  We have accurately determined the exciton binding energy and reduced mass of
single crystals of methylammonium lead tri-iodide using magneto-reflectivity at
very high magnetic fields. The single crystal has excellent optical properties
with a narrow line width of $\sim 3$meV for the excitonic transitions and a 2s
transition which is clearly visible even at zero magnetic field. The exciton
binding energy of $16 \pm 2$meV in the low temperature orthorhombic phase is
almost identical to the value found in polycrystalline samples, crucially
ruling out any possibility that the exciton binding energy depends on the grain
size. In the room temperature tetragonal phase, an upper limit for the exciton
binding energy of $12 \pm 4$ meV is estimated from the evolution of 1s-2s
splitting at high magnetic field.
