The transport properties of Fe/MgO/Fe(100) tunnel junctions are studied from first principles at finite bias. For parallel alignment of the Fe leads and voltages below 25mV the current is carried by both majority and minority spins, with the largest contribution coming from the minority. Their transmission is dominated by a sharp resonance through surface states, whose contribution to the current decreases rapidly as the bias increases. The same minority surface state leads to resonant transmission also for the antiparallel alignment of the Fe leads. However, in contrast to the parallel case the resonance is weakly dependent on the bias, leading to a large magnetoresistance at small voltages, which rapidly decreases with increasing voltage and approximately saturates at about 25mV.