SOLUTION: Hi, I am working on a word problem. How long dies it take for 5000 to grow to 10000 at 12% compounded continuously. The assistance the book gives is using the A=Pernt. I tried

Question 411511: Hi,
I am working on a word problem. How long dies it take for 5000 to grow to 10000 at 12% compounded continuously. The assistance the book gives is using the
A=Pernt. I tried using my scientific calculator but not having any success. Can you help?
Thanks Ed
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
How long dies it take for 5000 to grow to 10000 at 12% compounded continuously.
..
The formula for continuous compounding:A=Pe^rt,with A=dollars after t years, r=annual interest rate,P=dollars invested,t=years.
10000=5000e^.12t
2=e^.12t
ln2=.12tlne=.12t (note: logarithm of base=1)
t=ln2/.12=5.78 years
ans: It will take approximately 5.78 years for $5000 to grow to $10000 when compounded continuously at an annual interest rate of 12%, that is, you will double your investment.
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