Step 1 :The question asks for the weekly, hourly, and monthly salary of Damian if he gets a job that pays $62,700 per year. However, since the instruction is to only answer the first question, we will only calculate the weekly salary.
Step 2 :To calculate the weekly salary, we need to divide the annual salary by the number of weeks in a year. There are 52 weeks in a year.
Step 3 :Let's calculate this: \(\frac{62700}{52} = 1205.7692307692307\)
Step 4 :Rounding to the nearest cent, we get \(\boxed{1205.77}\) dollars as Damian's weekly salary.