Can't vouch for LA, but property typically is taxed at eithter the appraised value, the most recent purchase price ("if it wasn't worth that much, you wouldn't have paid that much"), or some combination of the two (usually highest of the two, to prevent "$1 and other goods and services" from lowering the tax to zero).

You have now _explicitly_ paid a total of $125k for the property; the fact that you bought it in two stages shouldn't be relevant. But "should" and law are only tangentially connected.

I'd recommend asking a tax accountant who know your local practices, unless someone here can give you an authoritative answer.