document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1168513>Question 1168513</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Kent sold his car to Carolyn for $1,000 down and monthly payments of $120.03 at the end of every month for 3 1/2 years. The interest rate charged is 12%, compounded monthly. What was the selling price of the car?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851564 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=851564\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down this problem step by step to find the selling price of the car.\r<BR>\n" );
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document.write( "**1. Understand the Problem**\r<BR>\n" );
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document.write( "* Kent sold his car to Carolyn.<BR>\n" );
document.write( "* Down payment = $1,000<BR>\n" );
document.write( "* Monthly payments = $120.03<BR>\n" );
document.write( "* Payment period = 3.5 years<BR>\n" );
document.write( "* Interest rate = 12% per year, compounded monthly\r<BR>\n" );
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document.write( "**2. Calculate the Number of Payments**\r<BR>\n" );
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document.write( "* Number of years = 3.5<BR>\n" );
document.write( "* Number of months = 3.5 * 12 = 42 payments\r<BR>\n" );
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document.write( "**3. Calculate the Monthly Interest Rate**\r<BR>\n" );
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document.write( "* Annual interest rate = 12% = 0.12<BR>\n" );
document.write( "* Monthly interest rate (r) = 0.12 / 12 = 0.01\r<BR>\n" );
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document.write( "**4. Calculate the Present Value of the Monthly Payments**\r<BR>\n" );
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document.write( "We need to find the present value (PV) of the annuity (monthly payments). The formula for the present value of an ordinary annuity is:\r<BR>\n" );
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document.write( "PV = PMT * [1 - (1 + r)^-n] / r\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "* PV = Present value of the annuity<BR>\n" );
document.write( "* PMT = Monthly payment = $120.03<BR>\n" );
document.write( "* r = Monthly interest rate = 0.01<BR>\n" );
document.write( "* n = Number of payments = 42\r<BR>\n" );
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document.write( "PV = 120.03 * [1 - (1 + 0.01)^-42] / 0.01<BR>\n" );
document.write( "PV = 120.03 * [1 - (1.01)^-42] / 0.01<BR>\n" );
document.write( "PV = 120.03 * [1 - 0.65584] / 0.01<BR>\n" );
document.write( "PV = 120.03 * 0.34416 / 0.01<BR>\n" );
document.write( "PV = 120.03 * 34.416<BR>\n" );
document.write( "PV ≈ 4131.05\r<BR>\n" );
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document.write( "**5. Calculate the Selling Price**\r<BR>\n" );
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document.write( "The selling price is the sum of the down payment and the present value of the monthly payments.\r<BR>\n" );
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document.write( "Selling price = Down payment + PV<BR>\n" );
document.write( "Selling price = $1,000 + $4,131.05<BR>\n" );
document.write( "Selling price = $5,131.05\r<BR>\n" );
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document.write( "**Therefore, the selling price of the car was approximately $5,131.05.**<BR>\n" );
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