Your older sister deposited $$2,000$ today at $6\mathrm{.}5$ percent interest for $5$ years. You would like to have just as much money at the end of the next $5$ years as your sister will have. However, you can only earn $6$ percent interest. How much more money must you deposit today than your sister did if you are to have the same amount at the end of the $5$ years?

Multiple Choice

$$32\mathrm{.}19$

$$47\mathrm{.}62$

$$38\mathrm{.}78$

$$40\mathrm{.}21$

$$53\mathrm{.}39$