Emma is $27$ years old and just started a new job at a company that offers a $401($k$)$ plan. Her annual salary is $$48,000,$ and she is paid biweekly. Emma would like to have $$800,000$ in her $401(k)$ when she reaches age $65.$ Her company does not offer any matching, and she expects that her investments can earn $8\%.$ What percent of salary should Emma contribute to her $401(k)$ to reach her goal?