Nominal interest rate surely depends on inflation rate, so only real interest rate is considered as below:
1.close economy:
Roughly inflation rate has no influence on real interest rate, just use the IS-LM Model.
2.open economy & flexible exchange rate:
Use the rational expectation of exchange rate and interest-rate parity, we can conclude that the domestic interest rate is related to so-called world's interst rate and the variation speed of exchange rate, i.e, the domestic interest rate also depends on the domestic inflation rate and world's inflation rate.