Explanation of The Name Ar-Rahim

The name Ar-Rahman refers to the one endowed with Mercy that extends to all of the creations in this world regardless of their beliefs as well as to the believers in the Hereafter.

The name Ar-Rahim, on the other hand, is specific to the believers as it means: the One endowed with Mercy that extends to only the believers.

My question: Is this Mercy in the name Ar-Rahim specified to the believers in the Hereafter alone? Or is this Mercy in the name Ar-Rahim including Mercy to to the believers both in the Hereafter and in the dunya as well?