$($Related to Checkpoint $5\mathrm{.}4)($Present value$)$ Sarah Wiggum would like to make a single investment and have $$2\mathrm{.}2$

million at the time of her retirement in $25$ 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 $16$ percent, how soon could she then retire?

a$.$ If Sarah can earn $7$ percent annually for the next $25$ years, the amount of money she will have to invest today is

$$405348\mathrm{.}19.($Round to the nearest cent.$)$

b$.$ If Sarah can earn an annual return of $16$ percent, the number of years until she could retire is $$ years. $($Round to

one decimal place.$)$