SYDNEY, Jan 31 (Reuters) - Sales of new homes in Australia rose for a third straight month in December, industry figures showed on Thursday, a sign lower mortgage rates were finally starting to bolster demand.

The Housing Industry Association (HIA) said its survey of large builders showed sales of new homes rose 6.2 percent in December, from November when they increased by 4.7 percent. Total sales were the highest in six months.

'The promising headline rise last December was driven by both detached house and multi-unit sales,' said HIA Economist, Geordan Murray.

'Furthermore, if we look at the under-performing market for 2012 - detached houses - the December improvement was broad-based as sales increased in all but one of the surveyed states.'

The Reserve Bank of Australia (RBA) cut interest rates in May, June, October and December, in part to help revive a moribund housing market.

(Reporting by Wayne Cole) Keywords: AUSTRALIA ECONOMY/HOMES

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