Question 509750: How long will it take a $300 investment to be worth $400 if it is continuously compounded at 9% per year?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! How long will it take a $300 investment to be worth $400 if it is continuously compounded at 9% per year?
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A=Pe^rt, P=$invested, r=annual rate of interest, A=amount after t years
..
400=300e^.09t
400/300=e^.09t
4/3=e^.09t
take ln of both sides
ln(4/3)=.09t*lne
log of base=1
.2877=.09t
t=.2877/.09=3.2 yrs
ans:
It will take about 3.2 years for a $300 investment to be worth $400
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