A typical laborer works $50$ hours per week for $20$ weeks of the year and $40$ hours per week for $29$ weeks of the year, and the remaining $3$ weeks per year comprises holiday leave, vacation, and sick leave, for which the laborers are paid for $40$ hours per week. Laborers are paid $$10\mathrm{.}50$ per hour and are paid time and a half on any hours worked over $40$ hours per week. In the past the laborers received a $$100$ Christmas bonus. Determine the annual wages paid to the typical laborer.