document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206658>Question 1206658</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Starting on July 1, 2000, Peter borrows $7600<BR>\n" );
document.write( " 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 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 #844248 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=844248\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "1206658<BR>\n" );
document.write( "Starting on July 1, 2000, Peter borrows $7600 each year for 4 years from his dear Aunt May <BR>\n" );
document.write( "to pay for college. (Note: the last date that he borrows money is July 1, 2003.) <BR>\n" );
document.write( "From the beginning, Aunt May agreed to defer all interest on the loans until Peter finds a job; <BR>\n" );
document.write( "i.e. Peter's loans will not accumulate any interest until the first day he starts working. <BR>\n" );
document.write( "After that, Peter will be charged 8 percent compounded semiannually, <BR>\n" );
document.write( "and he will pay Aunt May back with 14 equal semiannual payments, <BR>\n" );
document.write( "the first coming 6 months after he starts his job. <BR>\n" );
document.write( "Peter finds a job as a photographer for a local newspaper, and his first day of work is July 1, 2004. <BR>\n" );
document.write( "For tax reasons, Peter needs to compute the total amount of interest that he will pay to Aunt May <BR>\n" );
document.write( "in the year 2007. How much in interest did Peter actually pay in 2007?<BR>\n" );
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document.write( "Let's make the timeline\r\n" );
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document.write( "    July 1, 2000  Peter borrows $7600   The debt becomes $7600 \r\n" );
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document.write( "    July 1, 2001  Peter borrows $7600   The debt becomes $15200 \r\n" );
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document.write( "    July 1, 2002  Peter borrows $7600   The debt becomes $22800\r\n" );
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document.write( "    July 1, 2003  Peter borrows $7600   The debt becomes $30400\r\n" );
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document.write( "    July 1, 2004  Peter found the job   The debt is      $30400 and Peter is charged 8% compounded semiannually from this date\r\n" );
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document.write( "So, starting from July 1, 2004 we have classic loan problem:\r\n" );
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document.write( "    the loan amount is $30400; it is 8% charged semiannually;\r\n" );
document.write( "    the debt should be repaid in 14 equal semiannual payments (two payments per year), \r\n" );
document.write( "    in 7 years (2005, 2006, 2007, 2008, 2009, 20010, 2011).\r\n" );
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document.write( "Make one more timeline\r\n" );
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document.write( "    1-st payment   Jan 1, 2005   first payment comes 6 months after he starts his job\r\n" );
document.write( "    2-nd payment   Jul 1, 2005\r\n" );
document.write( "    3-rd payment   Jan 1, 2006\r\n" );
document.write( "    4-th payment   Jul 1, 2006\r\n" );
document.write( "    5-th payment   Jan 1, 2007\r\n" );
document.write( "    6-th payment   Jul 1, 2007\r\n" );
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document.write( "They want you determine the total amount of interest Peter pays in 2007.\r\n" );
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document.write( "So, they want you find the sum of the interest portions of the 5-th and 6-th payments.\r\n" );
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document.write( "Use the Excel function IPMT, which is specially designed to calculate the interest part \r\n" );
document.write( "of a classic loan scheme for the specific payments.\r\n" );
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document.write( "For description of this function see these sources\r\n" );
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document.write( "    wording/text description    \r\n" );
document.write( "    https://www.wallstreetprep.com/knowledge/ipmt-function/\r\n" );
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document.write( "    Youtube videos\r\n" );
document.write( "    https://www.youtube.com/watch?v=xZq4RNqE7ts\r\n" );
document.write( "    https://www.youtube.com/watch?v=bni0l75lc-8\r\n" );
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document.write( "The format of the function IPMT is as follows\r\n" );
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document.write( "    = IPMT(rate, per, nper, principal, fv, type)\r\n" );
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document.write( "In this format \"rate\" is the rate per period = 0.04   (= 0.08/2 semiannually)         required parameter\r\n" );
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document.write( "                per  =  5  - the payment, of which we want to get the interest part;  required parameter\r\n" );
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document.write( "                nper = 14  - total number of payments;                                required parameter \r\n" );
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document.write( "                principal = 30400;                                                    required parameter\r\n" );
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document.write( "                fv                                                                    is optional (we can omit it);\r\n" );
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document.write( "                type                                                                  is optional (we can omit it, which means that \r\n" );
document.write( "                                                                                         the payment is due at the end of the half-year period)\r\n" );
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document.write( "So, we write in Excel cell/spreadsheet for the interest part of the 5-th payment\r\n" );
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document.write( "    = IPMT(0.04, 5, 14, 30400),  and we get the value of the interest for the 5-th payment of $933.71.\r\n" );
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document.write( "Next, we write in Excel cell/spreadsheet for the interest part of the 6-th payment\r\n" );
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document.write( "    = IPMT(0.04, 6, 14, 30400),  and we get the value of the interest for the 6-th payment of $855.64.\r\n" );
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document.write( "So, total interest part of the two Peter's payments of the year 2007 is the sum  $933.71 + $855.64 = $1,789.64.    <U>ANSWER</U>\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Solved.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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