Problem 52 - College Algebra Essentials

Question

A job pays an annual salary of \(\$ 33,150\), which includes a holiday bonus of \(\$ 750 .\) If paychecks are issued twice a month, what is the gross amount for each paycheck?

Step-by-Step Solution

Answer

The gross amount for each paycheck is \$1350.

Step 1: Excluding the Bonus

First, exclude the holiday bonus from the total annual salary. This is done by subtracting the bonus from the total salary, \( $33150 - $750 = $32400 \). Now, $32400 is the total amount that is paid evenly throughout the year.

Step 2: Calculate the Gross Paycheck Amount

The next step is to calculate the gross monthly salary, considering that there are 12 months in a year. This is done by dividing the annual salary (minus the bonus) by the number of months in a year. Thus, \( $32400 / 12 = $2700 \) is the gross monthly salary.

Step 3: Calculate Bi-monthly Paycheck

Finally, calculate the amount of each paycheck. As the salary is paid twice a month, divide the monthly salary by 2 to get the gross amount for each paycheck. \($2700 / 2 = $1350 \). Therefore, the gross amount for each paycheck is $1350.