Answer
6 years
Work Step by Step
$P=2000$
$A=3000$
$r=.07$
$n=12$
$A=P*(1+(r/n))^{n*t}$
$3000=2000*(1+(.07/12))^(12*t)$
$3000/2000=2000/2000*(1+(.07/12))^(12*t)$
$1.5=1.0058333^{12*t}$
$ln 1.5 = 12*t* ln 1.00583333$
$ln 1.5/ln 1.00583333 =12*t* ln 1.00583333/ ln 1.00583333$
$69.710 = 12*t$
$69.71/12 = 12*t/12$
$5.809 = t$
