Our problem is motivated by an exchange rate control problem, where the control is composed of a direct impulsive intervention and an indirect, continuously acting intervention given by the control of the domestic interest rate. Similarly to Cadenillas and Zapatero (Math Financ 10:141-156, 2000) we formulate it as a mixed classical-impulse control problem. Analogously to Cadenillas and Zapatero (Math Financ 10:141-156, 2000), our approach builds on a quasi-variational inequality, which we consider here in a weakened version, and we too start by conjecturing the optimal solution to have a specific structure. While in Cadenillas and Zapatero (Math Financ 10:141-156, 2000) the horizon is infinite thus leading to a time-homogeneous solution and the value function is supposed to be of class throughout, we have a finite horizon T and the value function is allowed not to be at the boundaries of the continuation region. By suitably restricting the class of impulse controls, we obtain a fully analytical solution.