Katie has a gross annual income of €52 460 - Junior Cycle Mathematics - Question 4 - 2019

Katie's income tax needs to be calculated in steps based on her taxable income:

1. Tax on the first €34,000:

   $$0.20 imes 34,000 = 6,800$$

2. Calculate tax on the remaining income:

   $$ext{Remaining Income} = 48,000.90 - 34,000 = 14,000.90$$

   Tax on remaining income:

   $$0.40 imes 14,000.90 = 5,596.36$$

3. Total income tax:

   $$ext{Total Tax} = 6,800 + 5,596.36 = 12,396.36$$

4. Deduct tax credits from total tax:

   $$ext{Net Tax} = 12,396.36 - 4,200 = 8,196.36$$

5. Finally, calculate net income:

   $$48,000.90 - 8,196.36 = 39,804.54$$

So, Katie's net income after tax is approximately €39,804.54.

To determine Katie's current credit card bill, we need to calculate the compounded interest:

1. Calculate the amount after 3 months with 2% monthly interest:

   For the first month:

   $$420 imes (1 + 0.02) = 420 imes 1.02 = 428.40$$

   For the second month:

   $$428.40 imes (1 + 0.02) = 428.40 imes 1.02 = 436.87$$

   For the third month:

   $$436.87 imes (1 + 0.02) = 436.87 imes 1.02 = 445.45$$

Thus, her bill now amounts to approximately €445.45.

If the motorbike is now worth €12,150 and it lost 10% of its value since purchase, we can express this mathematically:

1. Let the original value be represented as $V$.

   Thus, after depreciation:

   $$V - 0.10V = 12,150$$

ightarrow 0.90V = 12,150

2. Now, solve for $V$:

V = rac{12,150}{0.90} ightarrow V = 13,500

$$Therefore, the value of the motorbike when Katie bought it was €13,500.$$