document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109126>Question 1109126</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 8%/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 60 months? Over a period of 72 months? <BR>\n" );
document.write( "(b) What will the interest charges be if she elects the 60-month plan? The 72-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 #724141 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=724141\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> price of the car is 12,000.<BR>\n" );
document.write( "down payment is 25%.<BR>\n" );
document.write( "finance rate is 8% compounded monthly.\r<BR>\n" );
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document.write( "(a) What monthly payment will she be required to make if the car is financed over a period of 60 months? Over a period of 72 months? <BR>\n" );
document.write( "(b) What will the interest charges be if she elects the 60-month plan? The 72-month plan?\r<BR>\n" );
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document.write( "using TI-BA-II, you would do the following:\r<BR>\n" );
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document.write( "for 60 month loan:\r<BR>\n" );
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document.write( "PV = .75 * 12,000 = 9,000<BR>\n" );
document.write( "FV = 0<BR>\n" );
document.write( "I/Y = 8% / 12 <BR>\n" );
document.write( "N = 60<BR>\n" );
document.write( "calculate PMT to get:<BR>\n" );
document.write( "PMT = 182.4875486 per month\r<BR>\n" );
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document.write( "for 72 month loan:\r<BR>\n" );
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document.write( "PV = .75 * 12,000 = 9,000<BR>\n" );
document.write( "FV = 0<BR>\n" );
document.write( "I/Y = 8% / 12<BR>\n" );
document.write( "N = 72<BR>\n" );
document.write( "calculate PMT to get:<BR>\n" );
document.write( "PMT = 157.7991655 per month\r<BR>\n" );
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document.write( "in the calculator:\r<BR>\n" );
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document.write( "the 9,000 is entered as positive because it's money that the bank gave to you.<BR>\n" );
document.write( "the monthly payment is shown as negative because it's money you gave to the bank.\r<BR>\n" );
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document.write( "with the 60 month loan, your payment is 182.4875486 per month.<BR>\n" );
document.write( "multiply this payment by 60 months and the total you paid to the bank is 10,949.25292.<BR>\n" );
document.write( "subtract 9,000 from this, and the interest you paid is 1,949.252916.\r<BR>\n" );
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document.write( "with the 72 month loan, your payment is 157.7991655 per month.<BR>\n" );
document.write( "multiply this payment by 72 months and the total you paid to the bank is 11,361.53992.<BR>\n" );
document.write( "subtract 9,000 from this, and the interest you paid is 2,361.539917.\r<BR>\n" );
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document.write( "rounded to 2 decimal places, you get:\r<BR>\n" );
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document.write( "60 month loan pays 182.49 per month with total interest of 1,949.25.<BR>\n" );
document.write( "72 month loan pays 157.80 per month with total interest of 2,361.54.\r<BR>\n" );
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document.write( "you can do this with formulas as well.<BR>\n" );
document.write( "the formula you would use is:\r<BR>\n" );
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document.write( "ANNUITY FOR A PRESENT AMOUNT WITH END OF TIME PERIOD PAYMENTS \r<BR>\n" );
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document.write( "a = (p*r)/(1-(1/(1+r)^n)) \r<BR>\n" );
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document.write( "a is the annuity.<BR>\n" );
document.write( "p is the present amount.<BR>\n" );
document.write( "r is the interest rate per time period.<BR>\n" );
document.write( "n is the number of time periods. \r<BR>\n" );
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document.write( "this formula was taken from <a  rel=nofollow HREF= \"https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#f9\" target = \"_blank\">https://www.algebra.com/algebra/homework/Finance/THEO-2016-04-29.lesson#f9</a>\r<BR>\n" );
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document.write( "using this formula on the 60 month loan, a = (p*r)/(1-(1/(1+r)^n)) becomes:\r<BR>\n" );
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document.write( "a = (9000*.08/12)/(1-(1/(1+.08/12)^60)), resulting in:<BR>\n" );
document.write( "a = 182.4875486.\r<BR>\n" );
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document.write( "using this formula on the 72 month loan, a = (p*r)/(1-(1/(1+r)^n)) becomes:\r<BR>\n" );
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document.write( "a = (9000*.08/12)/(1-(1/(1+.08/12)^72)), resulting in:<BR>\n" );
document.write( "a = 157.7991655.\r<BR>\n" );
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document.write( "you enter the interest rate as a rate, not a percent.<BR>\n" );
document.write( "8% divided by 100 = .08.\r<BR>\n" );
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document.write( "you need to make sure you enter the parentheses in your calculator exactly as shown.<BR>\n" );
document.write( "otherwise, you may not be able to duplicate the answer that the financial calculator gave you.\r<BR>\n" );
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document.write( "if you wish to do this using an online financial calculator, then one such calculator that can be used is found at <a  rel=nofollow HREF= \"https://arachnoid.com/finance/\" target = \"_blank\">https://arachnoid.com/finance/</a>\r<BR>\n" );
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document.write( "that calculator works the same as the TI-BA-II, but it does some rounding on the inputs and outputs, so the answer is less detailed as with the TI-BA-II.\r<BR>\n" );
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document.write( "using that calculator, i got:\r<BR>\n" );
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document.write( "60 month loan monthly payment is 182.49<BR>\n" );
document.write( "72 month loan monthly payment is 157.80\r<BR>\n" );
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document.write( "calculating total interest based on that result, i would have gotten.\r<BR>\n" );
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document.write( "total interest on 60 month loan is 60 * 182.49 - 9000 = 19,49.40<BR>\n" );
document.write( "total interest on 72 month loan is 72 * 157.80 - 9000 = 2,361.60\r<BR>\n" );
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document.write( "the difference between that and what i got above using the TI-BA-II is intermediate rounding of results.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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