Both loans are priced with standard fixed-rate amortization, payments in arrears, monthly compounding. The figure compared is principal and interest only.
Your current payment comes from the balance you still owe and the term you have left, not from the loan you originally took out. A fully amortizing loan sitting at its current balance with its remaining term left has exactly its original payment, so the original loan amount and original term are not needed as inputs. The new loan is priced on your balance, plus the closing costs if you choose to roll them in.
Interest over a term is the monthly payment times the number of payments, minus the amount borrowed. The lifetime interest figure compares the interest you would still pay if you kept your current loan against the interest on the new one. It is positive when the refinance saves interest and negative when it costs more.
The break-even month answers one narrow question: how long the monthly savings take to repay the cash you handed over at closing. It is rounded up to a whole month, because you are not whole until the month that carries you past the outlay. Three things can make it meaningless, and in each case it is withheld rather than guessed. If the new payment is higher than the old one, there are no savings to recoup and no break-even exists. If you roll the closing costs into the loan, no cash left your pocket, so there is nothing to recoup on a cash basis; the cost has moved into your balance instead, where it accrues interest for the whole new term, and that shows up in the lifetime interest figure.
Property tax, homeowners insurance, HOA dues, and escrow are excluded. They attach to the home rather than the loan, so they are the same before and after a refinance and cancel out. Also excluded: PMI, which a refinance can add or remove depending on the appraised value; discount points as a separate line; prepayment penalties on your old loan; and any tax treatment of mortgage interest. Closing costs are a single dollar figure here rather than an itemized list. Use the quote from your lender, and the closing costs calculator to break one down.
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