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.