When the premium is not mandated by the government, it is usually derived from the calculations of an actuary, based on statistical data. The premium can vary depending on many factors that are believed to affect the expected cost of future claims. Those factors can include the car characteristics, the coverage selected (deductible, limit, covered perils), the profile of the driver (age, gender, driving history) and the usage of the car (commute to work or not, predicted annual distance driven).
Vehicles kept in the UK must now be continuously insured unless a Statutory Off Road Notification (SORN) has been formally submitted. This requirement arose following a change in the law in June 2011 when a regulation known as Continuous Insurance Enforcement (CIE) came into force. The effect of this was that in the UK a vehicle that is not declared SORN, must have a valid insurance policy in force whether or not it is kept on public roads and whether or not it is driven.
In South Australia, since July 2016, CTP is no longer provided by the Motor Accident Commission.The government has now licensed four private insurers - AAMI, Allianz, QBE and SGIC, to offer CTP insurance SA. The scheme allocates one provider for 3 years as part of vehicle registration. After July 2019, vehicle owners can choose a different CTP insurer and new insurers may also enter the market. 
Comprehensive insurance covers all of the above and damage to the vehicle caused by the driver themselves, as well as vandalism and other risks. This is usually the most expensive type of insurance. It is custom in the UK for insurance customers to refer to their Comprehensive Insurance as "Fully Comprehensive" or popularly, "Fully Comp". This is a tautology as the word 'Comprehensive' means full.
Auto insurance is financial protection, and not just for the investment you made when you bought your car. After a really serious accident, bills for damage and injuries can easily reach into hundreds of thousands of dollars. If you happen to cause such a wreck, the victims could sue you. In the worst case scenario, assets such as your savings and home could be seized.