Question 1173946: 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%
Table 2
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! Absolutely! Let's break down this tax calculation problem.
**a) Mathematical Model**
We'll create a piecewise function to represent the tax brackets. Let `I` be the annual taxable income, and `T(I)` be the total tax owed.
* **10% Bracket:**
* If 0 ≤ I ≤ $9,875, then T(I) = 0.10 * I
* **12% Bracket:**
* If $9,876 ≤ I ≤ $40,125, then T(I) = $987.50 + 0.12 * (I - $9,875)
* **22% Bracket:**
* If $40,126 ≤ I ≤ $85,525, then T(I) = $3,617.50 + 0.22 * (I - $40,125)
* **24% Bracket:**
* If $85,526 ≤ I ≤ $163,300, then T(I) = $13,627.50 + 0.24 * (I - $85,525)
* **32% Bracket:**
* If $163,301 ≤ I ≤ $207,350, then T(I) = $32,208.50 + 0.32 * (I - $163,300)
* **35% Bracket:**
* If $207,351 ≤ I ≤ $518,400, then T(I) = $46,304.50 + 0.35 * (I - $207,350)
* **37% Bracket:**
* If I ≥ $518,401, then T(I) = $155,142.00 + 0.37 * (I - $518,400)
**b) Calculating Tax for a Monthly Income of $13,750**
1. **Calculate Annual Income:**
* Annual Income = $13,750 * 12 = $165,000
2. **Determine the Tax Bracket:**
* $165,000 falls within the 32% tax bracket ($163,301 to $207,350).
3. **Calculate the Tax:**
* T($165,000) = $32,208.50 + 0.32 * ($165,000 - $163,300)
* T($165,000) = $32,208.50 + 0.32 * $1,700
* T($165,000) = $32,208.50 + $544
* T($165,000) = $32,752.50
**Therefore, the annual income tax would be $32,752.50.**
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