  We propose and analyze an algorithm to approximate distribution functions and
densities of perpetuities. Our algorithm refines an earlier approach based on
iterating discretized versions of the fixed point equation that defines the
perpetuity. We significantly reduce the complexity of the earlier algorithm.
Also one particular perpetuity arising in the analysis of the selection
algorithm Quickselect is studied in more detail. Our approach works well for
distribution functions. For densities we have weaker error bounds although
computer experiments indicate that densities can also be approximated well.
