$($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 $32$ years. She has found a mutual fund that will

earn $7$ percent annually. How much will Sarah have to invest today? If Sarah earned an annual return of $17$ percent, how soon could she then retire?

a$.$ If Sarah can earn $7$ percent annually for the next $32$ years, the amount of money she will have to invest today is $$240,956\mathrm{.}37.($Round to the nearest cent.$)$

b$.$ If Sarah can earn an annual return of $17$ percent, the number of years until she could retire is years. $($Round to one decimal place.$)$