So about $12,500 if I'm doing my math right.  

You can have a contingent lease with the tenant, i.e. the lease depends on you closing on the property.When they do the math they are going to want to see at least two months of reserves for the payment after you close still in your account, though in reality you want more for when something goes wrong (and it will).

Make sure you price both of the insurances before you do the math.

•Determing ARV(after repair value)-I'm a math wiz but I need help learning the fomula to learn whether or not a potential property would make a successful flip/investment.I have MANY more questions on things I simply do not know or understand and I'm reading many BP guides and articles on tips to become a great REI.

Could somebody help me with the math where this number comes from?

You can buy lots of super cheap properties in rough areas, but do your homework

You should have already done your homework on this before putting the properties under contract.  

But all I have ever known are laws of physics, equations, math and numbers.

It is better if you know what you can qualify for.Always do the math analysis on your prospective properties and try to look at them before you make an offer or have a clause that will allow you some time (about 15 days) to make a detailed inspection and possibly back out of the deal without a penalty that will hurt you.  

Any other reason other than what the cold hard math on the paper says usually means you are making a poor decision based on some emotion.