Suppose a certain business pays $10\%$ tax on its first $$10,000$ in come, $12\%$ tax on income above $$10,000$ but below $$40,000,$ and $22\%$ tax on income above $$40,000.$ Suppose the business earns $$50,000$ in income this year. It tax liability is $\_\_\_\_\_\_\_\_.$

$$9,800$

$$6,800$

$$11,000$

$$5,800$