Salary Project
Use evidence to make a decision—not just a guess.
A salary is one number. A decision needs a model: time, earnings, expenses and a clear explanation of what you are comparing.
Use the classroom instructions for the assigned options and required time span. The explorations below use illustrative numbers so you can develop a strategy before completing your own project.
Annual pay is not total pay.
A salary is an amount earned per year. Total earnings add the amounts from all completed years. A one-time bonus is added once. A one-time payment does not repeat every year.
For a fixed annual salary S and a starting bonus B, total earnings after t completed years are T = St + B. A compounded percentage raise changes the annual salary each year, so one constant-rate line does not describe its cumulative earnings.
What changes when the base changes?
| Year | Annual pay: fixed dollar raise | Annual pay: compounded raise | Total compounded pay so far |
|---|
Values are calculated without intermediate rounding and displayed to cents. This classroom model omits taxes, inflation and changes in employment. Year 1 has no raise yet.
Make the comparison fair.
- Choose the same completed-year values for every option.
- Decide whether the vertical axis represents annual pay or total earnings, and label it clearly.
- Include each one-time amount once, with a stated time convention.
- Explain whether a straight line fits each option and why.
- Use calculations and your graph to justify how the choice can change over time.
The starting point and the yearly change both matter.
With constant annual salary S, expenses E and starting balance B, this simplified model gives N = (S − E)t + B. A loan can be represented by a negative starting balance. A positive annual change can take time to overcome a negative start.
| Completed years | Balance ($) |
|---|
Points show completed years; the line connects the model's constant change. Real finances include effects this model leaves out. Use the assignment's stated conventions for the project.
Before you submit, show the evidence.
- Define variables, quantities and units.
- Use a consistent scale, labelled axes, a title and a legend.
- Include a table and the appropriate equation or rule for each option.
- Show sample calculations at the chosen comparison time.
- State which option you would choose and support the decision with mathematical evidence.
- Explain the assumptions and any limits of the model.
These prompts support the classroom checklist; they do not replace the CBE proficiency indicators or your assigned requirements.