Becky took a loan that requires payments of $$2,000$ every $6$ months for the next $3$ years. The loan carries an annual percentage rate $($APR$)$ of $10\%$ with semi$-$annual compounding. Which of the following is closest to the value of the loan today?

Question options:

a$)$

$$8,711$

b$)$

$$10,151$

c$)$

$$4,974$

d$)$

$$9,947$