The success of calculating and displaying the Fraunhofer diffraction patterns for various apertures using the fast Fourier transform algorithm on an IBM compatible personal computer has been well documented in the recent literature. In this paper the technique is extended to the simulation of optical holography on the computer. Using this method, Fourier transform holograms are easily generated. Their optically reconstructed images are compared to the ones reconstructed and displayed by the computer. These computer generated images allow for a quantitative verification of the holographic theory presented and can serve as the basis of a tutorial on this subject suitable for advanced undergraduates. The calculations and graphics were accomplished using the mathcad(R) for windowsTM software package.