Is fostering economic growth ‘only’ a question of political will or ‘unavoidable’ to maintain economic stability? It is disputed whether such a ‘growth imperative’ is located within the current monetary system, creating conflicts with sustainability. To examine the claim that compound interest compels economies to grow, we present five post-Keynesian models and show how to perform a stability analysis in the parameter space. A stationary state with zero net saving and investment can be reached with positive interest rates, if the parameter ‘consumption out of wealth’ is above a threshold that rises with the interest rate. The other claim that retained profits from the interest revenues of banks create an imperative is based on circuitist models that we consider refutable. Their accounting is inconsistent, and a modeling assumption central for a growth imperative is not underpinned theoretically: Bank’s equity capital has to increase even if debt does not. This is a discrepancy between the authors’ intentions in their texts and their actual models. We conclude that a monetary system based on interest-bearing debt-money with private banks does not lead to an ‘inherent’ growth imperative. If the stationary state is unstable, it is caused by agents’ decisions, not by structural inevitableness.