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Study Guides > Mathematics for the Liberal Arts Corequisite

Putting It Together: General Problem Solving

Now that you have seen a number of general problem solving techniques and plenty of examples in this module, let’s try to put it all together.  In real life, sometimes we have to make big decisions.  A major career change or relocation can throw your life into disarray, but perhaps even more importantly, such a change can have lasting effects on your financial future. Graphic of balance scale with stack of bills on one side and a lightbulb on the other. An arm is holding the balance point.   Suppose you are currently working as a bank teller in your hometown.  Your job pays $11 per hour, with 10% taxes taken out of each paycheck.  For simplicity, assume you have to work 260 days of the year (you don’t work weekends), 8 hours a day.  By carefully budgeting you can keep you monthly expenses to about $1500. But now another job offer has come up.  You have the opportunity to become an assistant manager.  The only catch is that you’ll have to move to a new branch of the bank opening up in a nearby metropolitan area.  So here are the details: The assistant manager salary starts at $32,000.  This puts you into the next tax bracket, which means that you will pay $2500 plus 15% of the amount earned over $25,000.  Because you are moving to a bigger city, your living expenses will rise as well.  After a little research, you determine that your monthly expenses will probably be around $2000.  

Should you make the move and take the job offer?

This is a tough decision!  Take some time to think this through.  What do you need to know and what pathway(s) could get you there?  Try it yourself first. for one possible approach.

Answer: One approach is to calculate the annual discretionary budget [the annual net income for each job minus annual expenses] for each position. Bank Teller:

  1. To calculate the annual discretionary budget, we must find annual net income and the annual expenses.
  2. To find annual expenses, we simply multiple the monthly expenses by 12.
  3. To determine the annual net income for the bank teller job, we need to find the gross income and subtract the amount of taxes paid.
  4. To find the amount of taxes paid, we need to multiply the gross income by the tax rate (10% = .10).
  5. To find the annual gross income, we need to determine how many total hours you work in a year.  Then we can multiply that by your hourly wage.
  6. To find out how many hours you work in a year, we multiply the number of hours you work each day by the number of days you work per year.
  We work backwards through the pathway to do our calculations: Step 6: The number of hours worked in a year is:

[latex]\displaystyle\frac{8 \; \textrm{hrs.}}{\textrm{day}} \times 260 \;\textrm{days} = 2080 \;\textrm{hrs.}[/latex]

Step 5: Multiply by the hourly wage to determine your annual gross income:

[latex]2080 \;\textrm{hrs.}\times \$11 / \textrm{hr.} = \$22,\!880[/latex]

Step 4: Calculate your taxes:

[latex]$22,880\times0.10=$2288[/latex]

Step 3: Net income is found by subtracting your taxes from your gross income:

[latex]$22,880-$2288=$20,592[/latex]   Your annual net income as a bank teller is $20,592.

Step 2: Ok, so now let’s figure out the yearly expenses.  If monthly expenses are $1500, then each year you will pay:

[latex]12\times$1500=$18,000[/latex]

Step 1: Finally, after the bills are paid, you can do what we want to with the remainder.  This is our discretionary budget.

[latex]\$20,\!592 - \$18,\!000 = \$2592[/latex]

The annual discretionary budget for the Bank Teller position is $2592. Next, let’s see what kind of discretionary budget you will have if you take the new job. Assistant Manager:
  1. To calculate the annual discretionary budget, we must find annual net income and the annual expenses.
  2. To find annual expenses, we simply multiple the monthly expenses by 12.
  3. To determine the annual net income for the bank teller job, we need to find the gross income and subtract the amount of taxes paid.
  4. To find the amount of taxes paid for this job, we need to multiply the amount of gross income OVER $25000 (i.e.: $32000-$25000 = $7000) by the tax rate (15% = .15) and add that to $2500.
Note that since you are given the annual gross income (salary) for this position, our pathway stops here. Step 4: This time, to find the amount of taxes paid (since you would be in a higher tax bracket), you will pay $2500 plus 15% of the difference between the salary and $25,000.

[latex]$2500+($7000\times0.15)=$3550[/latex]

Step 3: The annual net income for the assistant manager position would be:

[latex]$32,000-$3550=$28,450[/latex]

Step 2: It’s a higher net income than you are currently making, but how will it stack up against the higher cost-of-living expenses in the city?  Let's find the annual expenses:

[latex]12\times$2000=$24,000[/latex]

Step 1: Finally, your new discretionary budget would be:

[latex]$28,450-$24,000=$4450[/latex]

That’s definitely an improvement over $2592!  Maybe it’s time to move to the big city and start advancing your career.  However, since it’s not that much more, you probably shouldn’t go out and buy a brand new car.  Just wait until you get your first promotion to full manager.

   

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  • Putting It Together: General Problem Solving. Authored by: Lumen Learning. License: CC BY: Attribution.

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