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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.

A company is offering two different salary packages to its staff. Plan A = £20,000 per annum + a pay rise of £200 every 6 months. Plan B = £19,000 per annum + a pay rise of 3.5% every year. What would an employee’s wage on plan A be like compared to an employee’s wage on plan B in year 15?

Compare two salary plans: one with a fixed pay rise and the other with a percentage-based increase. Understand how the difference grows over 15 years, highlighting the impact of linear vs. exponential growth. Includes step-by-step calculations for Plan A and Plan B.

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