John invested $\$5,000$ in a savings account that offers a simple annual interest rate of $8\%$. After three years, he invested the total value of his investment in a new account with a simple annual interest rate of $r\%$ for two years. If the total value of his investment after the two years was $\$6,120$, what is the annual interest rate $r$ of the second account? Let's think step by step and output the final answer within \boxed{}.
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