .085t = ln 2
t = ln 2/.085
= 8.15

I assume you know the basic rules for working with logarithms.