Kyoko has $$10,000$ that she wants to invest. Her bank has several investment accounts to choose from, all compounding daily. Her goal is to have $$15,000$ by the time she finishes graduate school in $6$ years. To the nearest hundredth of a percent, what should her minimum annual interest rate be in order to reach her goal? $(20$ Points$)$

$10\mathrm{.}31\%$

$3\mathrm{.}44\%$

$6\mathrm{.}87\%$

$20\mathrm{.}62\%$