Springfield mogul Montgomery$$ Burns, age $80,$ wants to retire at age $100$ so he can steal candy from babies full time. Once Mr$.$ Burns$$ retires, he wants to withdraw $$$$1$ billion at the beginning of each year for $10$ years from a special offshore account that will pay $20$ percent annually. In order to fund his$$ retirement, Mr$.$ Burns will make $20$ equal$$ end$-$of$-$the$-$year deposits in this same special account that will pay $20$ percent annually. How much money will Mr$.$ Burns need at age$100,$ and how large of an annual deposit must he make to fund this retirement$$ account?