Sarah Wiggum would like to make a single investment and have $$$$2\mathrm{.}1$ million at the time of her retirement in $25$ years. She has found a mutual fund that will earn $7$ percent annually. How much will Sarah have to invest$$ today? If Sarah earned an annual return of $16$percent$,$ how soon could she then$$ retire?$$

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Part $1$

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