4.E: Human Resources and Economic Applications (Exercises)
- Page ID
- 38100
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4.1 Exercises
Mechanics
- Laars earns an annual salary of $60,000. Determine his gross earnings per pay period under each of the following payment frequencies:
- Monthly
- Semi-monthly
- Biweekly
- Weekly
- A worker earning $13.66 per hour works 47 hours in the first week and 42 hours in the second week. What are his total biweekly earnings if his regular workweek is 40 hours and all overtime is paid at 1.5 times his regular hourly rate?
- Marley is an independent sales agent. He receives a straight commission of 15% on all sales from his suppliers. If Marley averages semi-monthly sales of $16,000, what are his total annual gross earnings?
- Sheila is a life insurance agent. Her company pays her based on the annual premiums of the customers that purchase life insurance policies. In the last month, Sheila's new customers purchased policies worth $35,550 annually. If she receives 10% commission on the first $10,000 of premiums and 20% on the rest, what are her total gross earnings for the month?
- Tuan is a telemarketer who earns $9.00 per hour plus 3.25% on any sales above $1,000 in any given week. If Tuan works 35 regular hours and sells $5,715, what are his gross earnings for the week?
- Adolfo packs fruit in cans on a production line. He is paid a minimum wage of $9.10 per hour and earns $0.09 for every can packed. If Adolfo manages to average 160 cans per hour, what are his total gross earnings daily for an eight-hour shift?
Applications
- Charles earns an annual salary of $72,100 paid biweekly based on a regular workweek of 36.25 hours. His company generously pays all overtime at twice his regular wage. If Charles worked 85.5 hours over the course of two weeks, what are his gross earnings?
- Armin is the payroll administrator for his company. In looking over the payroll, he notices the following workweek (from Sunday to Saturday) for one of the company's employees: 0, 6, 8, 10, 9, 8, and 9 hours, respectively. Monday was a statutory holiday, and with business booming the employee will not be given another day off in lieu. Company policy pays all overtime at time-and-a-half, and all hours worked on a statutory holiday are paid at twice the regular rate. A normal workweek consists of five, eight-hour days. If the employee receives $22.20 per hour, what are her total weekly gross earnings?
- In order to motivate a manufacturer's agent to increase his sales, a manufacturer offers monthly commissions of 1.2% on the first $125,000, 1.6% on the next $150,000, 2.25% on the next $125,000, and 3.75% on anything above. If the agent managed to sell $732,000 in a single month, what commission is he owed?
- Humphrey and Charlotte are both sales representatives for a pharmaceutical company. In a single month, Humphrey received $5,545 in total gross earnings while Charlotte received $6,388 in total gross earnings. In sales dollars, how much more did Charlotte sell if they both received 5% straight commission on their sales?
- Mayabel is a cherry picker working in the Okanagan Valley. She can pick 17 kg of cherries every hour. The cherries are placed in pails that can hold 13.6 kg of cherries. If she works 40 hours in a single week, what are her total gross earnings if her piecework rate is $17.00 per pail?
- Miranda is considering three relatively equal job offers and wants to pick the one with the highest gross earnings. The first job is offering a base salary of $1,200 semi-monthly plus 2% commission on monthly sales. The second job offer consists of a 9.75% straight commission. Her final job offer consists of monthly salary of $1,620 plus 2.25% commission on her first $10,000 in monthly sales and 6% on any monthly sales above that amount. From industry publications, she knows that a typical worker can sell $35,000 per month. Which job offer should she choose, and how much better is it than the other job offers?
- A Canadian travel agent is paid a flat rate of $37.50 for every vacation booked through a certain airline. If the vacation is in North America, the agent also receives a commission of 2.45%. If the vacation is international, the commission is 4.68%. What are the total monthly gross earnings for the agent if she booked 29 North American vacations worth $53,125 and 17 international vacations worth $61,460?
- Vladimir's employer has just been purchased by another organization. In the past, he has earned $17.90 per hour and had a normal workweek of 37.5 hours. However, his new company only pays its employees a salary semi-monthly. How much does Vladimir need to earn each paycheque to be in the same financial position?
Challenge, Critical Thinking, & Other Applications
- An employee on salary just received his biweekly paycheque in the amount of $1,832.05, which included pay for five hours of overtime at time-and-a-half. If a normal workweek is 40 hours, what is the employee's annual salary?
- A graduated commission scale pays 1.5% on the first $50,000, 2.5% on the next $75,000, and 3.5% on anything above. What level of sales would it take for an employee to receive total gross earnings of $4,130?
- A sales organization pays a base commission on the first $75,000 in sales, base + 2% on the next $75,000 in sales, and base + 4% on anything above. What is the base commission if an employee received total gross earnings of $7,500 on $200,000 in sales?
- A typical sales agent for a company has annual sales of $4,560,000, equally spread throughout the year, and receives a straight commission of 2%. As the new human resource specialist, to improve employee morale you have been assigned the task of developing different pay options of equivalent value to offer to the employees. Your first option is to pay them a base salary of $2,000 per month plus commission. Your second option is to pay a base commission monthly on their first $100,000 in sales, and a base + 2.01% on anything over $200,000 per month. In order to equate all the plans, determine the required commission rates, rounded to two decimals in percent format, in both options.
- Shaquille earns an annual salary of $28,840.50 paid biweekly. His normal workweek is 36.25 hours and overtime is paid at twice the regular rate. In addition, he is paid a commission of 3% of sales on the first $25,000 and 4% on sales above that amount. What are his total gross earnings during a pay period if he worked 86 hours and had sales of $51,750?
- Mandy is paid $9.50 per hour and also receives a piecework wage of $0.30 per kilogram, or portion thereof. A regular workday is 7.5 hours and 37.5 hours per week. Overtime is paid at time-and-a-half, and any work on a statutory holiday is paid at twice the regular rate. There is no premium piecework wage. Mandy's work record for a two-week period is listed below. Determine her total gross earnings.
| Week | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | |
|---|---|---|---|---|---|---|---|
| 1 | Hours worked | 7.5 | 7.5 | 9 | 8 | 7.5 | 3 |
| 250 g items produced | 1,100 | 1,075 | 1,225 | 1,150 | 1,025 | 450 | |
| 2 | Hours worked | 4 Statutory holiday, no day off in lieu | 7.5 | 10 | 7.5 | 8 | |
| 250 g items produced | 575 | 1,060 | 1,415 | 1,115 | 1,180 | ||
Section 4.2 Exercises
Use the provincial and federal tax tables introduced earlier in this chapter when you determine income taxes in these exercises.
Mechanics
For questions 1–3, determine only the federal income taxes on the following gross taxable incomes.
- $22,375
- $158,914
- $102,100
For questions 4–6, determine only the provincial income taxes on the following gross taxable incomes.
- $61,000 in Newfoundland and Labrador
- $83,345 in Saskatchewan
- $78,775 in British Columbia
For questions 7 and 8, determine the total federal and provincial/territorial taxes on the following gross taxable incomes.
- $48,910 in the Northwest Territories
- $65,525 in Prince Edward Island
Applications
- Nadia lives in Manitoba and has three part-time jobs. Her gross annual taxable income from each job was $5,300, $21,450, and $25,390. How much federal and provincial income tax does Nadia owe?
- If Delaney's gross taxable income increases from $71,000 to $79,000, by what dollar amount will her after-tax pay change once federal and provincial income taxes are deducted in the province of Quebec?
- Helen just moved from Saskatchewan to her new job in Alberta at the same rate of pay of $51,225. By what dollar amount will her provincial income taxes change?
- Jane has received two job offers that she thinks are relatively equal. The only difference lies in the salary. The first job offer is for a position in Nova Scotia earning gross taxable income of $63,375. The second job offer is for a position in British Columbia earning gross taxable income of $61,990. If Jane will select the job that has the highest after-tax income, which one should she choose? How much better is this option in dollars?
- Suppose an employee earns $111,300 in gross taxable income. Calculate the federal and provincial income taxes that need to be deducted if he lives in either Saskatchewan, Ontario, or the Northwest Territories. In which province or territory will he earn the most income after income tax deductions? The least? What is the dollar amount difference among the three alternatives?
- After both federal and provincial income taxes are deducted, who would earn more money, an individual earning $85,000 in New Brunswick or an individual earning $79,000 in Nunavut?
Challenge, Critical Thinking, & Other Applications
- Rawatha is the human resources manager for her firm located in Yukon. The salespeople for her organization are paid an annual base salary of $30,000 plus 8% straight commission on their annual sales. If the average salesperson sells $210,000 annually, what is the total annual federal and provincial income tax owing on the salesperson's gross taxable income?
- Esmerelda works on the production line and is paid a piecework rate of $2.25 per unit produced. She is capable of producing an average of five units per hour, and works eight hours every weekday. Assuming a 52-week year, what is the annual federal income tax and provincial income tax owing if she lives in Prince Edward Island?
- Mary Jane is paid biweekly at a rate of $34.68 per hour and works 36.25 hours every week. Assuming a 52-week year, what are the amounts of the federal income tax deduction and provincial income tax deduction that must be removed from each paycheque if Mary Jane lives in Manitoba? (Hint: income tax would be deducted equally across all paycheques for the year.)
- Felix was transferred from his head office in Ontario to Alberta. In accepting the transfer, his employer agreed to increase his salary of $88,000 by $7,000. What is the percent change in Felix's after-tax income?
- If a wage earner paid $2,277.98 in total annual Ontario provincial income taxes, determine his annual gross taxable income.
- Perform a comparison across all territories and provinces of the income earned after both federal and provincial income taxes are deducted for a Canadian who earns $56,738 in gross taxable income. Which province or territory has the highest income after deductions? Which has the lowest? What is the percent difference between the two?
Section 4.3 Exercises
Mechanics
For questions 1–4, solve for the unknown variables (identified with a ?) based on the information provided. Round index numbers to one decimal and base values to the nearest integer.
| Chosen Quantity ($) | Base Quantity ($) | Base Value | Index Number | |
|---|---|---|---|---|
| 1. | $559.99 | $539.99 | 100 | ? |
| 2. | $315,000.00 | ? | 1,000 | 12,415.9 |
| 3. | $114.30 | $112.50 | ? | 101.6 |
| 4. | ? | $248.75 | 1,000 | 1,548.9 |
For questions 5–9, solve for the unknown variables (identified with a ?) based on the information provided.
| Consumer Price Index (CPI) | Purchasing Power of a Dollar (PPD) | |
|---|---|---|
| 5. | 107.9 | ? |
| 6. | ? | 80% |
| Nominal Income ($) | Consumer Price Index (CPI) | Real Income (RI) | |
|---|---|---|---|
| 7. | $45,000.00 | 120.0 | ? |
| 8. | ? | 105.0 | $29,523.81 |
| 9. | $86,000.00 | ? | $80,298.71 |
Applications
- In Regina, a 4 L bag of 2% milk has an average price of $3.71. Prices in Toronto and Montreal are $4.55 and $5.40, respectively. Calculate an index of these prices using Regina as the base.
- If Sabrina is currently earning $53,000 and the CPI changes from 105.9 to 107.6, how much money does she need to earn next year just to keep up with inflation?
- If the CPI rises from 103.4 to 108.8, how much money at the start is required to have the same purchasing power as $100 at the end?
- George currently earns $28,000 per year. As per his union salary grid, next year he will earn $32,500 per year. If the CPI increases from 104.0 to 106.1 over the same time frame, how much of his raise is real income?
- Last year the purchasing power of a dollar was 84.3%. This year the purchasing power of a dollar is 81.4%. What is the percent change in the CPI between the two years?
Challenge, Critical Thinking, & Other Applications
- An investor had $200,000 invested in an S&P/TSX Composite Index portfolio in 2009. By 2011, the index rose to 14,136.50. If the index in 2009 was 8,694.90, how much money would the investor have in her portfolio in 2011, if she was able to match the market performance?
- Over the years, Hannah's income has changed from $36,000 to $40,000 to $45,000. If the CPI changed from 102.9 to 105.1 to 108.6 over the same time period, determine Hannah's percent change in real income from year to year.
- The CPI rose from 102.6 in 2003 to 116.5 in 2010. The S&P/TSX Composite Index rose from 6,569.49 to 11,294.42 over the same time period. If an investor had $125,000 invested in 2003, how much of the growth (in dollars) for the portfolio over the seven years represents real growth?
- An enterprise has 136 employees earning an average income of $42,250 per year. If the CPI rises from 103.7 to 107.2, by what amount do total wages rise if all employee wages are adjusted to match the CPI?
- Using January 2003 as your base year with a base value = 100, compute a series of indexes for the S&P/TSX Composite Index from select years in 2003 to 2011. Interpret your results.
| 2003 | 2005 | 2007 | 2009 | 2011 | |
|---|---|---|---|---|---|
| January index | 6,569.49 | 9,204.05 | 13,034.12 | 8,694.90 | 13,551.91 |
- Below is select information on the CPI from 2004 to 2010:
| 2004 | 2006 | 2008 | 2010 | |
|---|---|---|---|---|
| July CPI | 105.0 | 109.6 | 115.8 | 116.8 |
Using this information, determine the following:
- The purchasing power of a dollar for each year. Interpret your results.
- If you were earning $34,500 in 2002, calculate the nominal income required each year to keep up with the changes in the CPI.
Chapter 4 Review Exercises
For any questions involving income tax calculations, refer to the tables previously introduced in this chapter for federal income taxes and provincial/territorial income taxes.
Mechanics
- Jim's annual salary is $45,670 paid weekly for 36.25 hours of work each week. Determine his total gross earnings for one pay period in which he worked 8.75 hours of overtime.
- Tracy is paid 4% commission on any sales above $150,000 plus a base salary of $500. What are her gross earnings for a pay period where her sales were $225,000?
- Sisko has annual gross taxable earnings of $99,990. Determine his annual federal income tax.
- Jean-Luc works two part-time jobs in Ontario. If his annual wages from each position are $17,444 and $16,430, determine his annual provincial income tax.
- If the CPI rises from 102.6 to 110.8, determine the percent change in the purchasing power of a dollar.
- Since Maybelline graduated from college in 2004, her salary has changed from $23,100 in 2004 to $27,800 in 2009. Over that time, the CPI has increased from 105.0 to 114.9. Express Maybelline's salary in real dollars and determine the percent change in her real earnings.
Applications
- You have been given two job offers. The first employer is offering $17.50 per hour. The second employer is offering a $33,000 annual salary. Both employers expect that you might be able to earn an additional two hours of overtime per week. Treat any holiday earnings as regular earnings and suppose there are no statutory holiday worked earnings. If both jobs have 7.5 regular hour workdays five times per week for 52 weeks, which employer is offering the higher annual gross earnings? By what amount in dollars?
- Juanita is an architect. She is paid $41.25 per hour and normally works eight-hour days, Monday through Friday. Her employer has agreed to pay her overtime at double her regular rate of pay and any time worked on a statutory holiday at 2.5 times her regular pay. What are Juanita's gross earnings in a single week from Sunday to Saturday where she worked 4, 9, 8, 11.5, 8, 0, and 6 hours, respectively, where Monday was a statutory holiday and her employer has decided to pay her in lieu of another day off?
- Lorelei works on the production line for eight hours each day. She earns $9.50 per hour plus $0.13 per kilogram of sardines that she packs in excess of 100 kg per day. What are her daily gross earnings in a single day where she manages to pack 200, 250 g cans of sardines per hour?
- Determine whether a wage earner in British Columbia or Ontario pays the least provincial income taxes on gross taxable earnings of $58,000. What percentage more does the wage earner with the higher income tax pay?
- If Henri had $200,000 invested in his S&P/TSX Composite Index portfolio in 1975, how much would the portfolio be worth in March of 2011 when the S&P/TSX Composite Index was 14,116.10?
- In the province of Saskatchewan, you are paid an hourly wage of $11.25 and you work 7.5-hour days for five days per week. Assuming a 52-week year, determine the amount of provincial income tax deducted from your biweekly paycheque.
Challenge, Critical Thinking, & Other Applications
- Karen is paid $12.00 per hour for her work as a cashier at an Alberta retail outlet. Her employer pays a standard overtime rate. Her regular workday is eight hours and 40 hours per week.
- What are her gross earnings in a single week from Sunday to Saturday where Karen worked 12, 8, 12, 8, 0, 8, and 8 hours, respectively?
- If this represents a typical week for Karen, what are the federal and provincial income taxes that should be deducted from her biweekly paycheques (assume 52 weeks in a year)?
- Living in Nova Scotia, Rufus pays $410.50 per biweekly pay period in total federal and provincial income tax. What are his gross taxable earnings?
- Gilligan is paid a graduated commission of 1⅞% on his first $50,000 in sales, 3½% on the next $75,000 in sales, 4⅛% on the next $75,000 in sales, and 5⅕% on all sales above that amount. If his total gross earnings were $9,516.25, determine his sales during the pay period.
- Last year your annual salary was $58,150. This year your salary was increased in accordance with the CPI. Last year, the CPI was 108.9 and this year it is 111.1. Determine the amount of federal income tax that is deducted from your semi-monthly paycheque throughout the current year.
- As a sales representative, you average $350,000 per month in sales. Your commission is calculated as 1% of the first $120,000, 2% on the next $120,000, and 3% for anything higher. If you live in Ontario, determine both of the federal and provincial income taxes that are removed from your monthly commission cheques.
- Rufaro is the payroll administrator for New Wave Industries. There are four employees on the payroll. Buck and Roger receive annual salaries of $41,000 and $85,555, respectively. Luke receives piecework wages of $2.50 per item and produces 45 items per day five days per week. Leah is paid a base salary of $200 per week and receives 6% commission on average weekly sales of $10,000. Assuming a 52-week year, determine the annual total federal income taxes that New Wave Industries must remit to the federal government on behalf of its employees.
- For every province in Western Canada (British Columbia, Alberta, Saskatchewan, and Manitoba), determine the total annual income tax deducted from an annual gross taxable income of $66,660. Express the total income tax as a percentage of gross income.
- For a weekly pay period, you know the following information about the payroll at Hopper Industries. Friday is a statutory holiday.
- Christie receives an annual salary of $44,880 based on a 36-hour workweek comprised of four, nine-hour days. She has two hours of overtime at time-and-a-half and did not work the statutory holiday.
- Marie is paid $16.75 per hour based on eight-hour days and a 40-hour workweek. All premium wages are paid at regulatory minimums. From Sunday to Saturday, she worked 8, 0, 8, 8, 8, 3, and 8 hours, respectively. She will not receive another day off in lieu for the statutory holiday.
- Norm receives a graduated commission of 2.25% on his first $100,000 in sales and 4.15% on anything higher. His sales during one week were $123,000. Ignore his holiday or statutory earnings in your calculations.
- Garth is paid a straight piecework wage of $1.12 per unit produced. He worked a total of 30 hours during the week, producing one unit every five minutes. Ignore his holiday or statutory earnings in your calculations.
For all employees combined, determine the total regular earnings, overtime earnings, holiday earnings, and holiday worked earnings that Hopper Industries must report on its weekly company payroll report.