What contract should Steve Luke take?

You should discount future cash at a $10\%$ interest rate.

Offer $1$

$$906,420$ immediate signing bonus

$$850,000$ at the end of each year for the next $5$ years

Offer $2$

$$203,210$ immediate signing bonus

$$100,000$ at the end of years $1$ through $4$

$$150,000$ at the end of years $5$ through $10$

$$1,000,000$ and the end of years $11$ through $40$

Offer $3$

$$1,001,284$ immediate signing bonus

$$500,000$ at the end of year $1$

$$1,000,000$ at the end of year $2$

$$1,500,000$ at the end of year $3$

$$2,500,000$ at the end of year $4$

$$156,420$ bonus for any year Luke is selected to play in the Pro Bowl All Star game $(25\%$ probability in each year$)$