1. If you can afford & qualify for a MAX loan amount of $440K, and you need to put something down in order to get that loan, the minimum would be 3.5% on an FHA loan, so your purchase price is going to need to be something like $455,400. Not $550K
2. Then, your sister is basically going to be giving you a $184,600 gift of equity (this is only money that can go in your bank account when YOU sell the property), which it doesn't sound like that's what she was shooting for with the scenario you had wanted to happen.
3. If you can't qualify for a $440K loan because you don't have any down payment money, she wouls just sell the home, for $640K to a buyer who can qualify for that type of purchase price w/ 3.5-20% or more down & you sister can take those proceeds from the sale & still GIFT you the $110K for a down payment for you on another house.
4. OR you could do an "All Inclusive Trust Deed" whereby you basically take over HER pymts on that $370K loan balance, this would require ZERO down payment from you. If your sister wants to be paid some more money, she could also take back a 2nd loan, on top of the existing $370K, in the amount up to $440K which would be another $70K, you & she can work out an interest rate & you'd be making pymts to her.
After keeping track of pymts you're making on the "AITD" & the 2nd lien to your sister, you can then, in the nearer future (2-3yrs) refinance the house into your name only, as borrower & owner & then you'd end up with the loan amt you can afford & a home with a lot of free equity from a Great Sister. And when you do go to refinance, you can finance that amount in the low $400's, payoff that $370K-ish loan & the difference can be paid to your sister in CASH.
If you'd like to talk to me some more about your options, feel free to shoot me an email directly, I don't look back on this same Trulia posting for answers after mine.
Emily S. Knell
Realtor Since 1996
Realty ONE Group