We are trying to refinance our mortgage. The mortgage has a balance of $123000. Our house was appraised at $266000. If we did the math correctly, we have $53200 in equity which gives us approximately $212000 to refinance. The bank is requiring a principal payment of approximately $3000. Why is the bank requiring this, if we have 20% equity?
The answer that first came to mind is that it's not really a "down payment"; it's "closing costs". There are costs associated with creating a mortgage (origination fees, guarantor fees) which can't be capitalized, because they're needed up front to defray overhead, pay other agencies involved in loan creation, etc. They're not willing to lend you this money, and they can't pay the bills with a little extra equity in your home. They need cash, and so you could have 20% equity or 99%, they'll charge you these costs.
You may not have seen this when you bought the home because it's such a buyer's market that sellers are willing to pay closing costs. If that was the case, all you had to bring to closing the first time around was your down payment and maybe some escrow advances (to cover property taxes, homeowner's insurance, etc). Now, though, there's no other party to pick up those costs, so you have to eat them. It's part of the cost of a re-fi.
If your balance is 123000 and you have appraised at 266000, you theoretically have 143000 in equity. Are you saying you would like to refinance 80% and keep 20% in equity? I'm assuming that's what you intended with your question based on the numbers.
20% is not a magic number for a down payment (or remaining equity). Every lender (and every loan) has different standards. Your credit may also affect the percentage they want to see.
I would recommend asking the bank about the requirements of the loan.