The essence of interest rate parity is risk-free arbitrage, so it does not involve the influence of inflation in essence, so there is no real interest rate, that is, it should be nominal interest rate.

Look at the example:

In the international finance textbook P73- RMB exchange rate analysis edited by Yi Gang and Zhang Lei, the nominal interest rate is used in the analysis.

The fourth chapter of Exchange Rate Theory and Policy Research, edited by Jiang Boke and Lu Qianjin, is about the derivation of actual theoretical parity conditions. The author deduces the real interest rate parity condition by purchasing power parity and uncompensated interest rate parity, from which it can be clearly seen that the nominal interest rate is used in the interest rate parity condition.

Lucio sarno and mark taylor's "Exchange Rate Economics" begins with the second chapter "Efficiency of Foreign Exchange Market": "I and i* in UIP conditions are the nominal interest rates of domestic and foreign securities respectively".

Among the four international parity conditions discussed in the discipline of international finance

Purchasing power parity (PPP) does not involve interest rates, but only the general price level.

Guaranteed interest rate parity (CIP) and unsecured interest rate parity (UIP) involve nominal interest rates.

Only real interest rate parity (RIP) involves real interest rate.