In one sentence
A servicer's statement of the exact amount required to pay a loan in full as of a given date, including principal, interest, and any fees or premiums.
The longer version
Payoffs happen at sale, refinance, or maturity. The letter states the precise number, dated and often with a per-diem, so the paying party can wire to the penny.
Prepayment premiums, yield maintenance, or defeasance costs show up here, which is why borrowers model exit cost long before they request a payoff.
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