Hi - I am surprised you have made the final payment before going to the Notary, that is usually when you hand over the last instalment, when you are sure everything is OK.
As for the money paid, they are interested in the source of the money, so that is what you will be asked about. If you can show it was from income, or the sale of another property, or whatever, then I don´t think you should have a problem.
Check with your lawyer, they should be able to tell you what level of proof the Notary will require.