Fe/Tb multilayers have been prepared which exhibit significant perpendicular magnetic anisotropy (PMA) even at RT. The effect of systematic variation in the interface roughness on PMA has been studied in these multilayers which were deposited simultaneously on a set of float glass substrates prepared with varying root mean square surface roughness. The amount of intermixing at the interfaces and uncorrelated part of the interface roughness of different multilayers remain similar, thus allowing one to separate out the effect of the correlated interface roughness only. X-ray reflectivity and conversion electron Mössbauer spectroscopy and SQUID magnetometry was used to characterise the systems. PMA was found to depend weakly on the correlated interface roughness.