Answer
11.87 years or 11 years and 10 months
Work Step by Step
500 dollars initial amount
800 dollars desired amount
4% interest
Compounds semiannually
$A=800$
$P=500$
$r=.04$
$n=2$
$A=P(1+(r/n))^{n*t}$
$800=500(1+(.04/2))^{2*t}$
$800/500=500(1+(.04/2))^{2*t}/500$
$1.6= (1+(.02))^{2*t}$
$1.6=1.02^{2*t}$
$ln 1.6= ln (1.02^{2*t})$
$ln 1.6=2*t* ln 1.02$
$ln 1.6/2*ln 1.02=2*t* ln 1.02/2*ln 1.02$
$ln 1.6/2*ln 1.02=t$
$.47/2*.0198=t$
$.47/.0396 =t$
$11.867 =t$
11.87 years or 11 years and 10 months
