To make CDs look more attractive as an investment than they really are, some banks advertise that their rates are higher than their competitors$$ rates; however, the fine print says that the rate is based on simple interest. If you were to deposit $$28,000$ at $13\mathrm{.}00\%$ per year simple interest in a CD$,$ what compound interest rate would yield the same amount of money in $3$ years? $($Round the final answer to three decimal places.$)$

The compound interest rate that would yield the same amount of money in $3$ years is $\_\%$ per year.