document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1109707>Question 1109707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A person purchased a &#8203;$143, 712 home 10 years ago by paying 10&#8203;% down and signing a&#8203; 30-year mortgage at 11.7&#8203;% compounded monthly. Interest rates have dropped and the owner wants to refinance the unpaid balance by signing a new 30&#8203;-year mortgage at %6.6% compounded monthly. How much interest will refinancing&#8203; save?\r<BR>\n" );
document.write( "\n" );
document.write( "Thank you in advance\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #724743 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=724743\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the home is purchased for $143,712.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "10% down leaves a mortgage of $129,340.8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "payment on this mortgage at 11.7% per year compounded monthly is equal to 1,300.624172 per month.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if this loan went to completion, total interest would be 12 * 30 * 1,300.624172 = 458,224.7021 minus 129,340.8 = 338,883.9021\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "that is the total of all the payments minus the cost of the original loan.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "after 10 years (120 months), the remaining balance on this loan is 120,401.032.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this is calculated by finding the present value of 240 monthly payments of 1,300.624172.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since the original loan was 360 months and it was stopped after 120 months, what remains is 240 months of payments.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the present value of those payments for 240 months gives you the remaining balance on the loan after 120 months.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the amount of the loan that has been paid off in 10 years is 129,340.8 minus 120,401.032 = 8,939.768002\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the total interest paid during those 10 years is 10 * 12 * 1,300.624172 = 156,074.9007 minus 8,939.768002 = 147,135.1326.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "monthly payment on the new loan at 6.6% for 30 years compounding monthly = 768.9518078.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "total interest on the new loan = 12 * 30 * 768.9518078 minus 120,401.032 = 156,421.6188.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "total interest on 10 years of the original loan plus total interest on the new loan = 147,135.1327 + 156,421.6188 = 303,556.7515\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "difference in interest on original loan if it was carried for 30 years and interest on the original loan for 10 years plus interest on the new loan = 338,8839.021 minus 303,556.7515 = 35,327.15056.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "round that to two decimal places to get 35,327.15.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i used an excel spreadsheet to verify this amount is correct, given the assumptions used in solving the problem, and the excel spreadsheet confirms the solution is correct.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "i also went online and used bankrate.com calculators to perform the same analysis. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "bankrate.com also confirmed the solution is correct, given the assumptions used in solving the problem are correct.\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( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );