A: Yes, the more you put down the more it increases your chances of being approved. More down isn't always required though.
No credit is actually better than bad credit, because with no credit you could do this: http://www.trulia.com/blog/shanethemortgageman/2011/06/no_sc
However with bad credit, all is not lost, because it depends on just how bad the credit is. You know your scores, so likely you also know what is on your credit report, and that is just as important as your scores. How has your past 12-24 months of credit history been?
FHA mortgages require a 500 credit score, and most FHA lenders minimum score requirements tend to be 600, 620, or 640 - with FHA anything less than a 580 score requires a 10% down payment, otherwise just 3.5% down is required.
VA mortgages have no score requirement, but VA lenders score requirements are similar to FHA's. VA is 100% financing for Veteran's.
USDA Rural Development mortgages are 100% financing, and have no score requirement - however if you go through a lender most will have 620 or 640 minimum scores, but if you go Direct to USDA they do not have any minimum score requirements, but it takes a little bit longer - Walkerton is in an eligible area, La Porte and South Bend are not. http://eligibility.sc.egov.usda.gov/eligibility/welcomeAction.do to check the eligible areas and also if your income is not too high/within eligibility limits as well.
Fannie Mae & Freddie Mac mortgage programs require a 620 score, however with less than 20% down you will likely need at least 660-680 scores.
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