Question 1173639: In USA there are seven federal tax brackets for the 2020 tax year: 10%, 12%, 22%, 24%, 32%,
35% and 37%. Your bracket depends on your taxable income and filing status. These are the
rates for taxes due in April 2021 if you are a single filer.
Taxable Income Tax Rate
$0 to $9,875 10%
$9,876 to $40,125 12%
$40,126 to $85,525 22%
$85,526 to $163,300 24%
$163,301 to $207,350 32%
$207,351 to $518,400 35%
$518,401 or more 37%
a) Create a Mathematical Model that represents the aforementioned information to calculate the
annual income tax of each slab.
b) How much annual income tax you will have to pay if your monthly taxable income is
$13,750.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's break down how to model and calculate the US federal income tax for a single filer in 2020.
**a) Mathematical Model**
We can represent the tax calculation as a piecewise function, where each piece corresponds to a tax bracket.
Let:
* `I` = Annual Taxable Income
* `T(I)` = Total Tax
The tax brackets and rates are:
1. **10% Bracket:**
* If $0 ≤ I ≤ $9,875, then `T(I) = 0.10 * I`
2. **12% Bracket:**
* If $9,876 ≤ I ≤ $40,125, then `T(I) = 0.10 * 9,875 + 0.12 * (I - 9,875)`
3. **22% Bracket:**
* If $40,126 ≤ I ≤ $85,525, then `T(I) = 0.10 * 9,875 + 0.12 * (40,125 - 9,875) + 0.22 * (I - 40,125)`
4. **24% Bracket:**
* If $85,526 ≤ I ≤ $163,300, then `T(I) = 0.10 * 9,875 + 0.12 * (40,125 - 9,875) + 0.22 * (85,525 - 40,125) + 0.24 * (I - 85,525)`
5. **32% Bracket:**
* If $163,301 ≤ I ≤ $207,350, then `T(I) = 0.10 * 9,875 + 0.12 * (40,125 - 9,875) + 0.22 * (85,525 - 40,125) + 0.24 * (163,300 - 85,525) + 0.32 * (I - 163,300)`
6. **35% Bracket:**
* If $207,351 ≤ I ≤ $518,400, then `T(I) = 0.10 * 9,875 + 0.12 * (40,125 - 9,875) + 0.22 * (85,525 - 40,125) + 0.24 * (163,300 - 85,525) + 0.32 * (207,350 - 163,300) + 0.35 * (I - 207,350)`
7. **37% Bracket:**
* If $I ≥ $518,401, then `T(I) = 0.10 * 9,875 + 0.12 * (40,125 - 9,875) + 0.22 * (85,525 - 40,125) + 0.24 * (163,300 - 85,525) + 0.32 * (207,350 - 163,300) + 0.35 * (518,400 - 207,350) + 0.37 * (I - 518,400)`
**b) Calculating Tax for a Monthly Income of $13,750**
1. **Calculate Annual Income:**
* Annual Income (I) = $13,750 * 12 = $165,000
2. **Determine the Applicable Tax Bracket:**
* $165,000 falls within the $163,301 to $207,350 bracket (32%).
3. **Calculate the Tax:**
* T(I) = 0.10 * 9,875 + 0.12 * (40,125 - 9,875) + 0.22 * (85,525 - 40,125) + 0.24 * (163,300 - 85,525) + 0.32 * (165,000 - 163,300)
* T(I) = 987.5 + 3,630 + 9,988 + 18,666 + 544
* T(I) = $33,815.5
Therefore, the annual income tax would be $33,815.5.
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