The collapse of the housing market means many South Floridian home buyers will have to scrimp and save even more if they’re going to become property owners. Lenders have tightened up standards and are asking for larger down payments — as much as 20 percent — and better credit scores. With $300 million in bad loans on the books, banks say they have no choice but to demand solid proof of income and to stop lending to borrowers with less than perfect payment histories. The tri-county area is also likely to be hit with the adverse market premium charged by Fannie Mae, the nation’s largest backer of home loans. Fannie’s recent 0.25 percent hike could translate to an additional $750 on a loan of about $300,000.