Final answer:
The correct method for recording billing and collection of special assessments and related debt transactions when the city is not obligated is through an agency fund.
Step-by-step explanation:
When it comes to the recording of billing and collection of special assessments and payment of debt principal and interest on special assessment debt for which the city has no obligation, the correct method is to use an agency fund. An agency fund is used in governmental accounting to account for resources for which the government is acting as an agent or custodian. These encompass situations where the city is managing the funds but does not have any fiscal responsibility for the debt itself. In contrast, a debt service fund is utilized when the government is obligated to pay off the debt. A special assessment fund could be considered when the assessment is solely for the purpose of servicing a debt for which the municipality is liable. Lastly, a private-purpose trust fund is for situations where the government is managing assets for the benefit of specific individuals or parties rather than for the public as a whole.