The answer is $763,808.48.
Four steps:
(1) Find annual interest based on the interest rate and principal balance ($765,000 × 5.5% = $42,075).
(2) Find one month’s interest by dividing the annual interest by 12 ($42,075 ÷ 12 = $3,506.25).
(3) Find the amount of the first monthly payment remaining after paying interest ($4,697.77 – $3,506.25 = $1,191.52).
(4) Find the principal balance after paying $1,191.52 against the balance ($765,000 – $1,191.52 = $763,808.48).