$($Do this in excel$)$ The price of a textbook fluctuates over time. If you want to secure the right to buy a textbook in three months $($you may choose to buy it$,$ and not to$),$ the bookstore will grant you this by issuing you a $$contract$.$ It allows you to buy the book at $$30$ in three months. But they will charge you $$10$ if you want this $$contract$.$ So you paid $$10$ and get the contract.

Suppose that in three months, the market price on this textbook can be $$10,$ $$20,$ $$30,$ $$40,$ or $$50.$ For each of these possible prices, answer: $(1)$ do you want to exercise the contract, $(2)$ what would be your payoff $(3)$ and profit?