Question

The Canada in 2019 had five federal income tax brackets, with rates of 15%, 20.5%, 26%, 29% and 33%. If you fall into the 33% bracket, that doesn’t mean that the entirety of your taxable income will be subject to a 33% tax. Instead, 33% is your top marginal tax rate.
FEDERAL TAX BRACKETS 2018 – 2019
Tax rate (%)
$46,605 or less
15
$46,605 to $93,208
20.5
$93,208 to $144,489
26
$144,489 to $205,842
29
More than $205,842
33

Create a Mathematical Model that represents the aforementioned information to calculate the annual income tax.
How much annual income tax you will have to pay if your monthly taxable income is $ 12,000.

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Answer 1

Given : five federal income tax brackets, with rates of 15%, 20.5%, 26%, 29% and 33%

 

To Find : a) Create a Mathematical Model that represents the aforementioned information to calculate the annual income tax.

b) How much annual income tax you will have to pay if your monthly taxable income is $ 12,000.

Solution:

TAX BRACKETS                  Tax rate (%)

$46,605 or less                            15

$46,605 to $93,208                   20.5

$93,208 to $144,489                  26

$144,489 to $205,842                 29

More than  $205,842                  33

Let say Income = x

Tax  = 0.15x     if  0 < x  ≤ $46,605

0.15 (46,605) = 6,990.75 $

Tax  = 0.205(x -46,605)   + 6,990.75 if  $46,605 < x  ≤ $93,208

= 0.205x - 2,563.275   if  $46,605 < x  ≤ $93,208

16,544.365

Tax  = 0.26(x - 93,208) + 16,544.365  if  $93,208 < x  ≤ $144,489

= 0.26x - 7,689.715  if  $93,208 < x  ≤ $144,489

29,877.425

Tax  = 0.29(x - 144,489) +29,877.425  if  $144,489 < x  ≤  $205,842  

= 0.29x - 12,024.385  if  $144,489 < x  ≤  $205,842

47,669.795

Tax  = 0.33(x - 205,842) +47,669.795  if  $205,842 < x  

= 0.33x - 20,258.065  if  $205,842 < x

monthly taxable income is $ 12,000.

=> annual = 12 x 12000 = $ 144000

$93,208 < x  ≤ $144,489  

0.26x - 7,689.715

= 29,750.285 $

annual income tax  29,750.285 $

Mathematical Model  :

0.15x     if  0 < x  ≤ $46,605

0.205x - 2,563.275   if  $46,605 < x  ≤ $93,208

0.26x - 7,689.715  if  $93,208 < x  ≤ $144,489

0.29x - 12,024.385  if  $144,489 < x  ≤  $205,842

0.33x - 20,258.065  if  $205,842 < x

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