You want to invest your money $($$$10,000),$ but you are not sure whether to invest in stocks or leave it in the bank. If you invest in stocks, you may gain $$1,000($if the stocks go up$,$ which you estimate at a $80\%$ chance$)$ or lose $$2,000($if stocks go down, with $20\%$ chance$).$ If you leave your money in the bank, you will get a certain $$400.$ To help you decide, you can ask an expert, who can provide a information about the stock market. Up to how much should you be willing to pay to the expert, assuming they can tell you what happens to the stock market with $100\%$ certainty?

A$.$ $$120$

B$.$ $$400$

C$.$ $$0$

D$.$ $$480$