document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1104548>Question 1104548</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Raymond took out a 25-year loan from his bank for $135,000 at an APR of 3.6%, compounded monthly. If his bank charges a prepayment fee of 6 months' interest on 80% of the balance, what prepayment fee would Raymond be charged for paying off his loan 5 years early? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #719736 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=719736\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> not exactly sure if it's done exactly this way, but this is what i think.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "25 year loan at 3.6% interest yields.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "number of month = 25 * 12 = 300 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "annual percent interest of 3.6% / 12 = monthly percent interest of .3.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the number of monthly payments on a loan of 135,000 for 300 months at .3% per month = 683.1036618.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you pay 683.1036618 every month for 300 months, the remaining balance on the loan is 0.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you pay 683.1036618 every month for 240 months, the remaining balance on the loan is 37,457.91765.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "so, if the loan is payed off 5 years early, there would still have been 37,457.9176 remaining balance on the loan.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the penalty would be assessed to this amount.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "assuming that they would simply take 1/2 of 3.6% = 1.8%, then the penalty assessed would be .018 * 37,457.9176 = 674.2425176.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you assume they are using monthly interest rate for 6 months, then the penalty assessed would be 37,457.9176 * (1 + .036/12) ^ 6 = 38137.23726 - 37457.9176 = 679.3196094.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "it's a very small difference that really depends on which way they are calculating 6 months worth of interest.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the key component here is what would have the remaining balance have been after 240 months of paying the loan off at 683.1036618 dollars a month.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that remaining balance would have been 37,457.9176 dollars.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the following excel spreadsheet printout shows this to be true.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "first printout shows you remaining balance of the loan in the beginning.<BR>\n" );
document.write( "second printout shows you remaining balance of the loan at the end of month 240.<BR>\n" );
document.write( "third printout shows you remaining balance of the loan at the end of month 300.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/121702.jpg\" alt=\"$$$\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/121703.jpg\" alt=\"$$$\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/121704.jpg\" alt=\"$$$\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the actual penalty charged depends on how they calculate a half a year's worth of interest.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that penalty will be assessed on what the remaining balance of the loan would have been had they not paid the loan off early.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "at least that's my opinion.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this opinion is based on my logical assessment of the problem.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i have no idea how it's actually done, since i don't work for the bank in question.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "to get better information on the penalty and how it's assessed, you would have to speak to a representative of the bank.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i am reasonably confident, however, that the remaining balance of the loan at the end of month 240 is the amount indicated.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since the loan was originally scheduled to go 300 months, then paying off the loan by the end of month 240 would be 5 years early, because 5 years is equal to 60 months and 300 - 60 is equal to 240.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "                                                                                                                     \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );