To determine how much extra money Luke will have after paying tax this year due to the increase in his taxable income, let's break the problem into two parts.

Step 1: Calculate Luke's taxable income for this year

Luke's taxable income increased by $16,800, so: $\text{New taxable income} = 87,000 + 16,800 = 103,800$

Step 2: Use the tax table to calculate Luke's tax payable this year

From the tax table, we know the tax rate for the income bracket of $87,001 - $180,000 is: $19,822 + 0.37 \times (\text{Taxable income} - 87,000)$

Substitute Luke's new taxable income: $\text{Tax payable} = 19,822 + 0.37 \times (103,800 - 87,000)$ $= 19,822 + 0.37 \times 16,800$ $= 19,822 + 6,216 = 26,038$

Step 3: Calculate the tax increase

Luke's tax payable last year was $19,822, and this year it is $26,038. Therefore, the increase in tax is: $\text{Tax increase} = 26,038 - 19,822 = 6,216$

Step 4: Determine how much extra money Luke will have after paying tax

The increase in Luke's taxable income was $16,800. After accounting for the extra tax of $6,216, the amount of extra money Luke will have this year is: $\text{Extra money} = 16,800 - 6,216 = 10,584$

Conclusion:

Luke will have an extra $10,584 this year after paying tax as a result of the increase in his taxable income.

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Would you like further details or have any questions? Here are some related questions to explore:

1. How would Luke's tax change if his income increased by $20,000 instead of $16,800?
2. What would Luke's tax be if his income fell within the highest tax bracket (above $180,000)?
3. How does the Medicare levy affect Luke's total tax if included?
4. What percentage of Luke's additional income is paid as tax?
5. What is the effective tax rate for Luke’s income this year?

Tip: Always verify which tax bracket applies to your income to estimate tax accurately.