Problem 52 - College Algebra

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 approximately \$1297.92.

Step 1: Identify and Subtract Bonus

Subtract the holiday bonus from the total annual salary to identify the amount earned from regular pay. So, \( \$33150 - \$750 = \$30400\).

Step 2: Calculate Pay per Paycheck

Determine the amount per paycheck by dividing the regular pay by the number of paychecks in a year. Since paychecks are issued twice a month and there are 12 months in a year, there are \(2*12=24\) paychecks. \( \$30400 / 24 \approx \$1266.67\).

Step 3: Determine Gross Paycheck Amount

The gross amount for each paycheck is a combination of regular pay and evenly distributed holiday bonus. Thus, divide the holiday bonus by the number of paychecks. \( \$750 / 24 \approx \$31.25\). Add this to the regular paycheck amount. \( \$1266.67 + \$31.25 = \$1297.92 \)