Jane won the $$70$ million lottery. She is to receive $$1$ million a year for the next $50$ years beginning one year from now, plus an additional lump sum payment of $$10$ million after $50$ years. The discount rate is $10$ percent. How much cash would she need to be offered today to tempt her to take a lump$-$sum cash offer instead, all things equal? Please show all your work.