Abstract <p>A mathematical model for credit debt repayment by a representative rational household has been developed. The model is formalized as an optimal control problem with a noncompact geometric control constraint and a nonfixed time horizon. An existence theorem for solutions in the class of functions admitting impulse control has been proved. Necessary optimality conditions in the form of Pontryagin’s maximum principle have been investigated. Optimality conditions for the early debt repayment regime have been derived.</p>