Help me understand Math: Refinancing FHA to Conventional Loan

[Jason Noah Choi]

I want to understand the math behind figuring out what a property needs to appraise at in order to get out of an FHA loan. For convenience, I'm not going to account for things like tax, PMI, and additional expenses.

Let's say I bought a property for $500K at 3.5% down. Therefore, I put down $17500. This means that the loan amount is $482,500. After a year goes by, I will have a balance due of $474,003 and I want to refinance because I'm sick of paying for PMI. I've been fortunate enough to be able to do some work and create some forced appreciation. It seems that most lenders will provide 75% LTV.

Does this mean I need the property to appraise at $643,334 to get out of my loan? I got this number with this math: $482,500 / 0.75

I'm just a little bit confused on how this works. At what appraisal amount do I need to hit to get out of my FHA loan and into my new conventional loan to make it so that I hit the 20-25% minimum? Don't necessarily need a cash out refi, more just want to get out of the FHA.