This paper describes the performance and sensitivity to neutrino mixing parameters of a Magnetised Iron Neutrino Detector (MIND) at a Neutrino Factory with a neutrino beam created from the decay of 10 GeV muons. Specifically, it is concerned with the ability of such a detector to detect muons of the opposite sign to those stored (wrong-sign muons) while suppressing contamination of the signal from the interactions of other neutrino species in the beam. A new more realistic simulation and analysis, which improves the efficiency of this detector at low energies, has been developed using the GENIE neutrino event generator and the GEANT4 simulation toolkit. Low energy neutrino events down to 1 GeV were selected, while reducing backgrounds to the 10−4 level. Signal efficiency plateaus of ~60% for νμ and ~70% for ν¯μ events were achieved starting at ~5 GeV. Contamination from the νμ→ντ oscillation channel was studied for the first time and was found to be at the level between 1% and 4%. Full response matrices are supplied for all the signal and background channels from 1 GeV to 10 GeV. The sensitivity of an experiment involving a MIND detector of 100 ktonnes at 2000 km from the Neutrino Factory is calculated for the case of sin22θ13∼10−1. For this value of θ13, the accuracy in the measurement of the CP violating phase is estimated to be ΔδCP∼3∘−5∘, depending on the value of δCP, the CP coverage at 5σ is 85% and the mass hierarchy would be determined with better than 5σ level for all values of δCP.