Let's break down the problem step by step.

You are comparing two salary plans:

• Plan A: £20,000 per annum, with a pay rise of £200 every 6 months.
• Plan B: £19,000 per annum, with a pay rise of 3.5% every year.

The question asks: What would an employee’s wage on Plan A be like compared to an employee’s wage on Plan B in year 15?

Calculating the salaries for year 15:

Plan A:

• Initial salary = £20,000.
• Pay rise every 6 months = £200, so the annual rise = £400.
• After 15 years (30 half-years), the salary increase would be:

$\text{Total increase in salary} = 30 \times 200 = £6,000.$

• Salary in year 15 for Plan A:

$\text{Year 15 Salary (Plan A)} = 20,000 + 6,000 = £26,000.$

Plan B:

• Initial salary = £19,000.
• Pay rise is 3.5% per year, so the salary grows exponentially each year.

To calculate the salary in year 15 under Plan B, we apply the formula for compound interest:

$\text{Year 15 Salary (Plan B)} = 19,000 \times (1.035)^{15}.$

Now, I'll calculate the result.The salary in year 15 for Plan B is approximately £31,832.

Comparison:

• Plan A (Year 15 Salary): £26,000.
• Plan B (Year 15 Salary): £31,832.

Now, the difference between the salaries: $\text{Difference} = 31,832 - 26,000 = 5,832.$

Thus, Plan B pays £5,832 more than Plan A in year 15.

The closest answer choice is £5,831 more.

Would you like any further details or have any questions?

Here are 5 related questions to expand on this:

1. How would the comparison look if the time frame was 10 years instead of 15?
2. What would the salary be for Plan A after 20 years?
3. How does compound interest affect long-term salary growth compared to fixed increments?
4. Can you calculate the total earnings over 15 years for both plans?
5. How does changing the percentage increase for Plan B affect the outcome?

Tip: When comparing salaries over time, exponential growth (percentage increase) generally outpaces linear growth, especially over long periods.