This paper analyses the transmission process of monetary policy in a closed-economy New Keynesian model with monopoly banking and a cost channel. The loan rate depends on the repayment probability, which in turn depends on firms' net worth and cyclical output. The supply of bank loans is perfectly elastic at the prevailing loan rate and so is the provision of central bank liquidity at the policy rate. Numerical simulations, based on an illustrative calibration, show that credit market imperfections and sluggish adjustment of bank deposit rates may impart a substantial degree of persistence in the response of output and inflation to monetary shocks. With flexible wages, a relatively high elasticity of the repayment probability with respect to cyclical output is required for a monetary contraction to lead to higher inflation, that is, to a price puzzle.