Question

If you invest a sum of money in an account earning 16% annual interest compounded continuously, how long will it take for your money to double?

Answer 1

\[A= Pe^{rt}\]
A= final amount = 2P
P= initial amount
r= rate = 16% = 0.16
t = time

\[2P = Pe^{rt}\]
\[2= e^{0.16t}\]
take ln of both sides, remember that ln(e) = 1
\[\ln(2) = \ln(e^{0.16t})\]
\[\ln(2) = 1(0.16t)\]
\[t= \frac{ \ln(2) }{ 0.16}\]
t=? You can solve this :)

Answer 2

Thank you!!!!!!! I had most of those steps I just didn't know the natural log part!

Answer 3

You're welcomed :) Yeah that's part a little tricky