This paper compares the impact of setting the money growth rate versus pegging the interest rate on aggregate real variables and their distributions. In either case, the monetary policy, in isolation, requires the price level to jump to ensure intertemporal solvency but has no real dynamic effects. The choice of monetary instrument has consequences for wealth and income inequality, doing so in potentially conflicting ways. Following real shocks, the accompanying monetary policy will influence the ensuing transition. For real variables, this operates entirely through its impact on the speed of convergence and is negligible. For financial variables, the impact also depends upon the initial jump in the price level. These effects vary more substantially between policies and have more significant distributional consequences. Overall, the impact on inequality is dominated by the real shocks themselves, rather than the accompanying monetary policy. Finally, we compare these two policies to inflation targeting, which is shown to be the least favorable for reducing wealth inequality, but the most favorable for reducing income inequality.