To study the effect on financial stability of persistent changes in the interest rate, this paper develops a recursive model of liquidity creation based on Diamond and Dybvig (1983). The model features two stable balanced growth paths: a good one with a healthy banking system and a bad one with a failed banking system. The paper's main result is that a critical interestrate level exists, below which a financial crisis takes place and the economy transitions from the good to the bad BGP. At this tipping point for the economy, banks' franchise value of deposits goes down, since their net interest margins are compressed. This leads to a fall in bank equity, which gives depositors an incentive to run. The tipping point is not necessarily negative or zero. It is an increasing function of the persistence of the change in the interest rate. Since a persistent fall in the interest rate compresses the net interest margin further in the future, it damages the franchise value of deposits more for any given interest-rate cut.