Charges depend on the journey
ICA states that fees depend on vehicle type, checkpoint and the entry date/time. Its driving page links the transport authority for the detailed charges and vehicle-entry requirements.
Foreign-registered vehicles
Citizens, PRs and pass holders generally cannot keep/use a foreign-registered vehicle in Singapore; ICA identifies an exception for certain work-pass holders who do not reside here. Check the actual eligibility and driving requirements through the official linked channel, rather than treating foreign registration as a general entitlement.
Official ICA source
Written independently from ICA’s English original. The linked source supplies the complete document and subsequent updates.