When Alfred Nobel$$ died, he left the majority of his estate to fund five$$ prizes, each to be awarded annually in perpetuity starting one year after he died$($the sixth$$ one, in$$ economics, was added$$ later$).$

a$.$ If he wanted the cash award of each of the five prizes to be $$33,000$

and his estate could earn $8\%$ per$$ year, how much would he need to fund his$$ prizes?