.A borrower asked a lender to lend her $1,000. The lender replied that he would do so only if the borrower's father would guarantee the loan. At the borrower's request the father mailed a signed letter to the lender: "If you lend $1,000 to my daughter, I will repay it if she doesn't." On September 15, the lender having read the father's letter, lent $1,000 to the borrower, which the borrower agreed to repay in installments of $100 plus accrued interest on the last day of each month beginning October 31. The father died on September 16. Later that same day, unaware of the father's death, the lender mailed a letter to the father advising that he had made the $1,000 loan to the borrower on September 15. The borrower did not pay the installments due on October 31, November 30, or December 31, and has informed the lender that she will be unable to make repayments in the foreseeable future. Assume that the borrower's entire $1,000 debt is due and that she has failed to repay any part of it.
In an action by the lender against the father's estate for $1,000 plus accrued interest, which of the following is true regarding the father's promise to pay?