Interest guarantees on loans and savings contracts are viewed as financial claims and priced by the no arbitrage principle in continuous time Markov interest models of diffusion type and of Markov chain type. Various forms of loan contracts and guarantees are considered, an important distinction being made between loans with fixed repayments and loans with fixed amortizations. Differential equations are obtained for the values of the guarantees, and some closed form expressions are obtained for standard contracts in certain well structured models.