The orbital period can be calculated using Kepler's 3rd law, which states that the square of the orbital period is proportional to the cube of the average distance from . In other words;
$T^2 prop R^3$
Where $T$ is the orbital period and $R$ is the body's average distance from the sun, or the semi-major axis. Furthermore, this ratio is the same for any body that orbits the sun. We can therefore rewrite this expression as a ratio in terms of some constant, $C$.
$T^2 / R^3 = C$
We know that the orbital period for the Earth is $1 " year"$, and the Earth's semi-major axis is defined as $1 " AU"$. Using this information we can solve for $C$.
$C = T_"Earth"^2/R_"Earth"^3 = (1 " year")^2/(1 " AU")^3 = 1 "year"^2/"AU"^3$
Remember that $C$ is the same for all bodies orbiting the Sun. We can calculate the semi-major axis for the spacecraft by taking the average of its perihelion and aphelion.
$R_"spacecraft" = ("perihelion" + "aphelion")/2 $
$R_"spacecraft" = (.5 " AU" + 3.5 " AU")/2 $
$R_"spacecraft" = 2 " AU"$
Now we can calculate the orbital period.
$T^2 = CR^3 $
$T^2 = (1 "year"^2/"AU"^3)(2 " AU")^3$
$T^2 = 8 " years"^2$
$T = 2 sqrt(2) " years"$
So the spacecraft has an orbital period of about $2.83$ years.
*Note: Kepler's 3rd law works for things orbiting bodies other than the sun, but the constant, $C$ will be different.
