SOLUTION: How long does it take for an investment to double in value if it is invested at 16​% compounded monthly question mark  Compounded​ continuously?

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Question 1153391: How long does it take for an investment to double in value if it is invested at 16​% compounded monthly question mark  Compounded​ continuously?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Use the formula A=P%281%2Br%2Fn%29%5E%28nt%29
r=16+%=0.16
n=12-compounded monthly
you want A+=+2P (double your money)
2P=P%281%2B0.16%2F12%29%5E%2812t%29
2=%2812%2F12%2B0.16%2F12%29%5E%2812t%29
2=%2812.16%2F12%29%5E%2812t%29.......use natural log
ln%282%29=ln%28%2812.16%2F12%29%5E%2812t%29%29
ln%282%29=%2812t%29+ln%2812.16%2F12%29
12t=ln%282%29%2F+ln%2812.16%2F12%29
t=ln%282%29%2F+%2812ln%2812.16%2F12%29%29
t≈4.36099 years

Compounded continuously:
A=P%2Ae%5E%28rt%29
you want A+=+2P, and r=16%=0.16
2P=P%2Ae%5E%280.16t%29
2=e%5E%280.16t%29.....use natural log
ln%282%29=ln%28e%5E%280.16t%29%29
ln%282%29=%280.16t%29+ln%28e%29
ln%282%29=%280.16t%29+%2A1
0.16t=ln%282%29
t=ln%282%29%2F0.16
t≈4.33217 years