Hi Beatriz!
Great question! This problem involves calculating a family's federal income taxes using the tax rules that were in effect in 2014.
Let's work through each part step by step!
Step 1: Determine the standard deduction
The family consists of two married adults and two dependent children.
Their filing status is Married Filing Jointly.
For the 2014 tax year, the standard deduction for married couples filing jointly was:
[
\boxed{$12,400}
]
Step 2: Calculate personal exemptions
In 2014, taxpayers could generally claim a personal exemption of $3,950 for themselves, their spouse, and each qualifying dependent.
This family has four eligible individuals:
- Husband: $3,950
- Wife: $3,950
- First child: $3,950
- Second child: $3,950
Total exemptions:
[
4\times $3,950=\boxed{$15,800}
]
Step 3: Calculate taxable income
Now subtract the standard deduction and personal exemptions from the family's income.
[
\text{Taxable Income}
=\text{Income}-\text{Deductions}-\text{Exemptions}
]
Substituting:
[
=68,000-12,400-15,800
]
[
\boxed{\text{Taxable Income}=$39,800}
]
Step 4: Determine the marginal tax rate
For married couples filing jointly in 2014, the relevant federal income tax brackets were:
| Taxable IncomeTax Rate | |
| $0–$18,150 | 10% |
| $18,150–$73,800 | 15% |
| $73,800–$148,850 | 25% |
Since the family's taxable income is $39,800, their highest applicable tax bracket is 15%.
Therefore:
[
\boxed{\text{Marginal Tax Rate}=15%}
]
Remember, the marginal tax rate is the rate applied to the next dollar of taxable income. It does not mean the entire income is taxed at 15%.
Step 5: Calculate the child tax credit
In 2014, the child tax credit was generally $1,000 per qualifying child under age 17.
Since the family has two qualifying children:
[
2\times $1,000=\boxed{$2,000}
]
This is a tax credit rather than a deduction.
A deduction reduces taxable income, while a tax credit directly reduces the amount of tax owed.
Step 6: Calculate federal income tax
Using the 2014 IRS Tax Table for married couples filing jointly, taxable income of $39,800 produces a federal income tax of:
[
$5,066
]
Now subtract the child tax credit:
[
5,066-2,000=\boxed{$3,066}
]
Therefore, the family's estimated federal income tax liability is $3,066.
Step 7: Calculate the average tax rate
The average income tax rate measures the percentage of total income paid in federal income taxes.
[
\text{Average Tax Rate}
=\frac{\text{Federal Income Tax}}{\text{Total Income}}\times100
]
Substituting:
[
=\frac{3,066}{68,000}\times100
]
[
\boxed{\text{Average Tax Rate}\approx4.51%}
]
Final Answers
| ItemAmount | |
| Standard deduction | $12,400 |
| Total personal exemptions | $15,800 |
| Child tax credit | $2,000 |
| Taxable income | $39,800 |
| Marginal tax rate | 15% |
| Average tax rate | 4.51% |
Key takeaway: The marginal tax rate and average tax rate are different!
The marginal rate tells us how the next dollar of taxable income is taxed, while the average rate measures the family's overall federal income tax burden relative to its income.
In this example, the family's marginal tax rate is 15%, but its average tax rate is only about 4.51% because of progressive tax brackets, deductions, exemptions, and credits.
One final note: These calculations assume no additional deductions, credits, or income adjustments. They also exclude state income taxes and payroll taxes.
Hope this helps!
Michael
