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I'd say it looks good as long as you keep your payments around 1125.00 Scores will get you approved and as long as you're current with everything else, all should be fine. Happy house hunting. Mortages are not like cc's. You can also include your monthly bonuses as long as it's something you regularly get and for at least 2 yrs. We've always had bonuses and they had no problem including them in our salary.
Most pre approvals last for 60-90 days and closing on a home after going under contract usually takes 30-45 days. You can get pre approved in December or early January if you want to close by late February. These are all rough estimates of course. Each lender will have different time frames for these types of things.
I don't think you should be concerned about your late payments. You might have to provide a letter of explanation for the lates but they shouldn't keep you from being approved.
You're definitely going about this the right way by. Asking questions in August when you want to close in February is very smart.