Sam's Year $2$ taxable income was $$175,000$ with a corresponding tax liability of $$30,000.$ For Year $3,$ Sam expects taxable income of $$250,000$ and a tax liability of $$50,000.$ In order to avoid a penalty for underpayment of estimated tax, what is the minimum amount of Year $3$ estimated tax payments that Sam can make?

A$.$ $$45,000$

B$.$ $$33,000$

C$.$ $$30,000$

D$.$ $$50,000$