Springfield mogul Montgomery Burns, age $85,$ 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 $8$ years from a special offshore account that will pay $24$ percent annually. In order to fund his retirement, Mr$.$Burns will make $15$ equal end$-$of$-$the$-$year deposits in this same special account that will pay $24$ 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?