We study the dynamic relationship between the public debt ratio and the real interest rate. By means of a macroeconomic model of simultaneous difference equations - one for the debt ratio and the other for the real interest rate - we focus on the role of monetary policy, fiscal policy and risk premium in affecting the stability of the debt ratio and the existence of steady states. We show that fiscal rules may not be enough to control the pattern of the debt ratio, and the adoption of a monetary policy, in the form of an interest rate rule, is necessary to control the pattern of the debt ratio for assuring its sustainability over time. The creation or disappearance of steady states, or periodic cycles, can generate scenarios of multistability.