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

a$.$ If he wanted the cash award of each of the five prizes to be$$$$5400$ and his estate could earn $11\%$ per$$ year, how much would he need to fund his$$ prizes?

b$.$ If he wanted the value of each prize to grow by $6\%$ per year$($perhaps to keep up with$$ inflation$),$ how much would he need to$$ leave?

c$.$ His heirs were surprised by his will and fought it$.$ If they had been able to keep the amount of money you calculated in$($b$),$ and had invested it at $11\%$ per$$ year, how much would they have in$2018,122$ years after he$$ died? How is the answer $1,827,246,639,298?$