On January $1,2023,$ Susana Lopez signed a note to buy a used car. Her semi$-$annual payments of $$1,740$ are due on June $30$ and Dec. $31.$ The note's maturity date is December $31,2024.$ The car dealer used an $8\%$ rate compounded semi$-$annually to determine the amount of the payments. Determine the carrying value of the note on December $31,2023.$

A$.$ $$3,480$

B$.$ $$3,282$

C$.$ $$3,978$

D$.$ $$2,885$

E$.$ $$4,636$