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Math · Consumer Math

Chapter 1: Earning an Income

Comparing Job Offers

Salary is only part of the package.

Lesson
3
Time
About 21 minutes
0 of 22 done
Part 1 of 8Picture It

Step 1: Picture It

Start with something you already know.

Two pizza deals

  1. Shop A sells a large pizza for $14, and delivery is free.
  2. Shop B sells the same pizza for $11, but delivery costs $4.
  3. Shop B has the smaller price on the menu.
  4. At your door, Shop A costs $14 and Shop B costs $15.

A salary is the menu price: the number you see first.

Total compensation is the price at the door: add what comes with the job, take away what the job costs you, then compare.

Where the picture turns around: with pizza you want the smaller total, and with a job you want the larger one.

Step 2: Let's Learn

Read it, or press Listen and follow the words.

Try it first

Job A pays $40,000 a year. Job B pays $42,000 a year, but getting there needs a $200 bus pass every month. How much does Job B leave you a year after the bus pass, in dollars?

dollars

Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.

Watch the idea first — 58 seconds. Then read on, and try it yourself in the next step.

Offer A: $50,000 with a 5% retirement match. Offer B: $53,000, no match, $3,000 a year commuting

  1. 1A: 50,000 + 0.05 × 50,000 = $52,500salary plus the match
  2. 2B: 53,000 − 3,000 = $50,000salary minus the commute
  3. AnswerA is worth $2,500 a year moredespite the smaller salary

Total compensation is salary plus the value of everything else the job provides, minus what the job costs. A retirement match and employer-paid insurance are real money. Commuting, parking and childcare reduce what a job is worth. Divide by hours worked before deciding.

Benefits have value

A 5% match on $50,000 is $2,500 a year. Employer-paid health insurance might be worth $6,000 a year that you would otherwise pay. Twenty days of paid leave on a $50,000 salary is about $3,850 of paid time.

Jobs have costs too

A 40 km round-trip commute at $0.30 a km for 250 days: $3,000 a year, plus parking. Required uniforms, tools, or childcare during the hours worked all come off the top.

Cost of living

A $60,000 job in a city with $2,000 rent leaves $36,000 after housing. A $50,000 job in a town with $900 rent leaves $39,200. Compare after housing, not before.

Per hour, not per year

A $60,000 salary demanding 60-hour weeks is 60,000/(60 × 50) = $20 an hour. A $45,000 job at 40 hours is 45,000/2,000 = $22.50 an hour. The larger salary pays less for each hour of your life.

What numbers cannot capture

Stability, learning, the people, and the commute time itself. An hour a day commuting is 250 hours a year. The arithmetic informs the decision rather than making it.

The method

Salary. Plus match, plus insurance value, plus paid leave. Minus commute, minus other costs. Divide by real hours worked. One number per offer, then judge the rest.

Step 3: Try It Yourself

Tap and try it out.

Press Next step. Build each total, then divide by the hours.

Offer A: $60,000, 55-hour weeks, $2,000 commute, no match. Offer B: $48,000, 40-hour weeks, no commute, 4% match, $4,000 insurance paid. Compare per hour after costs

  1. 1A: 60,000 − 2,000 = $58,000salary minus the commute
Step 0 of 4
Two offers costed: salary, plus the match, minus what the job costs. The bigger salary does not always win.
Offer A: really worth$52,500
  • Salary after job costs$50,000
  • Employer match 5%$2,500
  • Job costs$0
Offer B: really worth$50,000
  • Salary after job costs$50,000
  • Employer match 0%$0
  • Job costs$3,000

Offer A: $50,000 + $2,500 match − $0 costs = $52,500. Offer B: $53,000 + $0 match − $3,000 costs = $50,000. Offer A is worth $2,500 a year more.

A match is pay you only receive by contributing. A commute is pay you never see. Count both before the salary.

Step 4: In Real Life

Two job offers

Job A pays 50,000 with health insurance. Job B pays 55,000 with none, and a plan costs 500 a month. B is 1,000 a year behind. Salary is only part of the package.

Step 5: Watch an Example

One step at a time.

Watch Ravi Weigh Insurance and Parking

Offer A pays $44,000, and the employer pays for health insurance: a plan that would cost Ravi $300 a month on his own. Offer B pays $47,000 with no insurance, and parking at that job costs $50 a month.

  1. Step 1

    The insurance in Offer A is real money, because it is a bill of $300 a month that Ravi never has to pay. Over a year that is 300 × 12 = $3,600, so Offer A is worth 44,000 + 3,600 = $47,600.

Watch Maya Compare Per Hour

Offer C pays $54,000 for 50-hour weeks. Offer D pays $42,000 for 40-hour weeks, plus a 5% retirement match. Both jobs have 50 working weeks a year. Maya works out Offer C, and you finish Offer D.

  1. Step 1

    Offer C first. Its year is 50 × 50 = 2,500 hours, so it pays 54,000 ÷ 2,500 = $21.60 for each hour worked.

Step 6: Your Turn

Practice makes it stick.

The Drive

Problem 1 of 17

Leo can walk to a job that pays $49,000 a year. A second job pays $52,000, but driving there costs $14 a day for 250 working days, and parking is $60 a month. What is the second job worth a year after its costs, in dollars?

dollars

The Long Weeks

Problem 2 of 17

Noor has two offers, each with 50 working weeks. Job A pays $57,000 for 60-hour weeks. Job B pays $47,000 for 40-hour weeks. Which job pays more for each hour, and by how many dollars an hour? Type the difference, to the cent.

dollars an hour

Weigh the Package

Salary, plus what the job gives, minus what it costs. Every amount for the same period.

Problem 3 of 17

An offer pays a $45,000 salary plus a 4% retirement match. What is the offer worth a year, in dollars?

dollars

Problem 4 of 17

A job pays $51,000 a year. The commute costs $15 a day for 250 working days. What is the job worth a year after the commute, in dollars?

dollars

Problem 5 of 17

A job pays $54,000 a year for 45-hour weeks, with 50 working weeks. What does it pay per hour, in dollars?

dollars an hour

Problem 6 of 17

An offer pays a $40,000 salary, employer-paid insurance worth $4,800 a year, and a 3% match. The commute costs $2,000 a year. What is the whole package worth a year, in dollars?

dollars

Problem 7 of 17

A job pays $58,000 a year in a city where rent is $1,800 a month. How much is left a year after rent, in dollars?

dollars

Whose Step?

One line in each comparison is a slip. Find it, then fix it.

Problem 8 of 17

Dev worked out what a job is worth after parking. One line is a slip. Which?

Dev's value of a $46,000 job with parking

  1. 1$46,000 a year; parking $90 a month
  2. 246,000 − 90 = $45,910
  3. Answerworth $45,910 a year

Problem 9 of 17

Redo Dev's work. What is the job worth a year after parking, in dollars?

dollars

Problem 10 of 17

Maya worked out what a job pays per hour. It asks for 55-hour weeks, with 50 working weeks. One line is a slip. Which?

Maya's pay per hour for a $55,000 job

  1. 1$55,000 a year; 55-hour weeks, 50 weeks
  2. 2hours: 40 × 50 = 2,000
  3. Answer55,000 ÷ 2,000 = $27.50 an hour

Problem 11 of 17

What does Maya's job really pay per hour, in dollars?

dollars an hour

Problem 12 of 17

Ana worked out what an offer with a retirement match is worth. One line is a slip. Which?

Ana's value of a $48,000 offer with a 5% match

  1. 1salary $48,000; 5% match
  2. 2match: 0.5 × 48,000 = $24,000
  3. Answertotal: 48,000 + 24,000 = $72,000

Problem 13 of 17

What is Ana's offer really worth a year, salary plus match, in dollars?

dollars

Pick the Move

Decide how to compare before you compute anything.

Problem 14 of 17

Offer A pays $63,000 for 60-hour weeks. Offer B pays $44,000 for 40-hour weeks. Both have 50 working weeks. Which move compares them fairly?

Problem 15 of 17

One job pays $62,000 in a city where rent is $1,900 a month. Another pays $51,000 in a town where rent is $1,000 a month. Which move makes the comparison fair?

Same Value?

Build each offer the same way, then see which ones match.

Problem 16 of 17

Which offers are worth exactly $50,000 a year in total? Select every one.

Problem 17 of 17

Each job has 50 working weeks. Which pay exactly $20 an hour? Select every one.

Step 7: Quick Check

Show what you know.

Question 1 of 2

A 6% match on a $40000 salary. Annual value in dollars?

Question 2 of 2

Why can the higher salary be the worse offer?

Ready for more?Optional. Past the lesson, for anyone who wants it.

Stretch 1 of 2

Offer A pays $50,000 with a 6% match. Offer B has no match, and its commute costs $1,500 a year. What is the smallest salary Offer B must pay to be worth as much as Offer A, in dollars?

dollars

Stretch 2 of 2

Offer A pays $60,000 for 50-hour weeks. Offer B pays $45,000 for 40-hour weeks and adds a retirement match. Both have 50 working weeks. What is the smallest whole-number percent match that makes Offer B pay more per hour than Offer A?

%

What You Learned

  • Total compensation is salary plus benefits minus job costs.
  • A retirement match, paid insurance and paid leave are real money.
  • Compare after housing, and divide by real hours worked before deciding.
  • The arithmetic informs the decision; stability and time decide the rest.
For the grown-up

The misconception this lesson targets is that the bigger salary is the better offer. A salary is one line of the package: a retirement match and employer-paid insurance add real money, and a commute, parking and a more expensive city take it away, so the offers have to be built out in full before they are compared. Two arithmetic slips ride alongside it. One is mixing periods, taking a monthly or daily cost straight off a yearly salary. The other is dividing by a 40-hour week out of habit when the job asks for more, which makes long hours look well paid. A useful question at home: what is each offer worth for each hour of your week, after what the job costs you?