This paper examines interest rate determination and monetary independence in a small economy with a fixed exchange rate. The risk premium is determined endogenously in the stochastic, general‐equilibrium model. The sign of the risk premium and the magnitude of the interest rate depend on the specification of the policy rule for the future exchange rate. Increases in domestic credit can decrease, increase or have no effect on the interest rate. The offset coefficient can differ from −1 (the ‘trilemma’ may not hold), but numerical calculations indicate that the offset is close to −1. Under certain conditions, empirical analyses overestimate monetary independence. Copyright © 2016 John Wiley & Sons, Ltd.