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couple things to check..
Are you under the FHA maximum sales price in your area?
not too many lenders will even look at conventional at 620 but the +20% down may work
3 lates from last year may also be a big issue (although again, the large down paymetn may be OK)
With the scores you are looking at, FHA rate will be as good or better than conventional.
First this would be considered a "jumbo fha loan amount" The rate will be adjusted as a result so 5% is probably a little low
However with the credit scores the rate along with the monthly MI will likely be more attractive than conventional.
Most lenders will not touch a 620 with conventional - if they do it has to be very clean
One bank I looked at uses a 3% (points not rate) adjustment for score at 620
plus a 1% adjustment for loan size - where with FHA it is .5% for score and 1% for rate
so
to compare
Par today would be 5.75% on a conventional
and right bwteeen 5.125% and 5.25% on FHA
Actually it looks like the cost in rate would be about the same when you add the MI in however in 5 years you could get rid of the MI on the FHA and have a great rate -