X Corporation anticipates the following purchases for the next three months: Month $1-$ $$400,000,$ Month $2-$ $$450,000,$ Month $3-$ $$500,000.$ The company's payment pattern is $40\%$ in the month of purchase and $60\%$ in the following month. What is the total expected cash payment for Month $3?$

$$290,000$

$$320,000$

$$360,000$

$$470,000$