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 $$54000$ 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 $1,827,246,639,298$ and not $1,827,246,639,000?$ How did you work this out on the calculator$/$classpad to get the full answer not in scientific notation?