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The inception of the euro allowed countries from the periphery to experience a large fall in the cost of borrowing. Lower nominal rates were only partially offset by lower inflation rates. We rationalize this real interest rate reversal using a two-region model of a monetary union where, consistently with real interest rate data, discount factors are initially heterogeneous, leading the periphery to be borrowing-constrained. We model the inception of the euro as a partial convergence process in inflation rates and a slow rise in the discount factor of the periphery, relaxing the borrowing constraint. This simple set-up accounts for the bulk of post-euro fluctuations in both regions. In particular, it replicates very well the observed joint dynamics of current accounts and terms of trade.