Tywin Lannister borrows $$749,000$ from the Iron Bank to buy a small castle for his youngest son. The adjustable rate mortgage carries a $2\mathrm{.}5$ percent rate for the first $2$ years. After that the rate will change annually to reflect market conditions. The annual cap is $3\%($i$.$e$.,$ the largest increase in any year is $3\%).$ The loan term is $30$ years and payments are made monthly.

What is the largest possible mortgage payment Tywin might owe when the interest rate resets at the beginning of the $3$rd year?

Group of answer choices

$$4,173$

$$3,048$

$$4,253$

$$2,108$

$$2,960$