Answer :
Below is a step‐by‐step explanation of how the calculations are performed.
1. First, assume that the monthly gross salary is
[tex]$$\text{Gross Salary} = 5000.$$[/tex]
2. The income tax rate is
[tex]$$\text{Income Tax Rate} = 20\% = 0.20,$$[/tex]
and the FICA tax rate is
[tex]$$\text{FICA Tax Rate} = 7.65\% = 0.0765.$$[/tex]
3. To find the combined tax rate, add the two tax rates:
[tex]$$\text{Total Tax Rate} = 0.20 + 0.0765 = 0.2765.$$[/tex]
This means that a total of 27.65% of the gross pay goes to taxes.
4. The total taxes paid are computed by multiplying the gross salary by the combined tax rate:
[tex]$$\text{Total Taxes Paid} = 5000 \times 0.2765 = 1382.5.$$[/tex]
5. The net income after taxes is then calculated by subtracting the total taxes paid from the gross salary:
[tex]$$\text{Net Income} = 5000 - 1382.5 = 3617.5.$$[/tex]
Since the provided gross salary is monthly, the monthly net income is
[tex]$$\text{Monthly Net Income} = 3617.5.$$[/tex]
6. Now, applying the 50/30/20 budgeting rule to the monthly net income:
- For Needs (50% of monthly net income):
[tex]$$\text{Needs} = 3617.5 \times 0.5 = 1808.75.$$[/tex]
- For Wants (30% of monthly net income):
[tex]$$\text{Wants} = 3617.5 \times 0.3 = 1085.25.$$[/tex]
- For Savings (20% of monthly net income):
[tex]$$\text{Savings} = 3617.5 \times 0.2 = 723.5.$$[/tex]
7. Next, we consider the housing and utility expenses if the person lives alone:
- The monthly housing payment is assumed to be
[tex]$$\text{Monthly Housing Payment (alone)} = 1200.$$[/tex]
- The utilities are estimated as follows:
- Water: [tex]$$50,$$[/tex]
- Electric: [tex]$$60,$$[/tex]
- Gas: [tex]$$40,$$[/tex]
- Sewer: [tex]$$30,$$[/tex]
- Internet: [tex]$$70,$$[/tex]
- Cable: [tex]$$80.$$[/tex]
8. If the person has a roommate, the housing and utility costs would be split equally (divided by 2). Thus, the roommate share becomes:
- Monthly housing payment split:
[tex]$$\text{Monthly Housing Payment (roommate)} = \frac{1200}{2} = 600.$$[/tex]
- Utilities when split between the two:
- Water: [tex]$$\frac{50}{2} = 25,$$[/tex]
- Electric: [tex]$$\frac{60}{2} = 30,$$[/tex]
- Gas: [tex]$$\frac{40}{2} = 20,$$[/tex]
- Sewer: [tex]$$\frac{30}{2} = 15,$$[/tex]
- Internet: [tex]$$\frac{70}{2} = 35,$$[/tex]
- Cable: [tex]$$\frac{80}{2} = 40.$$[/tex]
The final numerical results are:
- Gross Salary: \[tex]$5000
- Income Tax Rate: 0.20
- FICA Tax Rate: 0.0765
- Total Tax Rate: 0.2765
- Total Taxes Paid: \$[/tex]1382.5
- Net Income: \[tex]$3617.5
- Monthly Net Income: \$[/tex]3617.5
- Needs: \[tex]$1808.75
- Wants: \$[/tex]1085.25
- Savings: \[tex]$723.5
- Monthly Housing Payment (alone): \$[/tex]1200
- Water (alone): \[tex]$50
- Electric (alone): \$[/tex]60
- Gas (alone): \[tex]$40
- Sewer (alone): \$[/tex]30
- Internet (alone): \[tex]$70
- Cable (alone): \$[/tex]80
- Monthly Housing Payment (roommate): \[tex]$600
- Water (roommate): \$[/tex]25
- Electric (roommate): \[tex]$30
- Gas (roommate): \$[/tex]20
- Sewer (roommate): \[tex]$15
- Internet (roommate): \$[/tex]35
- Cable (roommate): \$40
This detailed explanation shows each step and corresponding calculation that leads to the numerical results provided above.
1. First, assume that the monthly gross salary is
[tex]$$\text{Gross Salary} = 5000.$$[/tex]
2. The income tax rate is
[tex]$$\text{Income Tax Rate} = 20\% = 0.20,$$[/tex]
and the FICA tax rate is
[tex]$$\text{FICA Tax Rate} = 7.65\% = 0.0765.$$[/tex]
3. To find the combined tax rate, add the two tax rates:
[tex]$$\text{Total Tax Rate} = 0.20 + 0.0765 = 0.2765.$$[/tex]
This means that a total of 27.65% of the gross pay goes to taxes.
4. The total taxes paid are computed by multiplying the gross salary by the combined tax rate:
[tex]$$\text{Total Taxes Paid} = 5000 \times 0.2765 = 1382.5.$$[/tex]
5. The net income after taxes is then calculated by subtracting the total taxes paid from the gross salary:
[tex]$$\text{Net Income} = 5000 - 1382.5 = 3617.5.$$[/tex]
Since the provided gross salary is monthly, the monthly net income is
[tex]$$\text{Monthly Net Income} = 3617.5.$$[/tex]
6. Now, applying the 50/30/20 budgeting rule to the monthly net income:
- For Needs (50% of monthly net income):
[tex]$$\text{Needs} = 3617.5 \times 0.5 = 1808.75.$$[/tex]
- For Wants (30% of monthly net income):
[tex]$$\text{Wants} = 3617.5 \times 0.3 = 1085.25.$$[/tex]
- For Savings (20% of monthly net income):
[tex]$$\text{Savings} = 3617.5 \times 0.2 = 723.5.$$[/tex]
7. Next, we consider the housing and utility expenses if the person lives alone:
- The monthly housing payment is assumed to be
[tex]$$\text{Monthly Housing Payment (alone)} = 1200.$$[/tex]
- The utilities are estimated as follows:
- Water: [tex]$$50,$$[/tex]
- Electric: [tex]$$60,$$[/tex]
- Gas: [tex]$$40,$$[/tex]
- Sewer: [tex]$$30,$$[/tex]
- Internet: [tex]$$70,$$[/tex]
- Cable: [tex]$$80.$$[/tex]
8. If the person has a roommate, the housing and utility costs would be split equally (divided by 2). Thus, the roommate share becomes:
- Monthly housing payment split:
[tex]$$\text{Monthly Housing Payment (roommate)} = \frac{1200}{2} = 600.$$[/tex]
- Utilities when split between the two:
- Water: [tex]$$\frac{50}{2} = 25,$$[/tex]
- Electric: [tex]$$\frac{60}{2} = 30,$$[/tex]
- Gas: [tex]$$\frac{40}{2} = 20,$$[/tex]
- Sewer: [tex]$$\frac{30}{2} = 15,$$[/tex]
- Internet: [tex]$$\frac{70}{2} = 35,$$[/tex]
- Cable: [tex]$$\frac{80}{2} = 40.$$[/tex]
The final numerical results are:
- Gross Salary: \[tex]$5000
- Income Tax Rate: 0.20
- FICA Tax Rate: 0.0765
- Total Tax Rate: 0.2765
- Total Taxes Paid: \$[/tex]1382.5
- Net Income: \[tex]$3617.5
- Monthly Net Income: \$[/tex]3617.5
- Needs: \[tex]$1808.75
- Wants: \$[/tex]1085.25
- Savings: \[tex]$723.5
- Monthly Housing Payment (alone): \$[/tex]1200
- Water (alone): \[tex]$50
- Electric (alone): \$[/tex]60
- Gas (alone): \[tex]$40
- Sewer (alone): \$[/tex]30
- Internet (alone): \[tex]$70
- Cable (alone): \$[/tex]80
- Monthly Housing Payment (roommate): \[tex]$600
- Water (roommate): \$[/tex]25
- Electric (roommate): \[tex]$30
- Gas (roommate): \$[/tex]20
- Sewer (roommate): \[tex]$15
- Internet (roommate): \$[/tex]35
- Cable (roommate): \$40
This detailed explanation shows each step and corresponding calculation that leads to the numerical results provided above.
