The rates and thresholds of the Universal Social Charge (USC) in Ireland (excluding the top rate) during 2020 are given in the table below - Leaving Cert Mathematics - Question 7 - 2021

To find the total USC payable at the maximum amounts for the first three rates, we calculate:

1. For the first €12,012 at 0%:

   • USC = 0% of €12,012 = €0

2. For the next €48,472 (from €12,012 to €60,484) at 2%:

   • USC = 2% of €48,472 = €969.44

3. For the next €49,560 (from €60,484 to €110,044) at 4.5%:

   • USC = 4.5% of €49,560 = €2,228.20

Adding these amounts gives the total:

$$Total = 0 + 969.44 + 2228.20 = €3,197.64$$

To calculate John's USC:

1. For the first €12,012 at 0%:

   • USC = 0% of €12,012 = €0

2. For the next €48,472 at 2%:

   • USC = 2% of €48,472 = €969.44

3. For the remaining income (€54,800 - €60,484 which is just about €54,800):

   • USC = 4.5% of (€54,800 - €60,484) at 4.5% (which does not apply here since income does not exceed the previous threshold).

Thus, his total USC is:

$$Total = 0 + 969.44 = €969.44$$

To find Mary's annual income based on her USC payment:

1. Assume the first €12,012 is at 0%, therefore:

   • USC from first band = €0

2. Next €48,472 at 2%:

   • USC from second band = 2% of €48,472 = €969.44

The remainder (€1602.72 - €969.44) falls into the third band:

3. Remaining USC:
   • €1602.72 - €969.44 = €633.28 at 4.5%
   • Equivalent income for this USC can be calculated as:

ext{Income in third band} = rac{633.28}{0.045} = €14,086.67

Adding this to the previous thresholds gives:

$$€12,012 + €48,472 + €14,086.67 = €74,570.67$$

To find the top rate of USC Patrick pays:

1. We calculate how much USC he pays according to the brackets:

   • Up to €12,012 at 0%: €0
   • Next €48,472 at 2%: €969.44
   • Next €49,560 at 4.5%: €2,228.20

2. Total up to these levels:

   • Total = 0 + 969.44 + 2228.20 = €3,197.64

3. Determine the overpayment:

   • Top rate USC is calculated based on the surplus he pays beyond €3,197.64:
   • Total paid as €3496.18 - €3,197.64 gives the need for an additional top percentage:
   • Calculate the difference and average it against his remaining income:

$$3496.18 - 3197.64 = 298.54$$

To find the relevant top rate based on €83,000:

• Assumed ceiling computation indicates the gap income falls into:
• The additional amount hence gives the top rate % of:

ext{Top rate USC} = rac{298.54}{(83000 - 70044)} imes 100 ext{ (estimate for significant percent)} ightarrow ext{actual final required percentage figure needs additional rounding.}