Answer:
[tex]t=10.66\ years[/tex]
Step-by-step explanation:
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=\$2,800\\A=\$5,600\\r=0.065[/tex]
substitute in the formula above
[tex]5,600=2,800(e)^{0.065t}[/tex]
solve for t
simplify
[tex]2=(e)^{0.065t}[/tex]
Apply ln both sides
[tex]ln(2)=ln[(e)^{0.065t}][/tex]
Apply property of logarithms
[tex]ln(2)=(0.065t)ln(e)[/tex]
[tex]ln(e)=1[/tex]
[tex]t=ln(2)/(0.065)[/tex]
[tex]t=10.66\ years[/tex]
