Kern Corporation was organized on January $1,$ with an authorization of $5,000,000$ shares of $$2$ par value common stock. During the year, Kern had the following common stock transactions:

Jan. $4$: Issued $300,000$ shares @ $$16$ per share.

Apr. $8$: Issued $100,000$ shares @ $$12$ per share.

July $29$: Purchased $90,000$ shares $($treasury$)$ @ $$14$ per share.

Oct. $18$: Sold $60,000$ shares held in treasury @ $$18$ per share.

Dec. $31$: Sold $30,000$ shares held in treasury @ $$12$ per share.

Kern had no other transactions affecting paid$-$in capital.

At December $31,$ what is the total amount of paid$-$in capital?

A$.$ $$6,240,000$

B$.$ $$6,180,000$

C$.$ $$5,320,000$

D$.$ $$5,440,000$