[thaumasiotes]

No, you don't.

You might in a state of nature, but the US has laws against prepayment penalties for mortgages. (Well, against the mortgage originator charging prepayment penalties.) You don't owe interest until it accrues.

[OJFord]

Right, you 'owe the full amount of accrued interest'... Which is not as much as the amount that would've accrued if held to term. I think this is rather beside the point anyway!