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Having in mind the various effects of an Economic Union with a common currency such as the EMU, we examine the existence of Real Interest Rate Parity conditions, as these are defined by the general theory of Purchasing Power Parity theory, among several European Union member states since after the introduction of the Euro an ideal setting has emerged for existence of such a parity (common currency, one central bank that regulates the markets and sets the reference interest rate for the participating members, introduction of common legislative guidelines for tax setting, removal of trade and fund transfer barriers etc.).The study contains three main sections. In the next section, we describe the establishment of the economic and monetary union. Moreover it is examined whether financial structures across European countries have become more similar after the introduction of the single currency. Section 2 assesses the progress toward financial integration in the major euro-area financial segments, namely money markets, bond markets, equity markets and banking. This section also describes some of the most interesting financial developments that occurred alongside with the integration process, partly spurred by the euro. In section 3 we present the general theory of PPP and a literature review of the previous studies in the subject of Real Interest Rate parity. In section 4 we present and our empirical analysis and the results that were derived and we conclude with Section 5.