Any territory annexed to a city or district shall be liable for payment of principal, interest, and any other amounts which shall become due on account of any outstanding or then authorized but thereafter issued bonds, including revenue bonds, or other contracts or obligations of the city or district, but not of any improvement district within the district. It shall be subject to the levying or fixing and collection of any of the following which may be necessary to provide for that payment:
(a) Taxes or assessments.
(b) Service charges, rentals, or rates.
(c) Both taxes or assessments and service charges, rentals, or rates.