Under a Chattel Mortgage, GST is charged on the purchase price of the car or vehicle. There is no GST charged, however, on the monthly repayments or the balloon (residual) payment.
Customers who are registered for GST on a Cash basis can generally claim the GST contained in the purchase price of the vehicle as an Input Tax Credit on their next BAS.
To do this in Billcue, go to add an expense, set the amount to zero, but the GST to the total GST amount
Sometimes, the finance company will take a separate payment which is the GST component. If this is how it is set up for you, then you should wait for that payment, and record that as the full amount with 100% GST. Then for future payments, they should be set to GST Free (just untick the 'GST paid' box.) The establishment costs and on road costs might need to be recorded separately, as some may not have GST included, unless the loan covered all of that as well, but it would be best to get advice from your accountant on that.