SYDNEY (Reuters) - Australian consumer sentiment bounced in August as rate fears subsided and the outlook for family finances improved due to the government's tax cuts and other cost-of-living measures, a survey showed on Tuesday.

The Westpac-Melbourne Institute index of consumer sentiment rose 2.8% in August from July, when it fell 1.1%. The index reading of 85 showed pessimists still far outnumbered optimists.

"Consumers breathed a small sigh of relief in August as the RBA Board left interest rates unchanged and the support coming from tax cuts and other fiscal measures became more apparent," said Westpac senior economist Matthew Hassan.

In particular, a measure of family finances jumped 11.7% in August, the biggest monthly gain in nine years, with gains most strong among low-income earners, Hassan said.

The Reserve Bank of Australia (RBA) held rates steady at its August policy meeting after debating whether or not to raise it further. It all but ruled out a near-term rate cut as core inflation is only projected to slow gradually.

Markets are now wagering on an easing by the year-end, having only recently implied there was a risk of a further hike.

The survey found the proportion of respondents expecting higher mortgage rates in the next 12 months fell 14.9% in August.

The index measuring whether it was a good time to buy major household items bounced 0.6%, but remains historically low at 82.6.

(Reporting by Stella Qiu; Editing by Jacqueline Wong)