document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=754221>Question 754221</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can you please help me with this problem?<BR>\n" );
document.write( "A car has a sticker price of $42,650 with factory and dealer rebates of $5,100.<BR>\n" );
document.write( "You can pay the sticker price at 0% interest for 60 months.<BR>\n" );
document.write( "You can pay the discount price at 2.5% add-on interest for 60 months.<BR>\n" );
document.write( "a) Find the monthly payment if financed for 60 months at 0% APR. (Round to the nearest cent.)<BR>\n" );
document.write( "b) Find the monthly payments if financed at 2.5% add-on interest for 60 months.<BR>\n" );
document.write( "c)use the APR approximation formula to find the APR for part (b). <BR>\n" );
document.write( "d? State whether the 0% APR or the 2.5% add-on rate should be preferred. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #459000 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=459000\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you can use an online calculator like the one shown below to do the add-on Interest Calculations.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.csgnetwork.com/addonintcalc.html\" target = \"_blank\">http://www.csgnetwork.com/addonintcalc.html</a>\r<BR>\n" );
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document.write( "you can use an online calculator like the one shown below to do the apr calculations.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://www.carpaymentcalculator.net/\" target = \"_blank\">http://www.carpaymentcalculator.net/</a>\r<BR>\n" );
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document.write( "it makes a difference whether you are paying add-on interest on the original purchase price of the car or whether you are paying add-on interest on the discount price of the car and getting a check back from the dealer for the rebate.\r<BR>\n" );
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document.write( "we'll look at each scenario and see which one looks the best.\r<BR>\n" );
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document.write( "scenario 1 is financing the purchase price of $42,650 at 0% interest for 60 months.\r<BR>\n" );
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document.write( "using the apr calculator, you will find that the monthly payment is equal to $710.83\r<BR>\n" );
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document.write( "scenario 2 is financing the discount price of $37,550 at 2.5% add-on interest for 60 months.\r<BR>\n" );
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document.write( "using the add-on calculator, you will find that the monthly payment is equal to $704.06\r<BR>\n" );
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document.write( "scenario 3 is financing the purchase price of $42,650 at 2.5% add-on interest for 60 months and receiving a rebate check of $5,100 from the dealer.\r<BR>\n" );
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document.write( "using the add-on calculator, you will find that the monthly payment is equal to $799.69\r<BR>\n" );
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document.write( "the next question is which is cheaper for you?\r<BR>\n" );
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document.write( "you can compare scenario 1 to scenario 2, or you can compare scenario 1 to scenario 3.\r<BR>\n" );
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document.write( "let's look at scenario 1 compared to scenario 2 first.\r<BR>\n" );
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document.write( "scenario 1 costs you $710.83 per month for 60 months.<BR>\n" );
document.write( "scenario 2 costs you $704.06 per month for 60 months.\r<BR>\n" );
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document.write( "you can compare these by taking the present value of the monthly payments at 2.5% interest rate.\r<BR>\n" );
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document.write( "the present value of $710.83 per month for 60 months at 2.5% apr is equal to $40136.16.\r<BR>\n" );
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document.write( "the present value of $704.06 per month for 60 months at 2.5% apr is equal to $39,753.90.\r<BR>\n" );
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document.write( "on a present value basis:\r<BR>\n" );
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document.write( "scenario 1 costs $40,136.16<BR>\n" );
document.write( "scenario 2 costs $39,753.90\r<BR>\n" );
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document.write( "scenario 2 is the winner.<BR>\n" );
document.write( "you have no cash in your pocket, but you are making less payments per month for the life of the loan.\r<BR>\n" );
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document.write( "let's look at scenario 1 compared to scenario 3 next.\r<BR>\n" );
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document.write( "scenario 1 costs you $710.83 per month<BR>\n" );
document.write( "scenario 3 costs you $799.69 per month but you have $5,100 cash in your pocket.\r<BR>\n" );
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document.write( "the present value of 60 payments of $710.83 per month at 2.5% apr is equal to $40,136.16.\r<BR>\n" );
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document.write( "the present value of 60 payments of $799.69 per month at 2.5% apr is equal to $45,153.53.<BR>\n" );
document.write( "take the $5,100 cash that you got back from the dealer and subtract it from $45,153.53 and you are left with $40,053.53\r<BR>\n" );
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document.write( "on a present value basis:\r<BR>\n" );
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document.write( "scenario 1 costs you $40,136.16<BR>\n" );
document.write( "scenario 3 costs you $40,053.53\r<BR>\n" );
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document.write( "scenario 3 is the winner but they're extremely close.<BR>\n" );
document.write( "it doesn't make much difference which one of these options you choose.<BR>\n" );
document.write( "on a present value basis, they are roughly equivalent.<BR>\n" );
document.write( "choose the one that fits your life style better.<BR>\n" );
document.write( "do you want the reduced payments or do you want the cash?<BR>\n" );
document.write( "in the long run, the net financial effect is the same.\r<BR>\n" );
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document.write( "this may or may not answer the question you posed.<BR>\n" );
document.write( "i'm assuming you wanted to make a financial comparison.\r<BR>\n" );
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document.write( "to answer your questions directly, these would be the answers:\r<BR>\n" );
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document.write( "a) Find the monthly payment if financed for 60 months at 0% APR. (Round to the nearest cent.)\r<BR>\n" );
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document.write( "the monthly payment would be $710.83 per month.\r<BR>\n" );
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document.write( "b) Find the monthly payments if financed at 2.5% add-on interest for 60 months.\r<BR>\n" );
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document.write( "the monthly payments depend on whether the add-on interest payments are made on the original purchase price of the car or on the discount price of the car.\r<BR>\n" );
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document.write( "if made on the original purchase price, then the payments would be $799.69 per month.<BR>\n" );
document.write( "if made on the discount price, then the payments would be $704.06 per month.\r<BR>\n" );
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document.write( "c)use the APR approximation formula to find the APR for part (b).\r<BR>\n" );
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document.write( "based on the original purchase price of $42,650, the equivalent apr would be:\r<BR>\n" );
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document.write( "if made on the original purchase price, then the equivalent apr would be 4.9%<BR>\n" );
document.write( "if made on the discount price, then the equivalent apr would be -0.4%\r<BR>\n" );
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document.write( "d? State whether the 0% APR or the 2.5% add-on rate should be preferred.\r<BR>\n" );
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document.write( "the comparisons are very close and the apr comparisons doesn't really tell the whole story because it doesn't consider the cash back in scenario 3.\r<BR>\n" );
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document.write( "bottom line is that taking the discount gives you a better deal because you are either making smaller payments (scenario 1 versus scenario 2), or you are making larger payments but getting cash back up front (scenario 1 versus scenario 3).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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