Answer
$6.25$ years.
Work Step by Step
The given values are
Initial amount $P=\$2000$
Rate of interest $r=4\%=0.04$
Interest $I=\$500$
Simple interest formula.
$\Rightarrow I=Prt$
Divide each side by $Pr$.
$\Rightarrow \frac{I}{Pr}=\frac{Prt}{Pr}$
Simplify.
$\Rightarrow \frac{I}{Pr}=t$
Substitute all the values.
$\Rightarrow \frac{500}{(2000)(0.04)}=t$
Simplify.
$\Rightarrow 6.25=t$
Hence, the time period is $6.25$ years.
