An applicant earns $9 per hour and works 40 hours per week in typical weeks. Four weeks out of the year the applicant works an extra 10 hours per week. (Any hours over 40 in a week, the applicant receives overtime pay at "time and 1/2") There are 52 weeks in a year.

Question

Calculate the applicant's yearly gross earnings?

Answer 1

To calculate the applicant's yearly gross earnings, we need to consider both the regular pay and the overtime pay.

1. Regular Hours Calculation:

   • The regular work hours in a typical week are 40 hours.
   • The applicant earns $9 per hour.
   • For 48 weeks (52 weeks - 4 weeks of overtime), the earnings are: \[ \text{Regular earnings} = 40 \text{ hours/week} \times 9 \text{ dollars/hour} \times 48 \text{ weeks} \] \[ \text{Regular earnings} = 40 \times 9 \times 48 = 17,280 \text{ dollars} \]

2. Overtime Hours Calculation:

   • The applicant works an extra 10 hours in each of the 4 overtime weeks, bringing the total hours worked in those weeks to 50 hours (40 regular + 10 overtime).
   • Overtime pay is at "time and a half," which is: \[ \text{Overtime rate} = 9 \text{ dollars/hour} \times \frac{3}{2} = 13.50 \text{ dollars/hour} \]
   • The hours eligible for overtime are the extra 10 hours per week for 4 weeks: \[ \text{Overtime earnings} = 10 \text{ hours/week} \times 13.50 \text{ dollars/hour} \times 4 \text{ weeks} \] \[ \text{Overtime earnings} = 10 \times 13.50 \times 4 = 540 \text{ dollars} \]

3. Total Yearly Gross Earnings:

   • Now, we add the regular earnings and the overtime earnings together: \[ \text{Total earnings} = \text{Regular earnings} + \text{Overtime earnings} \] \[ \text{Total earnings} = 17,280 + 540 = 17,820 \text{ dollars} \]

Thus, the applicant's yearly gross earnings are $17,820.