Offer $1$

$$927,505$ immediate signing bonus

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

Offer $2$

$$213,753$ 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 $3$

$$1,005,501$ 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 $4$

$$177,505$ bonus for any year Luke is selected to play in the Pro Bowl All Star game $(25\%$ probability in each year$)$

Canadian Football League

$$1,127,505$ immediate signing bonus

$$2,000,000$ at the end of Years $1$ through $3$

Only signing bonus is guaranteed $(80\%$ probability of being on team each year$)$ How much is the signing bonus worth today? $$913,753$ $$772,650$ $$927,505$ $$941,258$