We introduce banks that issue liquid deposits backed by illiquid bonds and capital into an otherwise standard cash-in-advance economy. Liquidity transformation can lead to multiple steady-state equilibria with different interest rates and real outcomes. Whenever multiple equilibria exist, one of them is a 'liquidity trap', in which nominal bond rates equal zero and banks are indifferent between holding bonds or reserves. Whether economic activity is higher in a liquidity trap or in a (coexisting) equilibrium with positive interest rates is ambiguous, but the liquidity trap equilibrium is more likely to go in hand with inefficient overinvestment. While liquidity transformation can lead to macroeconomic instability in the form of multiple equilibria, aggregate consumption is higher than in a cash-only economy, regardless of which equilibrium is selected.