Sarah Wiggum would like to make a single investment and have $$$$1\mathrm{.}9$ million at the time of her retirement in $35$ years. She has found a mutual fund that will earn $5$ percent annually. How much will Sarah have to invest$$ today? If Sarah earned an annual return of $15$percent$,$ how soon could she then$$ retire?$$

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Part $1$

a$.$If Sarah can earn $5$ percent annually for the next $35$years$,$ the amount of money she will have to invest today is $$$

$$

$344451\mathrm{.}54.($Round to the nearest$$ cent.$)$

Part $2$

b$.$If Sarah can earn an annual return of $15$ percent$,$ the number of years until she could retire is

$$

enter your response here years