SOLUTION: Please Help. I am stuck on how to write out this problem. If $ 2500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $ 500

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Question 573760: Please Help. I am stuck on how to write out this problem.
If $ 2500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $ 5000 at 4%? Round to the nearest tenth
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
If $ 2500 is invested in an account that pays interest compounded continuously, how long will it take to grow to $ 5000 at 4%?
Round to the nearest tenth
:
The continuous compound interest formula: A+=+P%2Ae%5E%28rt%29, where
A = amt after t time ($5000)
P = initial principal ($2500)
r = interest rate in decimal form (.04)
t = time in yrs
:
2500%2Ae%5E%28.04t%29+=+5000
divide both sides by 2500
e%5E%28.04t%29+=+5000%2F2500
e%5E%28.04t%29 = 2
use natural logs here
ln%28e%5E%28.04t%29%29 = ln(2)
:
The log equiv of exponents
.04t*ln(e)= ln(2)
:
the ln of e = 1, find ln of 2; therefore we have
.04t = .693
t = .693%2F.04
t = 17.325 ~ 17.3 yrs
;
:
Check this on your calc, enter: 2500*e^(.04*17.325); results: 4999.3 ~ 5000