document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163381>Question 1163381</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A.	According to the Turkish tax legislation, there are two main types of tax statuses regulated on the basis of residence: resident taxpayers and non-resident taxpayers. Individual income tax rates applicable on resident taxpayers for 2018 - 2019 are as follows:<BR>\n" );
document.write( "Income Scales (TRY)	Rate (%)<BR>\n" );
document.write( "Up to 14,800                    15<BR>\n" );
document.write( "14,801 - 34,000	                20<BR>\n" );
document.write( "34,001 - 120,000	        27<BR>\n" );
document.write( "120,001 and over	        35\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a)	Create a Mathematical Model that represents the aforementioned information to calculate the annual income tax.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b)	How much annual income tax you will have to pay if your monthly taxable income is TRY 9,000.<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 #854380 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2264)</B></A><img src=\"/images/stars/stars-13.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=854380\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Based on the 2018  -  2019 Turkish tax brackets provided, here is the mathematical model and the calculation for the specified income.\r<BR>\n" );
document.write( "\n" );
document.write( "### a) Mathematical Model<BR>\n" );
document.write( "Let $I$ represent the **Annual Taxable Income** (in TRY) and $T(I)$ represent the **Annual Income Tax**. The progressive tax system is modeled as a piecewise function:\r<BR>\n" );
document.write( "\n" );
document.write( "$$<BR>\n" );
document.write( "T(I) = <BR>\n" );
document.write( "\begin{cases} <BR>\n" );
document.write( "0.15I & \text{if } 0 < I \le 14,800 \\<BR>\n" );
document.write( "2,220 + 0.20(I - 14,800) & \text{if } 14,800 < I \le 34,000 \\<BR>\n" );
document.write( "6,060 + 0.27(I - 34,000) & \text{if } 34,000 < I \le 120,000 \\<BR>\n" );
document.write( "29,280 + 0.35(I - 120,000) & \text{if } I > 120,001 <BR>\n" );
document.write( "\end{cases}<BR>\n" );
document.write( "$$\r<BR>\n" );
document.write( "\n" );
document.write( "**Breakdown of Cumulative Constants:**<BR>\n" );
document.write( "* **$2,220$**: Tax on the first bracket ($14,800 \times 0.15$).<BR>\n" );
document.write( "* **$6,060$**: Total tax through the second bracket ($2,220 + [34,000 - 14,800] \times 0.20$).<BR>\n" );
document.write( "* **$29,280$**: Total tax through the third bracket ($6,060 + [120,000 - 34,000] \times 0.27$).\r<BR>\n" );
document.write( "\n" );
document.write( "---\r<BR>\n" );
document.write( "\n" );
document.write( "### b) Annual Income Tax Calculation\r<BR>\n" );
document.write( "\n" );
document.write( "**1. Determine Annual Taxable Income**<BR>\n" );
document.write( "Since the tax rates apply to annual income, we first convert the monthly taxable income:<BR>\n" );
document.write( "$$I = 9,000 \text{ TRY/month} \times 12 \text{ months} = 108,000 \text{ TRY}$$\r<BR>\n" );
document.write( "\n" );
document.write( "**2. Identify the Relevant Bracket**<BR>\n" );
document.write( "The annual income of $108,000$ TRY falls into the **third bracket** ($34,001$ to $120,000$).\r<BR>\n" );
document.write( "\n" );
document.write( "**3. Apply the Formula**<BR>\n" );
document.write( "Using the third part of our piecewise model:<BR>\n" );
document.write( "$$T(108,000) = 6,060 + 0.27 \times (108,000 - 34,000)$$<BR>\n" );
document.write( "$$T(108,000) = 6,060 + 0.27 \times (74,000)$$<BR>\n" );
document.write( "$$T(108,000) = 6,060 + 19,980$$<BR>\n" );
document.write( "$$T(108,000) = 26,040$$\r<BR>\n" );
document.write( "\n" );
document.write( "**Final Answer:**<BR>\n" );
document.write( "If your monthly taxable income is TRY 9,000, you will have to pay an annual income tax of **TRY 26,040**. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );