It would take 10.27 years to double the initial money invested
What does double the money mean?
Doubling in this case refers to the number of years it will take the investor to grow the initial investment of $500 to $1000($500*2)
In order to determine the number of years it takes to double the initial amount and based on the fact that interest is compounded continuously, the below future value formula for a continuously compounded interest can be used:
FV = PV x e^(i x t)
FV=future value=$1000
PV=initial investment=$500
e=an exponential constant=2.7182818
i=interest rate=6.75%
t=time or years it takes to double initial investment=unknown
$1000=$500*2.7182818^(6.75%*t)
$1000/$500=2.7182818^(6.75%*t)
2=2.7182818^(6.75%*t)
take log of both sides
ln(2)=0.0675t* ln(2.7182818)
divide both sides by ln(2.7182818)
ln(2)/ln(2.7182818)=0.0675t
0.693147187816848=0.0675t
divide both sides by 0.0675
0.693147187816848/0.0675=t
t=0.693147187816848/0.0675
t=10.27 years
Find out more on compounded continuously interest rate https://brainly.com/question/3932907
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