The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $8 each and will sell 500 tickets. There is one $1,000 grand prize, four $200 second prizes, and thirteen $40 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.

Please show all the work on how to solve the equation. So I can learn how to solve these type of equations.