$($Related to Checkpoint $5\mathrm{.}4)($Present value$)$ Sarah Wiggum would like to make a single investment and have $$1\mathrm{.}6$ million at the time of her retirement in $25$ years. She has found a mutual fund that will earn $8$ percent annually. How much will Sarah have to invest today? If Sarah earned an annual return of $14$ percent, how soon could she then retire?

a$.$ If Sarah can earn $8$ percent annually for the next $25$ years, the amount of money she will have to invest today is $$,($Round to the nearest cent.$)$