Your big brother deposited $$10,000$ today at $5\%$ interest for $6$ years. You would like to have just as much money at the end of the next $6$ years as your brother. However, you can only earn $3\%$ interest. How much more money must you deposit today than your brother did if you are to have the same amount at the end of the $6$ years?Question $13$ options: $$11,223\mathrm{.}09$ $$2,487\mathrm{.}63$ $$1,223\mathrm{.}09$ $$1,648\mathrm{.}21$ None of the above