document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1173639>Question 1173639</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In USA there are seven federal tax brackets for the 2020 tax year: 10%, 12%, 22%, 24%, 32%,<BR>\n" );
document.write( "35% and 37%. Your bracket depends on your taxable income and filing status. These are the<BR>\n" );
document.write( "rates for taxes due in April 2021 if you are a single filer.<BR>\n" );
document.write( "Taxable Income                 Tax Rate<BR>\n" );
document.write( "$0 to $9,875                    10%<BR>\n" );
document.write( "$9,876 to $40,125               12%<BR>\n" );
document.write( "$40,126 to $85,525              22%<BR>\n" );
document.write( "$85,526 to $163,300             24%<BR>\n" );
document.write( "$163,301 to $207,350            32%<BR>\n" );
document.write( "$207,351 to $518,400            35%<BR>\n" );
document.write( "$518,401 or more                37%\r<BR>\n" );
document.write( "\n" );
document.write( "a) Create a Mathematical Model that represents the aforementioned information to calculate the<BR>\n" );
document.write( "annual income tax of each slab.<BR>\n" );
document.write( "b) How much annual income tax you will have to pay if your monthly taxable income is<BR>\n" );
document.write( "$13,750.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850727 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850727\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down how to model and calculate the US federal income tax for a single filer in 2020.\r<BR>\n" );
document.write( "\n" );
document.write( "**a) Mathematical Model**\r<BR>\n" );
document.write( "\n" );
document.write( "We can represent the tax calculation as a piecewise function, where each piece corresponds to a tax bracket.\r<BR>\n" );
document.write( "\n" );
document.write( "Let:\r<BR>\n" );
document.write( "\n" );
document.write( "* `I` = Annual Taxable Income<BR>\n" );
document.write( "* `T(I)` = Total Tax\r<BR>\n" );
document.write( "\n" );
document.write( "The tax brackets and rates are:\r<BR>\n" );
document.write( "\n" );
document.write( "1.  **10% Bracket:**<BR>\n" );
document.write( "    * If $0 ≤ I ≤ $9,875, then `T(I) = 0.10 * I`<BR>\n" );
document.write( "2.  **12% Bracket:**<BR>\n" );
document.write( "    * If $9,876 ≤ I ≤ $40,125, then `T(I) = 0.10 * 9,875 + 0.12 * (I - 9,875)`<BR>\n" );
document.write( "3.  **22% Bracket:**<BR>\n" );
document.write( "    * If $40,126 ≤ I ≤ $85,525, then `T(I) = 0.10 * 9,875 + 0.12 * (40,125 - 9,875) + 0.22 * (I - 40,125)`<BR>\n" );
document.write( "4.  **24% Bracket:**<BR>\n" );
document.write( "    * 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)`<BR>\n" );
document.write( "5.  **32% Bracket:**<BR>\n" );
document.write( "    * 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)`<BR>\n" );
document.write( "6.  **35% Bracket:**<BR>\n" );
document.write( "    * 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)`<BR>\n" );
document.write( "7.  **37% Bracket:**<BR>\n" );
document.write( "    * 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)`\r<BR>\n" );
document.write( "\n" );
document.write( "**b) Calculating Tax for a Monthly Income of $13,750**\r<BR>\n" );
document.write( "\n" );
document.write( "1.  **Calculate Annual Income:**<BR>\n" );
document.write( "    * Annual Income (I) = $13,750 * 12 = $165,000\r<BR>\n" );
document.write( "\n" );
document.write( "2.  **Determine the Applicable Tax Bracket:**<BR>\n" );
document.write( "    * $165,000 falls within the $163,301 to $207,350 bracket (32%).\r<BR>\n" );
document.write( "\n" );
document.write( "3.  **Calculate the Tax:**<BR>\n" );
document.write( "    * 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)<BR>\n" );
document.write( "    * T(I) = 987.5 + 3,630 + 9,988 + 18,666 + 544<BR>\n" );
document.write( "    * T(I) = $33,815.5\r<BR>\n" );
document.write( "\n" );
document.write( "Therefore, the annual income tax would be $33,815.5.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );