A stochastic growth model with money introduced via a cash-in-advance constraint is used to analyze the behaviour of the income velocity of real monetary balances. Agents can purchase consumption goods only using government issued money and capital is a credit good. The cash-in-advance constraint may become nonbinding because of the uncertainty about the realization of the state of the economy. Changes in the income velocity of money due to a precautionary money demand are studied. We find that despite the precautionary money demand does not introduce significant changes into the volatility of the income velocity, its presence can alter the relationship between the growth rate of money supply and the income velocity.