Say the nominal interest rate is 12%pa but it is compounded daily
Then the real interest rate will be a little higher.
r= $${\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{0.12}}}{{\mathtt{365}}}}\right)}^{{\mathtt{365}}}{\mathtt{\,-\,}}{\mathtt{1}} = {\mathtt{0.127\: \!474\: \!615\: \!638\: \!402\: \!6}}$$
So the real interest rate is 12.7%
Obviously if you are comparing interest rates you want to compare the real ones.
Say the nominal interest rate is 12%pa but it is compounded daily
Then the real interest rate will be a little higher.
r= $${\left({\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{0.12}}}{{\mathtt{365}}}}\right)}^{{\mathtt{365}}}{\mathtt{\,-\,}}{\mathtt{1}} = {\mathtt{0.127\: \!474\: \!615\: \!638\: \!402\: \!6}}$$
So the real interest rate is 12.7%
Obviously if you are comparing interest rates you want to compare the real ones.