document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178748>Question 1178748</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this, thank-you. Installment plant mike's sporting goods sell elliptical trainers under under 2 payment plans cash or installment under the installment plan the customer pays $22/month over 3 years with interest charged on the balance at rate of 18%per year compounded monthly.find cash price for an elliptical trainer if it is equivalent to the price paid by a customer using the installment plan answer </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850301 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=850301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's break down how to find the equivalent cash price of the elliptical trainer.\r<BR>\n" );
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document.write( "**1. Calculate the Total Number of Payments:**\r<BR>\n" );
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document.write( "* The customer pays $22 per month for 3 years.<BR>\n" );
document.write( "* Total payments: 3 years * 12 months/year = 36 payments\r<BR>\n" );
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document.write( "**2. Calculate the Monthly Interest Rate:**\r<BR>\n" );
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document.write( "* The annual interest rate is 18%.<BR>\n" );
document.write( "* The monthly interest rate is 18% / 12 = 1.5% = 0.015.\r<BR>\n" );
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document.write( "**3. Use the Present Value of an Ordinary Annuity Formula:**\r<BR>\n" );
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document.write( "* The cash price is equivalent to the present value of the installment payments.<BR>\n" );
document.write( "* The formula is: 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 (cash price)<BR>\n" );
document.write( "* PMT = Monthly payment ($22)<BR>\n" );
document.write( "* r = Monthly interest rate (0.015)<BR>\n" );
document.write( "* n = Number of payments (36)\r<BR>\n" );
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document.write( "**4. Plug in the Values and Calculate:**\r<BR>\n" );
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document.write( "* PV = 22 * [1 - (1 + 0.015)^-36] / 0.015<BR>\n" );
document.write( "* PV = 22 * [1 - (1.015)^-36] / 0.015<BR>\n" );
document.write( "* PV = 22 * [1 - 0.580039] / 0.015<BR>\n" );
document.write( "* PV = 22 * [0.419961] / 0.015<BR>\n" );
document.write( "* PV = 22 * 27.9974<BR>\n" );
document.write( "* PV ≈ $615.94\r<BR>\n" );
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document.write( "**Therefore, the cash price for the elliptical trainer is approximately $615.94.**<BR>\n" );
document.write( " </SPAN>\n" );
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