Business Mathematics: Payroll - Net Pay

A deduction is anything that decreases gross pay. For instance, gross pay may be reduced by deductions for union dues or for taxes (either federal, state, or city). Net pay is the amount of money that an employee takes home and is equal to gross pay less any deductions.

Example 9
If Bob’s gross pay is $300 and if his employer deducts $10 for union dues and $30 for taxes, how much does Bob take home?
Total deductions: $10 + $30 = $40
Gross pay – total deductions = take-home or net pay
$300 – $40 = $260

Deductions required by law are called mandatory deductions and include:
Federal Withholding Taxes. Under the federal withholding tax system (commonly known as “pay as you go”), federal income tax is collected in the year in which the income is received, rather than in the following year. Thus, employers must withhold funds for the payment of their employees’ federal income taxes that will come due the following year. The amount to be withheld depends upon the number of exemptions the employee is allowed (on Form W-4), the amount of the employee’s earnings, and the employee’s marital status. An employee is entitled to one personal exemption and one for his or her spouse and each dependent.
Federal Insurance Contributions Act (FICA). The FICA tax (a combination of social security and Medicare) helps pay for federal programs for old age and disability benefits, Medicare, and insurance benefits to survivors. During working years, money is set aside from an employee’s earnings and placed along with all other employees’ contributions to the Social Security fund. When the employee’s earnings cease because of disability, retirement, or death, money from this fund is made available to his or her dependents, survivors, or to the employee himself or herself. A combined tax rate of 7.65% [6.2% for old-age, survivors, and disability insurance (OASDI), also known by the more popular term “Social Security,” and 1.45% for hospital insurance (Medicare)] is imposed on both employer and employee. The OASDI rate (6.2%) applies to wages within the OASDI wage base, which is $72,600 (1999). The Medicare rate (1.45%) applies to all wages with no limit.

Example
If, in a given payroll period, a total of $85 was withheld from employees’ wages for Social Security taxes, the employer must remit $170 to the government. The $170 represents the $85 contribution by the employees plus the employer’s matching share.
Wages in excess of $72,600 paid to a worker in one calendar year by one employer are not subject to the social security tax portion of FICA taxes.

Example
Barbara’s earnings prior to this week were $72,000. This week her salary is $500. Her FICA deduction would be $38.25 ($500 × 7.65%). If Barbara had earned $72,400 prior to this pay period, instead of the $72,000, only $200 of this week’s $500 salary would be subject to the Social Security tax ($200 × 6.2% = $12.40) but the entire $500 would be subject to Medicare tax ($500 × 1.45 = $6.25) for a total FICA deduction of $18.65.
Note that the withholding of any wages represents, from the employer’s viewpoint, a liability, because the employer must pay to the government the amount withheld from the employee.
In addition to taxes, or involuntary deductions, there may be a number of voluntary deductions made for the convenience of the employee, such as group insurance premiums, hospitalization programs, savings plans, retirement payments, union dues, and charitable contributions.

Example
Harold Eccleston earned $300 for the week. Deductions from his pay were as follows: federal withholding taxes of $50, FICA tax of $23, insurance of $6, and union dues of $10. What is his net pay?


Solved Problems

3.35   The federal income tax withheld from B. Sheppard’s gross pay is $17.56 and the FICA tax is 7.65%. What is her net pay if her gross earnings for the week ending January 12 are $236.87?
 

Solution

* FICA tax: $236.87 × 0.0765 = $18.12

3.36  If H. Bart has $25 withheld from his gross pay for U.S. savings bonds and also contributes $15 per week directly through his employer to his favorite charitable organization, what is his net pay, to the nearest cent, if his gross pay is $489.55 per week, federal income tax deduction is $33.98, and the FICA tax is 7.65%?
 

Solution

* FICA tax: $489.55 × 0.0765 = $37.45

3.37   The following deductions were made from S. Sarles’ gross pay:
 

If her gross pay is $333.33, what is her net pay?
 

Solution


3.38   At Schmidt Electric the employees’ contribution to the pension plan is 3% of their gross pay. If A. Levinson’s gross pay is $543.21, federal income tax withheld is $40.65 and FICA tax is 7.65%, what is his net pay?
 

Solution

* FICA tax: $543.21 × 0.0765 = $41.56
** Pension plan: $543.21 × 0.03 = $16.30

3.39  Find the net pay for P. Doyle if her gross pay is $257.34 per week and her deductions are $20.57 in federal income tax per week, $19.69 in FICA tax per week, and $20 in hospitalization insurance per month.
 

Solution

* Hospitalization insurance: $20/mo ÷ 4 wk/mo = $5/wk

3.40   D. Feldman pays $5.75 per week union dues. If his gross pay is $445.98 for the pay period and $23,190.96 for the year to date, his federal income tax withholding is $32.67, and his FICA tax is 7.65%, what is his net pay?
 

Solution

* FICA tax: $445.98 × 0.0765 = $34.12

3.41   An employee’s year-to-date gross pay is $36,799. Her current week’s earnings amount to $735.98, her federal income tax withheld is $52.67, and her FICA tax is 7.65%. What is her net pay?

Solution


3.42   At Lord Enterprise the employees contribute 1 % of their gross pay to their favorate charitable organization, 2% toward union dues, 3% toward life insurance, and 4% toward hospitalization insurance. If B. Hill’s gross pay is $675, federal income tax withholding is $49.87, and FICA tax is $51.64, what is his net pay?
 

Solution

* Charitable organization: $675.00 × 0.01 = $6.75
** Union dues: $675.00 × 0.02 = $13.50
*** Life insurance: $675.00 × 0.03 = $20.25
† Hospitalization insurance: $675.00 × 0.04 = $27.00

3.43   L. Bolt’s gross pay so far this year totals $73,000. Her gross pay for the week ending December 27 is $640.75, federal income tax withheld is $50.87, FICA tax is 7.65% and union dues deduction is $7.50. She also has deducted $50 for U.S. savings bonds and $50 for her automatic savings account. Find her net pay.
 

Solution

* $640.75 × 1.45% (Medicare tax) = $9.29

3.44   Ascertain the net pay for an employee whose gross pay is $256.93 per week, federal income tax withheld is $20.41, FICA tax is 7.65%, hospitalization insurance is $6.70, union dues deduction is $4.60, and life insurance is $5. In addition, the employee has made a loan through his employer whereby the employee agreed to a deduction of $25 per week from his paycheck until said loan is paid.

* FICA tax: $256.93 × 0.0765 = $19.66

3.45   Kaufmann Insulation pays its employees biweekly. In addition to the federal income tax withheld, each employee’s deductions are as follows:

Each employee also receives a $20 uniform allowance. Given the following gross pay, federal income tax withheld, and year-to-date gross pay for each employee, find the respective net pay to the nearest cent.

 

Solution

* FICA tax: ($72,600 ÷ $72,500) × 6.2% = $100 × 0.062 = $6.20 $1,570.90 × 0.0145% = $22.78

* Social security tax is taken only on the first $72,600 in gross yearly earnings.
Medicare tax $1,734.66 × 0.0145 = $25.15

* FICA tax: $1,269.70 × 0.0765 = $97.13

* FICA tax: $1,041.12 × 0.0765 = $79.65

* FICA tax: $867.24 × 0.0765 = $66.34

3.46  At Pond Computer Systems, the following deductions are made from the employees’ pay, in addition to the federal income tax withheld:

Given the gross pay, federal income tax withheld, year-to-date gross pay, and optional deductions, find the net pay to the nearest cent for the following employees:

More Problems

3.47  Sarah Litt worked 32½ hours last week at an hourly rate of $6.20. Find her gross pay.
3.48  Find the gross pay of an employee who worked 22¾ hours at an hourly rate of $6.70.
3.49  Richard Hammer’s time card shows the following hours worked:

His hourly rate is $7.50 plus time-and-a-half for any hours worked over 40 per week. Determine (a) his total hours worked and (b) gross pay.

3.50 Determine the total hours worked and the gross pay for the following employees of Tyson Automotive:


3.51 Patricia Gray received $239.25 gross pay for 33 hours worked. What is her hourly rate?
3.52 An employee received $221 gross pay and worked 34 hours. What is the employee’s hourly rate?
3.53 Given the gross pay and the hours worked, find the hourly rate for the following:


3.54 Determine the total hours worked by George Townsend if his hourly rate is $8.40 and his gross pay is $302.40.
3.55 Janis Klein works as a carpenter for Johnston Construction Company. Her gross pay for last week was $316.80 and her hourly rate is $9.60. Calculate her total hours worked.
3.56 Given the following information, determine the hours worked.


3.57 An employee worked the following hours during the week:

Calculate his gross pay at an hourly rate of $6.40 plus time-and-a-half for any hours over 8 per day.

3.58 On Tuesday and Thursday Margaret Darder worked 9½ hours each day. On Monday, Wednesday, and Friday, she worked 7 hours each day. Her hourly rate is $9.00 plus time-and-a-half for any hours in excess of 8 per day. What is her gross pay?

3.59 Find the gross pay for John Devore if he earns $6.80 per hour, time-and-a-half for any hours over 8 per day, and double time for working on Sundays. His time card for the week ending September 24 is as follows:


3.60 The following employees of B&B Concrete, Inc. each receive an hourly rate of $6.20, plus time-and-a-half for hours in excess of 8 per day, and double time for Sundays and holidays. (New Year’s Day is designated as a holiday.) Calculate each employee’s gross pay.


3.61 Calculate the gross pay for Rita Hansen. Her time card for the week ending June 27 shows 51¼ hours worked. Her rate of pay is $8.60 per hour plus time-and-a-half for any hours over 40 per week.

3.62 Given the hours worked and hourly rate of pay, find the overtime rate (at time-and-a-half) and gross pay for the following. Overtime is paid for hours worked in excess of 40 per week.


3.63 For the following employees of Brog Sewing Machine Company, calculate
   (a)   Regular hours
   (b)   Regular pay
   (c)   Overtime hours (hours in excess of 40 per week)
   (d)   Overtime rate (time-and-a-half)
   (e)   Overtime pay
   (f)   Gross pay


3.64 V. Friedman is paid $35,600 annually. Her pay period is biweekly. What are her gross earnings per pay period to the nearest cent?
3.65 An employee receives $17,900 per year and is paid monthly. Determine the gross earnings per pay period to the nearest cent.
3.66 Given the following, find the annual salary for (a), the pay period for (b), and the gross earnings per pay period for (c).


3.67  Harry Lober receives a 7½% commission on all his real estate sales. Half the commission goes to his broker. Of his commission on $133,300 in sales, how much does Harry get to keep?

3.68 During a month’s time an automobile salesperson receives 6% commission on the first $5,000 in sales, 7% commission on the next $5,000 in sales, and 8% commission on anything over $10,000. What is her commission on $36,000 in sales?

3.69 Victor Link receives a biweekly salary of $500 plus a 5½% commission on his total sales for the month. What are his gross monthly earnings if his total sales for the month were $3,485?

3.70 Elise Thompson is paid a 5% commission on the first $800 in paint sales, 6% on the next $800, and 7% on anything over $1,600 in sales. She also receives a $150 per week draw. To the nearest cent, find the difference she receives at the end of the week between the draw and the commission. Her net sales for the week totaled $3,600.

3.71 Assuming the federal income tax withheld from C. Thomas’ gross pay is $26.94 and the FICA tax is 7.65%, what is his net pay to the nearest cent, if his gross earnings for the week ending January 5 are $345.70?

3.72 At Vallone Computer Company the employees’ contribution to the pension plan is 2½% of their gross pay. If B. Kinney’s gross pay is $467.36, federal income tax withheld is $38.62, and FICA tax is 7.65%, what is her net pay?

3.73 Find the net pay for T. Fagan if his gross pay is $298.76 per week and his deductions are $23.69 federal income tax per week, $22.86 FICA tax per week, and $10 life insurance per month.

3.74 An employee’s year-to-date gross pay is $38,670. Her current week’s earnings amount to $660.20, her federal income tax withheld is $47.81, and her FICA tax is 7.65%. What is her net pay?

3.75 Bush Inc. pays its employees biweekly. In addition to the federal income tax withheld, each employee’s deductions are as follows:

   Given gross pay, federal income tax withheld, and year-to-date gross pay, find the net pay to the nearest cent for the following employees:

Answers to Problems:

3.47 $201.50
3.48 $152.42
3.49 (a) 40, (b) $280 No overtime
3.50 (a) 34.75 h, $225.88; (b) 36 h, $288
3.51 $7.25/h
3.52 $6.50/h
3.53 (a) $8.00/h, (b) $11.20/h, (c) $6.77/h, (d) $7.70/h
3.54 36
3.55 33
3.56(a) 36, (b) 31, (c) 39, (d) 22
3.57 $316.80
3.58 $373.50
3.59 $336.60
3.60 (a) $288.30, (b) $325.50
3.61 $489.11
3.62 (a) $12.00/h, $244.23; (b) $9.525/h, $308,77; (c) $11.25/h, $460.31
3.63 B. Halper: (a), 40, (b) $260, (c) 2, (d) $9.75/h, (e) $19.50, (/) $279.50 T. Shaver: (a) 36.25, (b) $210.25, (c) 0, (d) $8.70/h, (e) $0, (/) $210.25
3.64 $1,369.23
3.65 $1,491.67
3.66 (a) $14,553.76, (b) 26 pay periods/per year or biweekly, (c) $1,750
3.67 $4,998.75
3.68 $2,730
3.69 $1,191.68
3.70 $78
3.71 $292.31
3.72 $392.99
3.73 $249.71
3.74 $561.89
3.75 (a) $1,038.02, (b) $1,612.74