First year partial rental in 2022 with refinance in 2020

Your basis in the condo that you are depreciating is what you paid for it.  So you paid your initial payment and the initial closing costs with lender A.  You also paid any major improvements that you made as well as your refinance costs with lender B.  All of this should be added together to be the basis (what you paid for the condo) when starting it as a rental in 2022.

You need to save the records - the initial purchase and the refinance and any receipts for major improvements - and then start the depreciation.  You'll depreciate it over 27.5 years and when you sell the place any depreciation that you have taken will be taxed as regular income.  

If you were to refinance the condo again while it was a rental the refinance costs with lender C would create an entirely new asset which would be depreciated at 27.5 years as well.  As would any improvements or renovations that you make now that it is a rental.

@gshforever