In economic studies and popular media, interest rates are routinely cited as a major factor behind commodity price fluctuations. At the same time, the channels of transmission are far from transparent, leading to long-running debates on the sign and magnitude of interest rate effects. Purely empirical studies struggle to address these issues because of the complex interactions between interest rates, prices, supply changes and aggregate demand. To move this debate to a solid footing, we extend the competitive storage model to include stochastically evolving interest rates. We establish general conditions for existence and uniqueness of solutions, as well as providing a systematic theoretical and quantitative analysis of the interactions between interest rates and prices.