Jaylen Brown, a forward for the Boston Celtics, has been offered a seven$-$year, $$750$ million contract, where he will be paid $$90$ million a year for the next three years, and $$120$ million a year for the following four years. The appropriate discount rate is $8\%.$

$($a$)$ What is the present value of this contract?

$($b$)$ He is weighing an alternative offer from the Los Angeles Lakers, where he will be paid $$80$ million a year for the next seven years and an additional $$250$ million at the end of the seventh year. What is the present value of this contract?

$($c$)$ What would the payment at the end of the seventh year need to be for Jaylen Brown to be indifferent between the two offers?