In Quebec, for the personal basic amount, does the federal tax credit and the provincial tax credit add up?

Question

E.g. if my income is 17000$, which is below the provincial basic (18056$) but above the federal one (maximum 15705$), do I pay taxes? Is it

federal_tax = min(0, federal_income_tax - federal_BPA * lowest_federal_tax_bracket)

quebec_tax = min(0, provincial_income_tax - 18056 * lowest_quebec_tax_bracket)

So total_tax = 0 + 1295 * lowest_federal_tax_bracket

Or is it

total_tax = min(0, federal_income_tax + provincial_income_tax - federal_BPA * lowest_federal_tax_bracket - 18056 * lowest_quebec_tax_bracket)

which would give

total_tax = min(0, 17000 * lowest_federal_tax_bracket - 15707 * lowest_federal_tax_bracket + 17000 * lowest_quebec_tax_bracket - 18056 * lowest_quebec_tax_bracket)

=

min(0, (17000-15707)*lowest_federal_tax_bracket + (17000 - 18056) * lowest_quebec_tax_bracket)

Which would be 0?

Thanks!

Answer 1

You calculate the federal and provincial taxes separately. So total_tax = 0 + 1295 * lowest_federal_tax_bracket would be correct. However that is just the basic tax owning, the actual amount gets complicated based on the various tax credits and CPP/EI payments, etc.