Answer
23.16 years or 23 years and 2 months
Work Step by Step
10000 dollars initial amount
40000 dollars desired amount
6% interest
Compounds monthly
$A=40000$
$P=10000$
$r=.06$
$n=12$
$A=P(1+(r/n))^{n*t}$
$40000=10000*(1+(.06/12))^{12*t}$
$40000/10000=10000*(1+(.06/12))^{12*t}/10000$
$4=(1+(.06/12))^{12*t}$
$4=(1+(.005))^{12*t}$
$4=1.005^{12*t}$
$ln 4=ln (1.005^{12*t)}$
$ln 4= 12*t*ln 1.005$
$ln 4/12*ln 1.005 = 12*t*ln1.005/12*ln 1.005$
$1.38629/12*.0049875 =t$
$1.38629/.05985=t$
$23.162 =t$
23.16 years or 23 years and 2 months
