Salary packages offered by a company Package A: 20000 per annum plus pay rise of 200 every 6 months Package b: 19000 per annum plus 3.5% pay rise every year Question: How will employee on Pacakge A be compared to an employee on Pacakge B in the next 15 years

To compare how employees under **Package A** and **Package B** fare over the next 15 years, we need to calculate the total earnings for each employee over that period, accounting for the periodic pay raises in each package.

### Package A:  
- Initial salary = 20,000 per annum  
- Pay rise = 200 every 6 months (or twice a year)  
- This means the employee gets a 400 increase per year (200 twice a year).

So, for year \( n \), the salary will be:

\[
S_A(n) = 20000 + 400 \times (n - 1)
\]

Where:
- \( S_A(n) \) is the salary at the end of the \( n \)-th year.
  
The **total earnings** after 15 years for Package A can be found by summing the salaries for each year, starting from year 1 up to year 15.

### Package B:  
- Initial salary = 19,000 per annum  
- Annual pay rise = 3.5%

For year \( n \), the salary will be:

\[
S_B(n) = 19000 \times (1.035)^{n-1}
\]

Where:
- \( S_B(n) \) is the salary at the end of the \( n \)-th year.
- \( 1.035 \) represents the 3.5% increase each year.

The **total earnings** after 15 years for Package B can be found by summing up the salaries over the 15-year period.

### Now let's calculate the total earnings over 15 years for both packages. I'll compute it for you.After 15 years:

- The total earnings for the employee under **Package A** will be **₹342,000**.
- The total earnings for the employee under **Package B** will be approximately **₹366,618**.

Thus, the employee on **Package B** will earn more over the 15-year period compared to the employee on **Package A** by about ₹24,618.

Would you like further details on how the salary evolves each year or any other clarification?

Here are 5 related questions to explore this further:
1. What would be the comparison if the evaluation period was extended to 20 years?
2. How would changing the pay rise in Package A (e.g., to ₹300 every 6 months) impact the total?
3. What if the annual increase for Package B were increased to 4%?
4. How do these salary packages compare if we account for inflation over the 15 years?
5. What is the breakeven point where both packages result in the same cumulative earnings?

**Tip:** When analyzing salary growth over time, always account for compounding effects in percentage-based raises as they can significantly influence total earnings over long periods.

How will an employee on Package A be compared to an employee on Package B in the next 15 years?

This problem compares salary growth under Package A (fixed pay rise of ₹400 per year) and Package B (3.5% annual increase) over 15 years. Learn how to calculate total earnings using linear and exponential growth models. Suitable for Grades 9-12.

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