To develops an adequate an monetary policy, in a small open economy like the Colombian, must take in to account, the Trilema of monetary policy and the nominal anchor of the economy, in this context, the central bank role is that the decide which is the nominal anchor to the economy, however exist simultaneously a close relationship between the monetary policy and the gross domestic product gap, the goal of this study is to illustrate this dynamic thought of an monetary policy model, the results show that the behavior of an optimal interest rate like a function of the subjacent inflation and the gross domestic product gap, one of the principal characteristics of the solutions is that the restrictions of no negativity over the interest rate is necessary to lowers levels of gross domestic product gap and lowers rates of inflation.