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Path-Integral-Monte-Carlo simulation has been used to calculate the properties of a two-dimensional (2D) interacting Bose system. The bosons interact with hard-core potentials and are confined to a harmonic trap. Results for the density profiles, the condensate fraction, and the superfluid density are presented. By comparing with the ideal gas we easily observe the effects of finite size and the depletion of the condensate because of interactions. The system is known to have no phase transition to a Bose-Einstein condensation in 2D, but the finite system shows that a significant fraction of the particles are in the lowest state at low temperatures.