The paper examines implications of both real and nominal convergence for a fully-funded pension system. The process of convergence implies that higher contribution rates are necessary in the converging economy for replacement ratios to be the same as in a steady-state economy. This effect in the converging economy is partially due to higher growth rates experienced during the process of real convergence and partially due to lower rates of return. Moreover, the lower rates of return are themselves due to nominal convergence, which is tied up with real convergence through the Balassa-Samuelson effect. Simulations show that, under plausible assumptions, contribution rates would have to be up to 60 percent higher in the Czech Republic, for example, due to convergence processes in order to achieve the same replacement ratio as in a steady-state economy.