John worked 43 hours last week. his hourly rate is $9.00. he has the following deductions taken from his pay: social security tax at the rate of 6.2 percent, medicare tax at the rate of 1.45 percent, health insurance premiums of $15.00, and 401(k) contributions of 5 percent of gross pay. john also has federal income tax withheld at the rate of 10 percent. federal taxes do not apply to the 401(k) contribution. john’s net pay for last week was

9514 1404 393

  $286.28

Step-by-step explanation:

We can add up the percentage deductions from gross pay to make the calculation simpler.

The federal tax deduction is 10% of the amount left after the 5% 401(k) contribution is deducted, so that is (10%)(1 -5%) = 9.5% of gross pay.

Then the percentage deductions from gross pay are ...

  Social Security + Medicare + 401(k) + Federal tax

  = 6.2% +1.45% +5% +9.5% = 22.15%

After these deductions are taken, 1 -22.15% = 77.85% remains. From that, a dollar deduction of $15 is taken. Then John's net pay for the week--assuming no premium for overtime--was ...

  (43 hours) × ($9.00 /hour) × 0.7785 - $15 = $286.2795

John's net pay for last week was $286.28.

Additional comment

We have made the above computation in a way that minimizes the number of arithmetic operations that need to be performed. In practice, the Social Security and Medicare deductions will be combined to a rate of 7.65% to compute a deduction of 29.6055 ≈ 29.61. The federal tax on the taxable wage of 367.65 will be 36.765 = 36.77. So, the net pay will be ...

  367.65 -29.61 -36.77 -15 = $286.27 . . . . a difference of 1 cent

Note that we have rounded up both the SS/Medicare tax and the income tax in this calculation. If john receives paychecks from this company over the long term, the rounding will be 'up' for some pay periods and 'down' for other pay periods. The payroll department will make sure that the long-term average percentages deducted match the required amounts exactly.

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