$($Related to Checkpoint $5\mathrm{.}4)($Present value$)$ Sarah Wiggum would like to make a single investment and have $$2\mathrm{.}1$ million at the time of her retirement in $28$ years. She has found a mutual fund that will earn $5$ percent annually. How much will Sarah have to invest today? If Sarah earned an annual return of $16$ percent, how soon could she then retire?

a$.$ If Sarah can eam $5$ percent annually for the next $28$ years, the amount of money she will have to invest today is $($Round to the nearest cent$)$