document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206601>Question 1206601</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Starting on July 1, 2000, Peter borrows $7000 each year for 4 years from his dear Aunt May to pay for college. (Note: the last date that he borrows money is July 1, 2003.) From the beginning, Aunt May agreed to defer all interest on the loans until Peter finds a job; i.e. Peter's loans will not accumulate any interest until the first day he starts working. After that, Peter will be charged 8.6 percent compounded semiannually, and he will pay Aunt May back with 14 equal semiannual payments, the first coming 6 months after he starts his job. Peter finds a job as a photographer for a local newspaper, and his first day of work is July 1, 2004. For tax reasons, Peter needs to compute the total amount of interest that he will pay to Aunt May in the year 2007. How much in interest did Peter actually pay in 2007? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #844161 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=844161\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> by july 1, 2003, he will owe aunt may 28000 dollars.<BR>\n" );
document.write( "there is no interest charged until he starts working.\r<BR>\n" );
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document.write( "i used the ti-business analyst 2 for determining the payment required at the end of each semi-annual time period.\r<BR>\n" );
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document.write( "inputs are:\r<BR>\n" );
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document.write( "percent value = 28000 <BR>\n" );
document.write( "future value = 0<BR>\n" );
document.write( "number of time periods = 14 half years.<BR>\n" );
document.write( "interest rate per time period = 8.6% / 2 = 4.3% per half year.<BR>\n" );
document.write( "payment made at end of each semi-annual time period.\r<BR>\n" );
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document.write( "calculator says that the payment at the end of each semi-annual time period = 2703.496789.\r<BR>\n" );
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document.write( "i then used excel to determine the payments and interest and equity charged for each semi-annual time period.\r<BR>\n" );
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document.write( "this is what the excel looks like.\r<BR>\n" );
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document.write( "the timeline for this problem is as follows:\r<BR>\n" );
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document.write( "7/1/2000           first 7000 is borrowed.\r\n" );
document.write( "7/1/2001           second 7000 is borrowed.\r\n" );
document.write( "1/1/2002           third 7000 is borrowed.\r\n" );
document.write( "7/1/2003           fourth 7000 is borrowed.\r\n" );
document.write( "7/1/2004           first day of work as a photographer.\r\n" );
document.write( "1/1/2005           first semi-annual payment is made.\r\n" );
document.write( "1/1/2007           remaining balance of loan at beginning of 2007.\r\n" );
document.write( "7/1/2007           interest on first payment in 2007.\r\n" );
document.write( "1/1/2008           interest on last payment in 2007.\r\n" );
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document.write( "the remaining balance on 1/1/2007 = 19829.40551.<BR>\n" );
document.write( "the interest charged on this balance is .043 * 19829.40551 = 852.6644369.<BR>\n" );
document.write( "the remaining balance on 7/2/2007 = 17978.57316.<BR>\n" );
document.write( "the interest charged on this balance is .043 * 17978.57316 = 773.0786458.\r<BR>\n" );
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document.write( "the total interest that peter had to pay in the year 2007 is the sum of these two = 1625.743083 = 1625.74 rounded to the nearest penny.\r<BR>\n" );
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document.write( "that should be your solution.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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