Mint Company had $300,000$ shares of common stock issued and outstanding at December $31,20$X$1.$ No common stock was issued or repurchased. On January $1,20$X$2,$ Mint issued $40,000$ shares of $3\%,$ $$100$ par convertible non$-$participating preferred stock. In $20$X$2,$ Mint earned net income of $$720,000$ and declared and paid total cash dividends of $$300,000.$ In computing diluted earnings per share, what is the numerator?

$$720,000$

$$816,000$

$$840,000$

$$600,000$