Question: A company is currently reviewing the compensation schemes offered to new employees because management must soon decide which salary structure will best attract and retain qualified workers while ensuring long-term financial sustainability. Before implementing a compensation package, management needs a data-driven analysis of four proposed plans: (A) a salary with a fixed annual increase, (B) a salary with a percentage-based annual increase, (C) an hourly wage with an increasing hourly rate, and (D) a salary with commission that grows by a fixed percentage each year. To support this important decision, you have been hired as a financial analyst and compensation consultant to evaluate and compare the earning potential of these compensation schemes. Prepare a Comparative Financial Analysis Report for the company's management team and prospective employees. Using concepts from business and finance, sequences and series, and functions and graphs, identify the type of sequence represented by each compensation plan, develop the appropriate formulas, compute salaries and total earnings over a specified period, and present the results through tables and graphs. Based on your analysis, determine which compensation plan offers the greatest financial advantage in the short term and long term, and provide a well-justified recommendation supported by mathematical reasoning. Your work will be evaluated based on the accuracy of the mathematical models and computations, the effectiveness of the graphical representations, the depth of the comparative analysis, the quality of the financial recommendations, and the overall organization and professionalism of the report.
do plan B
salary is 27k monthly = 324k per year
1. **Problem Statement:**
We analyze Plan B: a salary with a percentage-based annual increase.
The initial annual salary is $324000$.
2. **Type of Sequence:**
Plan B represents a geometric sequence because the salary increases by a fixed percentage each year.
3. **Formula for Salary in Year $n$:**
If the annual increase rate is $r$ (expressed as a decimal), then the salary in year $n$ is:
$$ S_n = S_1 \times (1 + r)^{n-1} $$
where $S_1 = 324000$.
4. **Total Earnings Over $n$ Years:**
The total earnings over $n$ years is the sum of the geometric series:
$$ T_n = S_1 \times \frac{(1 + r)^n - 1}{r} $$
5. **Assumptions:**
Since the percentage increase $r$ is not given, let's assume a typical raise of $5\%$ annually, so $r = 0.05$.
6. **Calculations:**
- Salary in year 1:
$$ S_1 = 324000 $$
- Salary in year 2:
$$ S_2 = 324000 \times (1 + 0.05) = 324000 \times 1.05 = 340200 $$
- Salary in year 3:
$$ S_3 = 324000 \times (1.05)^2 = 324000 \times 1.1025 = 357210 $$
- Total earnings over 5 years:
$$ T_5 = 324000 \times \frac{(1.05)^5 - 1}{0.05} = 324000 \times \frac{1.2762815625 - 1}{0.05} = 324000 \times \frac{0.2762815625}{0.05} = 324000 \times 5.52563125 = 1791032.25 $$
7. **Summary Table:**
| Year | Salary ($) |
|-------|------------|
| 1 | 324000 |
| 2 | 340200 |
| 3 | 357210 |
| 4 | 374070.5 |
| 5 | 392773 |
Total earnings over 5 years: $1791032.25$
8. **Interpretation:**
The salary grows exponentially due to the percentage increase, leading to higher earnings over time compared to fixed increases.
This plan benefits employees more in the long term.
9. **Recommendation:**
If the company wants to attract and retain employees with increasing compensation that rewards tenure, Plan B is advantageous.
It also aligns with inflation and performance-based raises.