Answer
3.67 years or 3 years and 8 months
Work Step by Step
5000 dollars initial amount
6000 dollars desired amount
5% interest
Compounds quarterly
$A=P(1+(r/n))^{n*t}$
$A=6000$
$P=5000$
$r=.05$
$n=4$
$A=P(1+(r/n))^{n*t}$
$6000=5000*(1+(.05/4))^{4*t}$
$6000/5000=5000*(1+(.05/4))^{4*t}/5000$
$1.2=(1+(.05/4))^{4*t}$
$1.2=1.0125^{4*t}$
$ln 1.2 = ln (1.0125^{4*t})$
$ln 1.2 = 4*t*ln 1.0125$
$ln 1.2/4*ln 1.0125 = 4*t*ln 1.0125/4*ln 1.0125$
$ ln 1.2/4*ln 1.0125 = t$
$.18232/4*.012422=t$
$.18232/.04969=t$
$t=3.669$
3.67 years or 3 years and 8 months
