Sarah Wiggum would like to make a single investment and have $$$$3\mathrm{.}1$ million at the time of her retirement in $25$ years. She has found a mutual fund that will earn $6$ percent annually. How much will Sarah have to invest$$ today? If Sarah invests that amount and could earn a $13$ percent annual$$ return, how soon could she$$ retire, assuming she is still going to retire when she has $$$$3\mathrm{.}1$million$?$