Cadetships are very limited in terms of the field they are offered in.
Cadetships are usually for people who have finished year 12 and in some instances are offered to first year uni students. I personally havent heard of an Actuaries cadetship (I think UNSW Co-op has something like that in its options) but someone else may know of one.
Universities other than this will not help you at all. Except if you get into UNSW Co-op (for just about any Business or Engineering area there is) and UTS BAcc (only accounting) the uni dont offer much help.
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There is a quasi-actuarial cadetship at Zurich Financial Services. I am starting it next year. You work in 3 divisions of general insurance over 2 years, claims, operations and underwriting. While not specifically actuarial, it gives you exposure to insurance in a global company. (Rare, as most insurers in Australia don't have global operations) In any case, after 2 years, dependent upon performance, you are offered a graduate role and you can expand into Actuarial. Spots are difficult to gain, however, to my knowledge only 2 spots were offered in general insurance, so competition is pretty fierce. Another great thing about Zurich GI is that they only offer GI to companies, and being a global company, you get exposure to GI from small firms in Australia to TNCs worldwide so it really gives you a great variety of work.
Work is at a minimum of 2 days a week, though you can choose to increase or decrease it dependent upon how you feel. In the holidays, you can choose to work full time if you wish.
Otherwise, there is the Actuarial co-op which offers 3 work placements over 4 years in actuarial roles. These could be at retail banks like Westpac, to big 4 like PwC. For a full list of the sponsors, look at the co-op website. It is a "scholarship" in the sense that you are given $16,750 a year in weekly payments, HOWEVER, you are not paid in your work placements. These work placements are full time over 2 months? (I'm not sure about duration, so correct me if I am wrong)