$($Future value of a complex annuity$)$ 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\mathrm{.}2$ billion at the beginning of each year for $9$ years from a special offshore account that will pay $23$ 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 $23$ 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?

a$.$ If the retirement account will pay $23$ percent annually, how much money will Mr$.$ Burns need when he retires?

billion $($Round to three decimal places.$)$

b$.$ How large of an annual deposit must he make to fund this retirement account?

million $($Round to two decimal places.$)$