This work studies optimal refinancing strategy for the debtors on the view of balancing the profit and risk, where the strategy could be formulated as the utility optimization problem consisting of the expectation and variance of the discounted profit if refinancing. An explicit solution is given if the dynamic of the interest rate follows the affine model with zero-coupon bond price. The results provide some references to the debtors in dealing with refinancing by predicting the value of the contract in the future. Special cases are considered when the interest rates are deterministic functions. Our formulation is robust and applicable to all of the short rate stochastic processes satisfying the affine models.