Answer:
[tex]36.62\ years[/tex]
Step-by-step explanation:
The value of r is the question is
r=0.03
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]t=?\ years\\ P=\$3,000\\A=\$9,000\\r=0.03[/tex]
substitute in the formula above
[tex]9,000=3,000(e)^{0.03t}[/tex]
solve for t
[tex]3=(e)^{0.03t}[/tex]
Apply ln both sides
[tex]ln(3)=ln[(e)^{0.03t}][/tex]
Apply property of logarithms
[tex]ln(3)=(0.03t)ln[(e)][/tex]
Remember that
[tex]ln(e)=1[/tex]
[tex]ln(3)=(0.03t)[/tex]
[tex]t=ln(3)/(0.03)=36.62\ years[/tex]
