document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200898>Question 1200898</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The price of a new car is $12,000. Assume that an individual makes a down payment of 25% toward the purchase of the car and secures financing for the balance at the rate of 6%/year compounded monthly. (Round your answers to the nearest cent.)<BR>\n" );
document.write( "(a) What monthly payment will she be required to make if the car is financed over a period of 48 months? Over a period of 60 months?\r<BR>\n" );
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document.write( "48 months:<BR>\n" );
document.write( "60 months:\r<BR>\n" );
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document.write( "(b) What will the interest charges be if she elects the 48-month plan? The 60-month plan?\r<BR>\n" );
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document.write( "48-month plan:    <BR>\n" );
document.write( " 60-month plan: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #835130 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=835130\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Part (a)\r<BR>\n" );
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document.write( "The car is priced at $12,000<BR>\n" );
document.write( "The buyer puts 25% down, so the remaining 75% is loaned.\r<BR>\n" );
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document.write( "75% of 12000 = 0.75*12000 = 9000 dollars is the loan amount\r<BR>\n" );
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document.write( "We'll be using this monthly payment formula<BR>\n" );
document.write( "P = (L*i)/( 1 - (1+i)^(-n) )<BR>\n" );
document.write( "where,<BR>\n" );
document.write( "P = monthly payment<BR>\n" );
document.write( "L = loan amount<BR>\n" );
document.write( "i = decimal form of the monthly interest rate<BR>\n" );
document.write( "n = number of months\r<BR>\n" );
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document.write( "In this case,<BR>\n" );
document.write( "P = unknown<BR>\n" );
document.write( "L = 9000<BR>\n" );
document.write( "i = 0.06/12 = 0.005<BR>\n" );
document.write( "n = 48 for now (we'll use n = 60 later)\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "P = (L*i)/( 1 - (1+i)^(-n) )<BR>\n" );
document.write( "P = (9000*0.005)/(1 - (1+0.005)^(-48))<BR>\n" );
document.write( "P = 211.365261431424<BR>\n" );
document.write( "P = 211.37<BR>\n" );
document.write( "This is the monthly payment if you go for the 48 month (aka 4 year) plan.\r<BR>\n" );
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document.write( "This calculator may come in handy<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.calculator.net/loan-calculator.html\">https://www.calculator.net/loan-calculator.html</a>\r<BR>\n" );
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document.write( "We'll repeat very similar steps for the 5 year plan, but use n = 60 this time. Keep everything else the same.<BR>\n" );
document.write( "P = (L*i)/( 1 - (1+i)^(-n) )<BR>\n" );
document.write( "P = (9000*0.005)/(1 - (1+0.005)^(-60))<BR>\n" );
document.write( "P = 173.995213764854<BR>\n" );
document.write( "P = 174.00<BR>\n" );
document.write( "This is the monthly payment if you go for the 60-month plan.\r<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "Monthly payment for 48 months: <font color=red>$211.37</font><BR>\n" );
document.write( "Monthly payment for 60 months: <font color=red>$174</font>\r<BR>\n" );
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document.write( "======================================================================<BR>\n" );
document.write( "Part (b)\r<BR>\n" );
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document.write( "Over the course of 48 months, the monthly payment is $211.37 calculated earlier in part (a).\r<BR>\n" );
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document.write( "Therefore, you'll pay back a total of 48*211.37 = 10,145.76 dollars.<BR>\n" );
document.write( "Subtract off the loan amount ($9000) to compute the interest<BR>\n" );
document.write( "10,145.76 - 9,000 = 1,145.76\r<BR>\n" );
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document.write( "Follow the same outline for the 60-month plan.<BR>\n" );
document.write( "(60 months)*($174 per month) = 10440 dollars paid back <BR>\n" );
document.write( "10440 - 9000 = 1440<BR>\n" );
document.write( "You pay slightly more interest due to the longer lifespan of the loan. \r<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "Interest charged for 48 months: <font color=red>$1,145.76</font><BR>\n" );
document.write( "Interest charged for 60 months: <font color=red>$1440</font><BR>\n" );
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