You just purchased two coins at a price of $$490$ each. Because one of the coins is more collectible, you believe that its value will increase at a rate of $6\mathrm{.}8$ percent per year, while you believe the second coin will only increase at $6\mathrm{.}2$ percent per year. If you are correct, how much more will the first coin be worth in $25$ years?

Multiple Choice

$$79\mathrm{.}04$

$$569\mathrm{.}04$

$$172\mathrm{.}58$

$$471\mathrm{.}68$