SYDNEY (Reuters) - Australian consumer sentiment hit a three-year high in March as slowing inflation and the first interest rate cut in over four years helped lift the gloomy mood for consumers, a survey showed on Tuesday.

The Westpac-Melbourne Institute index of consumer sentiment rose a solid 4% in March from February. The index was 13.6% higher on a year earlier, although at 95.9 showed pessimists still outnumbered optimists.

The Reserve Bank of Australia last month cut interest rates by a quarter-point to 4.1%, having held them steady for over a year. However, policymakers still warned that prospects of further easing are not guaranteed.

Swaps imply a scant chance that the RBA will follow up with another cut in April, but a move in May is about 80% priced in. Rates are seen reaching 3.5% by the end of the year.

"The RBA’s February decision has bolstered confidence that interest rates will continue to move lower," said Matthew Hassan, Westpac’s head of Australian macro-forecasting.

"Consumers are becoming more positive on the labour market, expectations suggesting a ’soft landing’ has already been achieved."

The breakdown of the survey showed the outlook for family finances over the next year was much better, with the index up 3.2% in the month to 108.3, showing optimists were in the majority.

The survey’s measure of the economic outlook for the next 12 months firmed 3.6%, while the outlook for the next five years jumped 4%.

Buyer sentiment also jumped with the measure of whether it was a good time to buy a major household item jumping 6.9% to 97.1.